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Making The CCSS Math Practices Readable: MP 6 - Robert Kaplinsky

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This is the sixth of an eight blog post series where I'll attempt to make a version of each of the Common Core State Standards' Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them...

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Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Introduction

Rich mathematical tasks engage students in sense-making through deeper learning that require high levels of thinking, reasoning, and problem solving. The VDOE Rich Mathematical Task Committee, composed of mathematics teacher leaders from across the Commonwealth, created mathematically rich tasks aligned to the 2016 Mathematics Standards of Learning. The committee created task implementation templates prior to administering the tasks in classrooms. For many of the tasks, the committee scored the tasks individually, calibrated their scoring with a team, provided scoring rationales and selected student work to serve as anchor papers. The Virginia Department of Education would like to extend a special thank you to the Rich Mathematical Task Committee, as well as their colleagues who supported this work in their divisions.

Planning for Remote Implementation of Rich Mathematical Tasks

These resources, along with the Planning for Remote Implementation of Rich Mathematical Tasks guidance document, are provided to support teachers in implementing the 2016 Mathematics Standards of Learning in their classrooms. Teachers are encouraged to not only use these tasks with their students, but also to endeavor to implement them with fidelity by utilizing the detailed information provided in the task implementation templates.

Webinars to Support Remote Implementation of Rich Mathematical Tasks

Kindergarten

Building Towers Task

Picking Apples Task

Sharing Cookies Task

Shape Riddles Task

Mixed Blocks Task

Morning Routine Task

Grade 1

Comparing Points Task

Toy Cars Task

Nature Walk Task

Doubles Game Task

Playing with Patterns Task

How Can They Be Equal? Task

Grade 2

Mystery Number Task

Sticker Sets Task

Bracelet Task

Brownie Pans Task

Talking Sticks Task

Coins in Pocket Task

How Many Tables Task

Number of Students Task

Grade 3

Packing Pencils Task

Pizza Party Task

Carnival Prizes Task

Baskets of Apples Task

Money in the Piggy Bank Task

Polygon Puzzles Task

Grade 4

Special Delivery Task

Taco Tuesday Task

Trip Transportation Task

Pouring Paints Task

Lunch at Leonardo's Task

Camping Combinations Task

Exploring Quadrilaterals Task

Equality Possibilities Task

Grade 5

Saving for a Bicycle Task

Room for Shoes Task

Trail Mix Time Task

Bus A or Bus B Task

Angle Design Task

Designing Windows Task

Grade 6

Winning the Game Task

Cookie Topping Task

Smart Shopper Task

Tracking Sharks Task

Designing a Dog Park Task

Pizza Delivery Task

Screen Time Task

Grade 7

Which Microscope Task

The Bake Sale Fundraiser Task

Shipping Box Task

A Walk in the Park Task

Spin, Spin, Spin Task

Summer Passes Task

Gardening Task

Grade 8

The Principal's Dilemma Task

Monster Transformations Task

Longest Path Task

It's Your Lucky Day Task

Peanut Butter Task

How Many Stones Will I Need Task

Algebra I

Shopping Translations Task

Flower Gardens Task

Seesaw Fun Task

Full Parking Lot Task

Radical Rocks Task

The Trampoline PartyTask

Bicycle Savings Task

The Soccer Competition Task

We're Playing Basketball Task

Geometry

Logical Drivers Task

Lines and Tigers and Bears, Oh My! Task

Airshow Task

Take Me Out to the Ball Game Task

Sea Cities Task

Shake, Rattle, and Roll Task

Algebra II

Drone's Best Friend Task

Function of a Ride Task

Animate It Task

Wildfires Task

Algae Attack Task

Blank Task Template

Rich Mathematical Task Rubric

Acknowledgments

The Virginia Department of Education would like to extend a special thank you to the Rich Mathematical Task Committee, as well as their colleagues who supported this work in their divisions.

Candice Barkley, Henrico County Public Schools

Jessica Brown, Gloucester County Public Schools

Kaitlyn Bookbinder, Henrico County Public Schools

April Cooke, Fairfax County Public Schools

Kelly Day, Virginia Beach City Public Schools

Michelle Deloach, Chesterfield County Public Schools

Allison Crisher DePiro, Virginia Beach City Public Schools

Katelyn Devine, Henrico County Public Schools

Jenna Filipowicz, Virginia Beach City Public Schools

Kris Gushue, Prince William County Public Schools

Kelly Halpin, Fairfax County Public Schools

Endia Hatcher, Portsmouth Public Schools

Melanie Jenkins, Gloucester County Public Schools

Jenny Jones, Hanover County Public Schools

Tisha Jones, Portsmouth Public Schools

Leslie Laden, Stafford County Public Schools

Kimberly Lawrence, Hanover County Public Schools

Lynn Meade, Henrico County Public Schools

Kathryn Munson, Chesterfield County Public Schools

Anna Papas, Stafford County Public Schools

Sarah Porter, Suffolk Public Schools

Candice Standley, Culpeper County Public Schools

Donna Snyder, Roanoke City Public Schools

Holly Tate, Alexandria City Public Schools

David VanVleet, Fairfax County Public Schools

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Rich Mathematical Tasks | Virginia Department of Education

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Rich mathematical tasks engage students in sense-making through deeper learning that require high levels of thinking, reasoning, and problem solving. The VDOE Rich Mathematical Task Committee, composed of mathematics teacher leaders from across the Commonwealth, created mathematically rich tasks aligned to the 2016 Mathematics Standards of Learning.

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PZ’s Thinking Routines Toolbox | Project Zero

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Lesson duration 02:58

From twigs to electrical toothbrushes, humans have been cleaning our teeth since the Ancient...

Riddle s can be relaxing - or devilishly difficult. Ready to tackle some brain teasers? Watch the...

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Lesson duration 02:58 From twigs to electrical toothbrushes, humans have been cleaning our teeth since the Ancient... Riddle s can be relaxing - or devilishly difficult. Ready to tackle some brain teasers? Watch the...

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These are problems selected from a variety of resources. Whenever possible I will list the source from which it came. There will be no solutions provided here, but if you follow the link to the source there may be solutions there.

For what dimension paper will these folds produce a kite?

Duelling Dice

Consider the following four dice and the numbers on their faces:

These are used to play a game for two people. Player 1 chooses one of theÂ die to use for the game. Then player 2 chooses a die. Now each player rolls their die. The player with the highest number showing gets a point. The first player to 7 points wins the game. If you are player 1 which die should you choose. If you are player 2 which die should you choose? [from the Mathematics Task Centre]

Arithmetic Series

Find the sum of the arithmetic series 13 + ... + 61.

Lost Primes

Three cards (see below) each have a prime number on the back. The sum of the number on the front and back of each card is the same as the other cards. What are the numbers on the back of each card?

Scrambled Dice

Imagine a typical 6-sided die, and notice that the sum of opposite faces is always seven. The one is across from the six, the two is across from the five, and so on. Now imagine that you were making your own six-sided die that did not have this restriction. How many different dice could be made?

Painted Cube

Paint all the sides of aÂ 3 x 3 x 3 cube. Once it is dry take it apart into its 1 x 1 x 1 unitÂ cubes. How many of these unit cubes have paint on three faces? Two faces? One face? No faces? Explore for 4 x 4 x 4, etc.

Differentiable Function

Consider the differentiableÂ function below. What are m and b?

Ferin and Ian play a game by alternately moving a hockey puck on a board with n concentric circlesÂ divided into r regions. For example, in the diagram below, we have n= 4 and r = 8.Â The game starts with the puck already on the board, as shown. A player may move either clockwiseÂ one position or one position towards the centre, but cannot move to a position that has been previouslyÂ occupied. The last person who is able to move wins the game.Â Ferin moves first. Can Ferrin win? Explore. [from Richard Hoshino]

How do you make a 9 minute egg if all you have is a 4 minute and 7 minute egg timer?

You have 27 small cubes, 3 each of nine colours.Â Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour. [from nRICH]

Square Peg in a Round Hole

What is a better fit, a square peg in a round hole or a round peg in a square hole?

Chessboard

How many squares on a chessboard? How many rectangles?

The Last Number

Consider the string 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Cross out any two numbers in this list and add the difference to the end of the list. This new number is now part of the list. Continue the process of crossing out two number on the list and adding the difference until there remains only one number. What can you say about the last number? Explore. [from Richard Hoshino]

The Desk Calendar

On the desk calendar below, what numbers have to be where in order for every date from 01 to 31 to be able to be represented?

The Pirates and the DiamondÂ

A band of 10 pirates are going to disband. They have divided up all of their gold, but there remains one GIANT diamond that cannot be divided. To decide who gets it the captain puts all of the pirates (including himself) in a circle. Then he points at one person to begin. This person steps out of the circle, takes his gold, and leaves. The person on his left stays in the circle, but the next person steps out. This continues with every second pirate leaving until there is only one left. Who should the captain point at if he wants to make sure he gets to keep the diamond for himself? What if there were 11 pirates? What if there were 12 pirates?What if there were 27Â pirates? Etc.

Honeybee Ancestors

Honeybees have a very interesting genealogy. While female honeybees come from a fertilized egg, male honeybees come from an unfertilized egg. That is, female honeybees have a mother and a father, while male honeybees have only a mother. Look at the family tree of a male honeybee. How many ancestors are there in the previous generation? The one before that? The one before that? How many ancestors 10 generations ago? Etc.

Crossing the Bridge

Adam, Bob, Clair and Dave are out walking: They come to rickety old wooden bridge. The bridge is weak and only able to carry the weight of two of them at a time. Because they are in a rush and the light is fading they must cross in the minimum time possible and must carry a torch (flashlight,) on each crossing.
They only have one torch and it can't be thrown. Because of their different fitness levels and some minor injuries they can all cross at different speeds. Adam can cross in 1 minute, Bob in 2 minutes, Clair in 5 minutes and Dave in 10 minutes.
Adam, the brains of the group thinks for a moment and declares that the crossing can be completed in 17 minutes. There is no trick. How is this done? [from Nigel Coldwell]

Triangle Perimeter

Determine the minimum perimeter of a triangle with one vertex at (7,1), one vertex on the x-axis, and one vertex on the line y = x. [from Richard Hoshino]

Intersecting Sets

Place 17 objects into the two circles below so that each circle has the same number of objects. How many ways can you do it?

What if you want the ratio of objects in one circle to the other circle to be 4:3 or 12:9?

1001 Pennies

There are 1001 pennies lined up on a table. I come along and replace every second coinÂ with a nickel. Then I replace every third coin with a dime. Finally, I replace every fourth coin with a quarter. How much money is on the table?

Frame the Cards

Arrange ten playing cards (ace to ten) in a rectangle with three cards on two sides and four cards on two sides such that the sum of the cards on every side add up to the same total. [from Annette Rouleau]

Palindromes

Consider the number 28. It is not a palindrome. So, I reverse the number and add it to itself (28 + 82 = 110). 110 is not a palindrome. So, I reverse it and add it to itself (110 + 011 = 121). 121 is a palindrome. This means that 28 is a depth 2 palindrome (it took two iterations to make it a palindrome).Â Â What is the depth of all two digit numbers?

Dart Board Probabilities

Two darts are thrown at a circular target. Where does the first dart have to land so that the probability that the second dart will be closer to the centre is 50%?

On Canada DayÂ Alex stacks dice on top of each other until the sum of the visible faces are equal to the year. When will he next be able to do this? Generalize.

10 Prisoner Release

AÂ warden has decided that hisÂ jail is too full, so he wants to release some of the prisoners. His strategy for doing this is that he will take ten prisoners at random and line them up in a row so that each prisoner can only see the prisoners in front of them. The warden will then place a black or white hat on the head of each prisoner. Starting at the back of the row the warden will then ask that prisoner what colour his hat is. If he guesses correctly then he is released. The warden then goes to the next prisoner in line, and so on. The tenÂ prisoners are allowed to meetÂ to discuss before they line up. If they are clever they will come up with a strategy that will guarantee to save some of them. How many could you save?

Fantastic Four

Make the numbers from 1 to 30 using four 4's and any operations.

Seed Numbers

Consider two whole numbers (for example 3 & 6). These will be the first two numbers. The third number is the sum of the first two (9). The forth is the sum of the previous two (15), and so on (3, 6, 9, 15, 24, 39, ...). What do the first two number have to be such that the fifth number is 100?

Bucky the Badger

Bucky the Badger is a mascot for his schools football team. Every time his team scores Bucky doesÂ aÂ number of push-ups equal to his team's total points at that time. If his team finished with 50 points, how many push-ups could Bucky have done? [from Dan Meyer].

Gopher Hunt

Imagine a series of equally spaced holes running along a line infinitely in both directions. A groundhogÂ is in one of the holes and every minute he jumps to a new hole that is some fixedÂ interval of holes away from his current hole. You do not know where he starts, or the intervalÂ that he jumps, or the direction that he goes in, but after each of his moves you can shine aÂ flashlight into one (and only one) hole. The problem is to find a method by which youÂ can guarantee to eventually find the groundhog.

How many 6 digit numbers are there whose digits sum to 51? [from Practice Fermat Number 4, #7]

Concave Polygons

We know that the sum of exterior angles of any convex polygon is 360Âº. But what if the polygon is concave? What adjustments or extension to the 'rule' must be made in order for the sum to still be 360Âº? [from Robert McGregor on the AAMT]

Gold Chain Extended

You are backpackingÂ through Europe. You have one month left until your flight home, but you have run out of money. However, you have a 50 link gold chain and you have found a hotelÂ that is willing to accept one link per night for payment of room and board. However, the manager wants payment every day and he is willing to help you out by cutting links for you. The problem is that he wants one gold link payment for every link he cuts. What is the most number of links that you will have left when you fly home? [my extension ofÂ TestFunda Â vol. 1 (p. 1)]

In how many ways can 105 be expressed as the sum of at least two consecutive positive integers? [from the Canadian Team Math Contest, 2014, #12]

Tax Man Â is played like this: Start with a collection ofÂ paychecks, from $1 to $12. You can choose any paycheck to keep.Â Once you choose, the tax collector gets all paychecks remaining thatÂ are factors of the number you chose. The tax collector must receiveÂ payment after every move. If you have no moves that give the taxÂ collector a paycheck, then the game is over and the tax collector getsÂ all the remaining paychecks.Â The goal is to beat the tax collector.

Example:
Turn 1: Take $8. The tax collector gets $1, $2 and $4.
Turn 2: Take $12. The tax collector gets $3 and $6 (the other factorsÂ have already been taken).
Turn 3: Take $10. The tax collector gets $5.

You have no more legal moves, so the game is over, and the taxÂ collector gets $7, $9 and $11, the remaining paychecks.

Questions:
Is it possible to beat the tax collector in this $12 game? If so,Â how? What is the maximum score you can get?
Bonus: What if you played the game with paychecks from $1 toÂ $24? How about $1 to $48? [from Numberplay, April 13]

Cereal Prizes

Suppose there was one of six prizes inside your favorite box of cereal. Perhaps it's a pen, a plastic movie character, or a picture card.Â How many boxes of cereal would you expect to have to buy, to get all six prizes?Â [fromÂ George Reese]

Figure out the Four Aces card trick. [from Peter Liljedahl]

Burning Rope

You have two ropes, each of which takes two hours to burn if lit at one end. These ropes are not homogeneous and some parts of the ropes burn quicker than others. Can you use the ropes to time out 1 hour and 30 minutes? 45 minutes? What other times could you get? [from TestFunda, book 1, #7]

How Many 7's

If you write out the numbers from 1 to 1000, how many times will you write the number 7?

Marching Band

Students in a marching band want to line up for their performance. The problem is that when they line up in 2â€™s there is 1 left over. When they line up in 3â€™s there are 2 left over. When they line up in 4â€™s there are 3 left over. When they line up in 5â€™s there are 4 left over. When they line up in 6â€™s there are 5 left over. When they line up in 7â€™s there are no students left over. How many students are there? [from John Grant McLoughlin]

Tire Tracks

â€œThis track, as you perceive, was made by a rider who was going from the direction of the school.â€ observedÂ Sherlock Holmes.
â€œOr towards it?â€, said Watson.
â€œNo, no my dear Watson... It was undoubtedly heading away from the school.â€

Which way was the bike travelling? [from Jamie Mulholland - presentation at CMEF 2014].

Pirate Hats

Once there was a group of pirates headed by Captain Francis Verney. One night Francis got a question that who among the group would be smart enough to lead the group after he steps down.

So he decided to conduct series of tests, to find the most smart one. As we all know testing the intelligence of pirates is not that simple, as they are clever and rational in nature.

Francis picks up 9 hats, a mix of white hats and black hats. He placed the hats on 9 pirates head and mentioned them that they should not talk and there is at least 1 white hat and black hats count is more than white hats.

Obviously they canâ€™t see their own hat but they can see the color of other 8 hats. If they guess wrong, their head will be blown. Francis gave them 20 mins time to figure out, but no one could.

So he gave another 10 mins. But still everyone kept quite. Finally he gave them 5 mins, and at the end all 9 knows their hat color, and all answered same time.Â Think about the logic that pirates used to figure out. [from |V|UR@|_I'S BLOG -Â June 17, 2013]

Black and White Marbles

We place in a box thirteen white marbles and fifteen black.Â We also have twenty-eight black marbles outside theÂ box. We remove two marbles from the box. If they haveÂ a different colour we put the white one back in the box.Â If they have the same colour we put a black marble in theÂ box. We continue doing this until only one marble is left inÂ the box. What is its colour?Â [fromÂ Vector 55(1)Â - p. 49]

Tangent Polygons

In the diagram various regular polygons, P, have been drawn whose sides are tangents to a circle, C.Â Show that for any regular polygon drawn in this way:

[from MEI Maths Item of the Month - March 2014]

100 Divided

When 100 is divided by a positive integer x, the remainder is 10.
When 1000 is divided by x, what will the remainder be? [from University of Waterloo CECM Past Contest Archive (2011 Caley, #18)]

Three jugs have the capacity for 8, 5 and 3 litres respectively. The 8 litre jug is filled entirely with water and the other two jugs are empty. Your task is, by decanting, to divide the water into two equal parts, that is, 4 litres in jug A and 4 litres in jug B, leaving the smallest jug empty.Â [from MathXTC - Neurological Nasties Â (problem set 9, #3)]

Escaped Prisoner

An escaped prisoner finds himself in the middle ofÂ a square swimming pool. The guard that is chasingÂ him is at one of the corners of the pool. TheÂ guard can run faster than the prisoner can swim.Â The prisoner can run faster than the guard canÂ run. The guard does not swim. Which directionÂ should the prisoner swim in in order to maximizeÂ the likelihood that he will get away? [from Vector 54(2) - p. 95]

A wealthy man needed to pay the mason building his house. He was running low on cash so he decided to pay the mason with a gold chain made of 7 links. The mason's fee was equal to one gold link each day. The wealthy man needed to pay the mason each day or he would stop working. But, at the same time he didn't want to pay the mason any more than one link in a day because he might run off and not return.

Cutting the chain was very difficult. What is the minimum number of cuts that the wealthy man could make in the chain and still pay the mason each day for seven days?

[from TestFunda vol. 1 (p. 1)]

Twisted Rope

Picture to yourself a length of rope, lying on a table in front of you. TheÂ cross section of the rope is a regular N sided polygon. Slide the ends ofÂ the rope towards you so that it almost forms a circle.

Now mentally grasp the ends of the rope in your hands. You are going toÂ glue the ends of the rope together but before you do, twist your right wristÂ so that the polygonal end rotates through one nth of a full revolution. RepeatÂ the twisting a total of T times, so that your mental wrist has rotatedÂ through T nths of a full revolution. NOW glue the ends together, so thatÂ the polygonal ends match with edges glued to edges.

When the mental glue has dried, start painting one facet (flat surface) ofÂ the rope and keep going until you find yourself painting over an alreadyÂ painted part. Begin again on another facet not yet painted, and use anotherÂ colour.

How many colours do you need?

[fromÂ Thinking Mathematically Â (2nd edition) - Mason, Burton, and Stacey (p. 103)]

Bridge Crossing

Five persons are standing on one side of a bridge.
They want to cross the bridge.

Without a torch, they cannot proceed.
Only one torch is available.
The torch has a remaining battery life of only 30 seconds.

Only two people can go over the bridge at one time.
The torch needs to be returned to the remaining persons.

The five people take different times to cross the bridge.
One takes 1 second to cross the bridge.
The others take 3 seconds, 6 seconds, 8 seconds and 12 seconds.

Everyone crosses the bridge within 30 seconds.

How do they proceed?

[fromÂ Brainteasers II]

Skyscrapers

You have to complete the grid such that every row and column contains the numbers 1 to 4.

Each row and column contains each number only once.

However, you have to follow the rules around the outside, which tell you how many skyscrapers you can see.

You can't see a shorter skyscraper behind a taller one.

The puzzles can be quite hard and can require Sudoku techniques.

[see Skyscrapers at Brainbashers for more of the same as well as the option to work on the problems online]
Locked Chest

In medieval times, the inhabitants of a remote village decided to lock the village valuables in a giant chest to protect them from marauding thieves. They placed a number of locks on the chest, with each lock needing its own distinct key. For additional security, the villagers made sure that any three people from the village would always have among them the keys needed to open the locks, but no two people would have the keys to do it. Â

How many locks were required, and how many keys?

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These are problems selected from a variety of resources. Whenever possible I will list the source from which it came. There will be no solutions provided here, but if you follow the link to the source there may be solutions there. For what dimension paper will these folds produce a kite?

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Same and Different Images

Lots of images to support students in developing the habit of comparing and connecting representations. Thanks Brian Bushart for pulling them together!

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Great tasks you can do in 10-15 minutes every day...click the image and they're yours.

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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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Citizen Math lessons teach standards-based math through real-world topics that students care about.

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Problem Solving & Improvement Science Padlet

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Problem Solving & Improvement Science Padlet

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Formative use of SBAC Resources PL Series Hyper Doc

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Formative use of SBAC Resources PL Series Hyper Doc

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Learn to lead coaching conversations, professional development, and teams that transform schools into joyful, resilient, and equitable places of learning. You're committed to building a more just and equitable organization and world, but you need support navigating the path forward. We'll help you turn your aspiration into a reality.

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Article Improving Math Intervention Blocks

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Article Improving Math Intervention Blocks

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Intervention blocks don't have to be rote review-this format based on computation practice and games can boost engagement and learning.

Every child can learn math well. Through a Multi-Tiered System of Support (MTSS), teachers can design a learning environment that allows every child to learn and thrive. An MTSS ensures that every child is meaningfully included in grade-level learning, while some children receive additional layers of instruction (intervention, extension, re-teaching) to meet their needs.

Identify priority concepts

When providing that second or third layer of instruction (Tier 2 and Tier 3) through a math-focused intervention, teachers sometimes think this translates into repeating the main lesson "louder and slower," or rote practice of procedures without conceptual understanding. A quality math intervention block should include a clear, manageable goal focused on the prioritized math content. This can include engaging activities like number sense routines, games, and problem-solving practice, as well as high-quality tasks that require reasoning and sense making.

All Learners Network, an organization that promotes math equity and inclusion for all students, identifies high leverage concepts, progressions, and assessments at each grade level. These are the key mathematical understandings at each grade level from pre-K to eighth grade that help focus instruction by identifying the mathematical ideas that will support students' access to grade-level content the following year.

Classroom teachers, special educators, and interventionists use the concepts, progressions, and assessments to identify the most meaningful areas for focus during specialized instruction and intervention. A quality Tier 2 or Tier 3 intervention takes into account students' misconceptions and incomplete understanding from previous grade levels and focuses time spent with students on essential understanding that will close the gap toward the current grade level's concepts.

Designing a Math Block that Works

Student engagement opens the door to learning: Students need to feel that the learning opportunities provided for them are authentic, relevant, and rigorous. When teachers believe that all students can achieve high levels of mathematics, students will rise to that challenge. This is especially important during a 30-minute math intervention block. Students should have the opportunity to communicate their thinking, compare their thinking with others', and support their understanding through exploration of concrete models moving to more abstract representations.

Here is one way to structure a math intervention block to keep students engaged throughout.

Launch/number sense routine (5 minutes): Launch is a welcoming, inclusive activity that is intended for purposeful, discussion-rich learning opportunities. The launch should be engaging, relevant, and open-ended enough that all students can participate. Launch/number sense routines build flexibility with numbers and deepen understanding of operations.

Computation practice and strategy share (10-15 minutes): Computation practice is an opportunity for students to practice with operations. Students need to practice strategies they've been taught while also practicing and discussing other strategies in a small group setting. Students should solve problems, share and model strategies, and then connect their models and representations to other, potentially more complex or abstract, models and representations.

Game (10 minutes): Playing games is an engaging way to allow students to think strategically while reinforcing the math concepts they are learning in a different context. Students solidify their understanding of a concept in far fewer repetitions through game play compared with rote practice. In the act of play, students are able to think freely and play with these mathematical concepts in a low-pressure environment.

I understand that we are working toward...

A new strategy I now get is...

Something I'm still thinking about is...

I'm wondering about...

This is like what I did in math class because...

Closure (5 minutes): Finally, plan closure activities that clearly revisit the purpose for the intervention and allow students to self-monitor progress. Closure is one of the most important yet often forgotten components of a math lesson. As part of an intervention block, closure allows students to summarize their thinking, connect back to the clear learning goal for their intervention, and evaluate their progress toward mastery. Closure can be part of a wrap-up activity as students are cleaning up or as they walk back to class. Some prompts to consider as part of the closure include:

This type of structure gives us the opportunity to consider the instructional design of our additional layers of instruction. Students need additional opportunities to explore a mathematical concept, engage in dialogue with their peers, and connect their small group instruction back to the work they are doing in their main lesson.

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Making the Most of Math Intervention Blocks

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Intervention blocks don't have to be rote review-this format based on computation practice and games can boost engagement and learning.

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High Leverage Concepts | All Learners Network

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High Leverage Concepts (HLCs) are a key resource to help teachers focus instruction by identifying the big ideas that support math success at every grade.

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Problems of the Month

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The Inside Problem Solving problems are non-routine math problems designed to promote problem-solving in your classroom. Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity. The problems were developed by the Silicon Valley Mathematics Initiative and are aligned to the Common Core standards.

To request the Inside Problem Solving Solutions Guide, please get in touch with us via the feedback form.

Why Problem Solving?

Problem solving is the cornerstone of doing mathematics. George Polya, a famous mathematician from Stanford, once said, "A problem is not a problem if you can solve it in 24 hours." His point was that a problem that you can solve in less than a day is usually a problem that is similar to one that you have solved before, or at least is one where you recognize that a certain approach would lead to the solution. Bu t in real life, a problem is a situation that confronts you and you don't have an idea of where to even start. Mathematics is the toolbox that solves so many problems. Whether it is calculating an estimate measure, modeling a complex situation, determining the probability of a chance event, transforming a graphical image or proving a case using deductive reasoning, mathematics is used. If we want our student s to be problem solvers and mathematically powerful, we must model perseverance and challenge students with non-routine problems.

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Inside Problem Solving | Inside Mathematics

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The Inside Problem Solving problems are non-routine math problems designed to promote problem-solving in your classroom. Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.

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Real World Math Lessons | 3 Act Math Tasks | Math Worksheets & Practice

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Contextual problem based real world math lessons with rich math tasks, multi-day 3 act math tasks, math practice materials and math worksheets

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Routines - Where THERE'S A WILLS, there's a way

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Students use the chat box to type their initial notices and wonders. Teachers can then purposefully select student responses and copy/paste them into the slide template. As the whole group discussion unfolds, students who prefer typing over mic can still have their voice heard.

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Welcome to the California Coalition for Inclusive Learning (CCIL) universal resources. It is our intent that educators in a variety of roles, find resources to support their practice in universally designing learning experiences for all learners. In anticipation to the barrier of time , we've designed three ways to engage on a particular :

- Past and future content (slides and video recordings)

- One-doc stops present best practices related to the topic.

Got a Minute? Learning Series - Flexibility to choose your learning pathway based on the amount of time available.

At CAST we believe that variability is the norm ! We'd love your on these iterative resources!

For more information on coaching and support, California educators may contact Shamryn Coyle, CCIL Director for the Placer County Office of Education at scoyle@placercoe.org .

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California Coalition for Inclusive Learning

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Welcome to the California Coalition for Inclusive Learning (CCIL) universal resources. It is our intent that educators in a variety of roles, find resources to support their practice in universally designing learning experiences for all learners. In anticipation to the barrier of time, we've

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Data Nuggets | Bringing authentic research and data into K-16 classrooms

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Free activities that bring real scientific data into the classroom, guiding students through the process of science while building their quantitative abilities.

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— Sarah Sanders, Special Education and Math teacher at Mott Hall High School in the Bronx, NY

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New Visions Math Curriculum - New Visions Math Curriculum

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Support students with Executive Functions

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Support students with Executive Functions

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Teachers can boost middle school students' self-management skills by using questions to get their mental gears turning.

Michael Morgenstern / The iSpot

Jumping on a giant trampoline as an adult is usually humbling and pretty awkward. Your trampoline muscles need some practice before they're ready for full use. Our students are having a parallel experience; after over a year away from physical school, many of them may need support in developing their executive function or "studenting" skills for doing well in person. Executive function (EF) skills are brain-based management abilities that encompass a wide range of future skills like planning, organizing, self-regulation (including managing attention and emotions), learning, and memory.

These skills are also learned at home when children do things like household chores. Reinforcing executive function at school helps students' brains understand the cueing system that activates the use of a particular skill. For example, a student needs to understand environmental cues in order to engage with self-regulation tools, and these cues will differ at home and at school.

Executive Function Skills Support Academic Success

Self-management skills are often the secret sauce of school success. Kids who soar at school are often those who have the most honed EF skill sets. Being an excellent writer, for example, isn't enough. It's important for students to demonstrate that they can manage time to write, chunk writing tasks into parts, manage attention to see an essay through, remember editing strategies, and more. Empowering students with these skills can boost academic performance, since grades and assessments rely on executive function as a baseline for demonstrating mastery.

Virtual school pushed students to learn self-management tools, like getting to class without auditory bell prompts and reducing distractions to support their focus. Now, students may need more time to develop the studenting skills required for in-person learning. Knowing how to identify and encourage developing studenting skills is a key component to our educational rebound.

Replace Directions With Thought-Provoking Questions

If you've ever heard one student coach another, you've probably realized that they're parroting you. As teachers, we give lots of the same directions. Replacing these directions with mid- and then low-level supportive questions can help pass the onus of navigating the day to students, developing their future-skills executive functions.

For example, the directive "Please take out your book" could be replaced with mid-level support questions like "What do you need to be ready for reading?" or "What do you picture on your desk during this time?" A low-level support question could be "Do you need 45 or 65 seconds to get ready?" You could even a tap the desk, signaling that something needs to be out.

There's no single right way to do this; the idea is that you're planning and adjusting the levels of support you offer so that students are gradually assuming the responsibility (similar to gradual release strategy for academic skills and tasks).

Teach Students to Question and Coach Themselves

Whenever I design a lesson, I hear the voice of my mentor teacher coaching me to consider, "What's the biggest takeaway you want every student to learn?" It's an automatic audio track that plays whenever I'm planning a lesson. Like coaches and mentor teachers, classroom teachers can coach students to prompt themselves with questions or reminders for repeating tasks.

Question what the steps will be, by either visualizing or noting each "scene" as a step

Consider what materials are needed

Identify when to do each step

Offer tips for how to remember what to do

For example, in planning a longer project or essay, a teacher can show students how to do the following:

Students who need deeper support can have a written list of these questions to access in times of planning. The idea is to create a format to make the student invisible and thinking skills visible. In this way, teachers can augment students' developing executive function skills.

Use 6 Problem-Solving 'Magic' Questions

1. What do you notice?

2. What parts do you understand?

3. What do you think you might need right now?

4. How can you tell?

5. Where could you look for that information?

6. How will you remember to use that strategy or take that action?

There are some great go-to questions for teachers who want to help develop learners' studenting skills but aren't yet automatic in their questioning techniques. These magic questions include:

When teachers ask these questions regularly, students get used to hearing them, and they can be applied automatically as students solve problems throughout their day. Teachers can also reply with these questions when students ask things like "Where is that assignment?" or "What do I need to do?" Think of how many times the students' questions for us are related to processing the task, rather than the task or its content. What a gift for students to be able to tackle that type of thinking on their own.

The Good News for Teachers

This isn't one more thing on your ever-growing list. These skills can be supported and extended by making small shifts, not additions, to your instruction. Replacing directions with questions can help increase students' awareness of patterns and routines, releasing the onus of self-management to the students. Coaching students to notice the executive function demands of assignments can empower them to independently seek strategies when approaching their work.

If all else fails, you can lean on those function magic questions, which are sure to get students' brain "muscles" flexing. Empowering our kids with multiple tools for studenting will reduce their barriers to growth and smooth out some of the bumps of getting through the school day, for students and teachers.

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Supporting Executive Function Skills by Asking Questions

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Teachers can boost middle school students' self-management skills by using questions to get their mental gears turning. Michael Morgenstern / The iSpot Jumping on a giant trampoline as an adult is usually humbling and pretty awkward. Your trampoline muscles need some practice before they're ready for full use.

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A UDL Guide To Curriculum and Technology Review

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Open in new window to see Excel Doc

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The Magic is in the Margins-Lambert's UDL+Math.pdf

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If learning is a staircase, then all steps are not created equal. In both reading and math, some skills are extraordinarily difficult for students to master. We call these skills Trip Steps because they can cause a stumble in learning. See lists of Trip Steps, which span kindergarten through high school.

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If learning is a staircase, then all steps are not created equal. In both reading and math, some skills are extraordinarily difficult for students to master. We call these skills Trip Steps because they can cause a stumble in learning. See lists of Trip Steps, which span kindergarten through high school.

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Example lessons from previous lesson studies, Protocol Document, lesson template and lesson observation template

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This page contains lesson plans that serve as detailed pathways through a variety of lessons. They are useful for teachers at all levels of experience and craftsmanship. They can also be used by principals and coaches as the instructional focus for lesson study. Please help make these better by sharing your learnings in the comment section of each write-up.

I've done over 100 lesson studies with teachers. Over the course of that time, I (and the teachers I've worked with) have gained a lot of wisdom from our efforts to make engaging and differentiated lessons flow naturally in the classroom so all learners can be successful. You'll find 3-Act Math lesson structures and lessons using Estimation180, clothesline math, numberless word problems (including data), number talks, and fraction talks resources. We've also reworked and opened up textbook problems so that they are more engaging for all learners.

Below, you'll find a brief description of the lesson, a link to my write-up and analysis of the lesson, and links to any lesson resources you'll need. While the lesson are broken up by grade bands, many lessons can be easily modified to meet the needs of your students.

Lesson Plans:
1st/2nd Grade
This lesson and write-up uses images in a Number Talk to help 1st grade students practice comparing numbers using the words "more" and "fewer." Then students practice these skills by examining a Numberless Data Problem. 1.MD.4

This Numberless Data Problem lesson and write-up and was created to help 2nd graders learn how to discuss and explore data presented in bar graphs. Without numbers and mathematical structure, students are forced to think, discuss, and collaborate with each other to figure out the story in the data. 2.MD.10

Bright Idea is a fun and compelling lesson by Graham Fletcher in their classrooms to engage their students in exploring addition strategies with regrouping. Here's my write-up. 2.NBT.5, 2.NBT.6, 2.NBT.9
3rd Grade
This Numberless Word Problem lesson was created to help all learners discuss and explore division conceptually. Without numbers, students are forced to think, discuss, and collaborate with each other. 3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.6

This write-up offers a lesson plan using Steve Wyborney's tile images for 3rd grade students. (See my write-up for the images and slide deck we used.) The tile problems are an effective tool to engage students in discourse about their mathematical reasoning about fractions. The lesson also allows teachers to identify existing student misconceptions about partitioning and grouping that often prevent students from understanding how to use the area model to reason about fractions. 3.NF.1
4th Grade
Looking for a way to make plotting fractions on a number line more tangible to 4th graders? This clothesline lesson is for you! Clothesline math activities are fun for teachers and students! I encourage you to try them out for yourself. Here's my write-up. You'll find everything you need to know about this engaging math manipulative in there. 4.NF.1, 4.NF.2

This Makeover of a Textbook Problem opens up exploration and discussion around common factors for 4th graders. 4.OA.4
5th/6th Grade
How Much Money is in the Bowl? is a lesson that uses estimation and number sense to let students explore decimal operations to figure out the value of a bowl full of change. Here's my write-up. 5.NBT.7, 6.NS.3

This engaging learning opportunity is ideal for any 6th (and 7th) grade teachers who are looking for ways to increase student engagement, thinking, and discourse around percents, fractions, and proportional reasoning. It uses this image by Andrew Stadel as a warm-up and the Kool-Aid Kid lesson by Graham Fletcher. 6.RP.A

Here's a great write up by Jenn Vadnais (@rilesblue) about a Desmos lesson on inequalities for 6th and 7th grade students. You'll find an excellent analysis of the lesson and a clear instructional pathway that can guide you along. It's great stuff. 6.EE.5, 6.EE.8
8th Grade

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This page contains lesson plans that serve as detailed pathways through a variety of lessons. They are useful for teachers at all levels of experience and craftsmanship. They can also be used by principals and coaches as the instructional focus for lesson study.

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"I Can Learn" statements establish learning targets that can be understood by students and others involved in their education. Wayne County special education teachers have taken the Essential Elements and developed scaffolded "I Can Learn" statements that represent the range of modifications that may be needed by students with cognitive impairments. The "I Can Statements" help to communicate the student's access to the grade standards. Use the "I Can Learn" statements to engage students in knowing what they are working on in class. There will be many students who can use these statements to understand their progress. Teachers can use the "I Can Learn" Statements in instructional planning as objectives that support a student's progress toward learning goals in the IEP.

MATH "I Can Learn" Statements

READING "I Can Learn" Statements

READING FOUNDATION SKILLS "I Can Learn" Statements

WRITING "I Can Learn" Statements

LANGUAGE "I Can Learn" Statements

SPEAKING & LISTENING "I Can Learn" Statements

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"I Can Learn" statements establish learning targets that can be understood by students and others involved in their education. Wayne County special education teachers have taken the Essential Elements and developed scaffolded "I Can Learn" statements that represent the range of modifications that may be needed by students with cognitive impairments.

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21-22 ATC Professional Learning Choice board

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21-22 ATC Professional Learning Choice board

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User Guide: The User Guide for each assessment explains what it assesses, how the foundational work is related to the grade level work, guidance for when to use the use the assessment and how to analyze student responses.

Teacher Guide: Each item in the assessment has an answer key, standards alignment, look fors, and specific resources to support teachers as they address unfinished learning.

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SCOE Readiness Assessments for Math Project - About the Resources

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What's In This Resource? Short formative assessments that assess foundational learning for the major work of each grade level with teacher support Alignment of assessments to the scope and sequence of the Eureka Math curriculum: K-5 6-8 Three components for each assessment:

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Discover Mathigon, the Mathematical Playground. Learning mathematics has never been so interactive and fun!

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Math Practice Video in friendly language

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Math Practice Video in friendly language

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Standards for Mathematical Practices student friendly language

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The standards for mathematical practices are the same for K-12 grade. Many times teachers need to know “How do I teach practice #1 at my grade level. The link above shows examples of the math…

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These projects do not have to be "End of Year" ;)

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These projects do not have to be "End of Year" ;)

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10 Awesome End of Year Math Project Ideas — Mashup Math

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Browse through over 60 complete K-12 math units of study chalked full of problem based investigations, 3 act math tasks, visual number talks, consolidation prompts and purposeful practice worksheets to Spark Curiosity & Fuel Sensemaking in every student.

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Real World Math Lessons | 3 Act Math Tasks | Math Worksheets & Practice

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Contextual problem based real world math lessons with rich math tasks, multi-day 3 act math tasks, math practice materials and math worksheets

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Accessing Blended Learning Digital Playbook

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Accessing Blended Learning Digital Playbook

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Moving Forward - NCSM and NCTM Joint Statement - National Council of Teachers of Mathematics

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"We live in uncertain times. Public health is at the forefront of our minds, and our schools have been disrupted in ways we have never seen. Although no one can predict how education might

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Important Prerequisite Math Standards 1-HS

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Important Prerequisite Math Standards 1-HS

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Next Steps to Orchestrate  Math Discussions

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Next Steps to Orchestrate  Math Discussions

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I'm currently rereading Five Practices for Orchestrating Productive Mathematics Discussions by Smith and Stein (2011) as part of a book study with a school. I've always appreciated this book as a great stepping stone from a classroom where the teacher is the ultimate knower of math to a classroom where students construct their own understanding. The book offers five immensely helpful strategies to ensure that a discussion of a math task (which, to me, is the hardest part to get right) yields fruitful mathematical conversation. The book is replete with helpful vignettes, strategies and commentary so post- or mid-problem discourse results in mathematical understanding.

However, in this reread I'm struck at how central the teacher is to the discussion itself. The teacher rarely recedes into the background, allowing for students to drive the discussion. Instead, the teacher anticipates the questions or problems that might arise, plans who speaks, and posits additional questions to probe deeper. This is absolutely a significant step forward in decentralizing the teacher. But how could we foster even more student ownership of the conversation?

It almost never happens naturally. Students typically have to learn how to drive the conversation, or at least move it forward. I wrote about one strategy I saw a teacher employ in the intro to the chapters on Effective Facilitation in Necessary Conditions. Sarah started off her year with a "question of the week" for nine successive weeks. Why nine? Because that's how many sleeves these things have:

In every one of these sleeves was an index card with these written on it.
Week 1: Can you justify that?
Week 2: What assumptions are we making?
Week 3: Does that align with our initial estimate?
Week 4: Is there a different way we could do this?
Week 5: Tell me how you know that.
Week 6: Did we consider everything?
Week 7: What other problem does this look like?
Week 8: How confident do you feel in your answer?
Week 9: Did you communicate the math clearly?
Each week a student had to actively seek to ask that week's question at least three times. And yes: for a grade. Sarah would listen carefully during groupwork and whole-class discussion for students to use that week's question. After about week three, she allowed students to use the question from that week as well as those from previous weeks.

Sarah, and her students, reported that it feels very artificial at first. New skills always feel artificial at first. Think about when you first learned to cook. You probably had to return to the recipe after each step or multiple times per step. It requires a lot more active brainwork to perform a new skill.

As a clunky requirement, at first, some students may ask it at the very beginning of class just to get it out of the way. That's fine. If a student isn't asking the question, Sarah instructs them to ask it for "homework" and tell her about it the next day. That's fine too. Eventually, student-to-student questions become routine.

Another strategy I love is from Hands Down, Speak Out by Kassia Omohundro Wedekind and Christy Hermann Thompson. To define directly from the book, a Hands-Down Conversations are "conversations that flow among students without the use of hand-raising, and in which the teacher is not the primary speaker." (p.3) (emphasis mine). This is an excellent encapsulation of my ideally orchestrated classroom conversation. Hands Down describes "conversation communities" and "conversation clubs" among students.

In a "conversation club" the students have had plenty of opportunity to engage as a class and engage in paris (such as in a "turn and talk" routine), but now students are ready to discuss with one another in small groups. Pairs of students group with other pairs of students to keep the conversation going.

Perhaps another distinction can be seen through the primary goal of the lesson. In Five Practices, the primary goal of the discussion is the mathematical content. Early in Sarah's class or a "Conversation Club" the primary goal is to support students in developing conversation skills. The secondary goal in these latter examples is the content. Eventually, after multiple iterations of these lessons, the math content becomes the primary goal and the students are habitualized into supporting that primary goal themselves.

Hands Down helpfully offers the notion of a conversation map (complete with a template in the appendix) to ensure that all students are engaging in the discussion. And, as importantly, that they are engaging one another in that discussion.

I too "gif'd" about this a while back when thinking about how lectures look. Namely, are the conversation connectors primarily between teacher-student or student-student?

Five Practices offers teachers an excellent first several steps at planning for classroom discourse. It helpfully offers a transition between complex work on discussion worthy tasks into mathematical knowledge. It also adeptly demonstrates how to elevate student work so that students may showcase their brilliants via multiple strategies. By no means would I suggest abandoning this crucial series of classroom practices. Teacher-orchestrated classroom conversations are essential for learning! However, a teacher looking to flatten the existing structure of expertise in the classroom will have to take it another step or two further: teaching, allowing and relying on students to become the maestros.

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The next steps in classroom conversation orchestration

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I'm currently rereading Five Practices for Orchestrating Productive Mathematics Discussions by Smith and Stein (2011) as part of a book study with a school. I've always appreciated this book as a great stepping stone from a classroom where the teacher is the ultimate knower of math to a classroom where students construct their own understanding....

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Capturing your students interest and curiosity during the first few minutes of class is the key to keeping them engaged for your entire lesson.

But not all math warm up activities are created equally.

Math teachers miss out on activating their students' critical thinking and reasoning skills when they assign routine, lower-level practice problems during the first five minutes of class.

However, when you use the right mix of fun and though-provoking math warm up activities to start your lessons, student engagement spikes, as your kids will constantly be wondering about what is coming next.

You probably already have some awesome math warm up activities-like Which One Doesn't Belong? and Think-Notice-Wonder-in your tool belt. But if you're looking for another great strategy for mixing up your instruction and engaging your students, then get ready for:
Two Truths and One Lie!
I recently started using Two Truths and One Lie (2T1L) activities, where students are presented with three mathematical statements (only two of which are true) and they have to identify which statement is a lie and justify why their choice is correct. The results? Pretty amazing. 2T1L taught me that my students love to argue and state their case (in small groups or to the whole class).

In short, 2T1L is a fun way to spark deep mathematical thinking and open discussion at the start (or end-2T1L activities make great exit tickets) of any lesson.

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Idea: How to Engage Your Students at the Start of Any Lesson - Mashup Math

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Capturing your students interest and curiosity during the first few minutes of class is the key to keeping them engaged for your entire lesson. But not all math warm up activities are created equally. Math teachers miss out on activating their students' critical thinking and reasoning skills when

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How is math used in video game designing and programming? originally appeared on Quora: the knowledge sharing network where compelling questions are answered by people with unique insights.
Answer by Matthew S. Stenquist, video game developer, on Quora:
Math is an absolute fundamental foundation to successful game development and game design.

Math is everything when it comes to games. From having the ability to calculating the trajectory of an Angry Bird flying through the sky, to ensuring that a character can jump and come back down to the ground. Without the help of mathematics, games simply wouldn't work. A character wouldn't be able to walk up a slope, slide down a slide, fire a bullet from a gun, or even jump without the help of the mathematics. The most basic of games use some form of math to the most complex of games. Math is essential to the production of games. It is the flour to the cake that game developers are trying to bake. Without it, the cake wouldn't rise.

Math is used in every aspect of game development, including art. Maya is a math-based program that plots out the vertices and normals in mathematical form while the artist just uses a tool that allows them to create stunning 3D graphics without worrying about math. Simply put, you could model Godzilla in notepad and push it into Maya, if you knew where to plot the points in numerical form (which is extremely difficult).

However, a lot of the math is computed at runtime and handled by the game engines that render back face culling, and the other nitty gritty things that would be too cumbersome to do without the use of using an engine to alleviate the math calculation portion at runtime.

A lot of math in gameplay scripting is fairly simple, but math used in game engine architecture is far more complex and a lot more taxing mentally. Math in game development is simulated either by the developer or handled by the engine at runtime by running computations to calculate the operation that is needed.
Here are some examples:

Ocean waves crashing nicely against your boat in ASC: Black Flag? Math.

Those bullets flying over your head in Call of Duty: Ghosts? Math.

That fancy UI animation that's procedurally generated? Math.

Sonic being able to run fast and Mario being able to jump? Math.

Drifting around that corner in Need for Speed at 80mph? Math.

Snowboarding down a slope in SSX? Math.

That rocket blasting off in Kerbal Space Program? Math.

Here's an expanded example using Mario's jumping mechanic.

When Mario jumps he isn't just going straight up and down on the Y-Axis but rather creating a parabola to jump up and down. It would be quite silly for Mario to beam up and then beam across on the X axis and then straight down on the Y-axis. Certainly, it would look goofy and not quite right.

Another example for instance is, Kerbal Space Program; a game that relies heavily on math. The entire game is pretty much all math when you think about it.

Newtonian physics are heavily simulated in KSP. Without the use of math in KSP, the game wouldn't be able to do much. Your rocket wouldn't be able to get off the ground and out of the atmosphere into space. The simulations in the game would be boring, and quite frankly the game wouldn't be able to do much. A rocket wouldn't be able to get off the ground because thrust doesn't exist, and or be able to pitch, yaw, and roll when in the sky.

In game development we're allowed to get away with faking math so that it is to work with the design of a game, but a lot of the time the math in games mirror real world physics and math principles. Math helps out with calculating everything from what a particles velocity should be, to the spread of a shotgun blast, to using gravity to bring a ball back down to the ground, and vice versa. These are all very basic math principles that a lot of games use. And their is still much more sophisticated and advanced math used in AAA games that I haven't covered.
What are the main branches of math used in game development?

Algebra

Discrete Mathematics

Trigonometry

Calculus

Linear Algebra

Applied mathematics

And much much more....

Some of the most important math used in games.

Dot Product, Cross Product.

Scaling Vectors, Unit Vectors, and Vectors.

Reflection, Matrices.

Scalar Manipulation.

COS,SIN,TAN.

Delta Time.

Domain and Range.

Most of these math topics are all used all together in very advanced games. But, in simpler games the math may only require trig and algebra, to a handful of math using only scalar multiplication.
How is math used in game programming and game scripting?
Math in game programming can be as easy as adding x + y, to calculating and manipulating cos, sin, tan with added variables while stringing it to your function, all the while their is still much much more advanced ways to use math in games.

Let's take a look at creating a constant variable called MAX_SPEED and MIN_SPEED (vectors) and adding that to the game update loop while adding a speed to a spaceship so that it can move, to creating an array that runs an algorithm that loads a random level every time the game is played, to simply altering a child's X (vectors) in the update loop, or to adjusting the angle of rotation once it hits a wall (reflection) on a spin wheel when a ball hits it. Doing any sort of basic thing, such as movement in a game will incorporate some form of math.

Math is an essential ingredient that is necessary to the production of games. Without the use of math in games we would just have pretty art that's semi-interactive. Math adds a whole new element to entertainment by blending the sciences and arts into a whole.
What can math do in game design?
With that being said, mathematics allows games to do incredible things that the real world cannot simulate by allowing new ways for the game script and engine to handle calculations on the fly that would not be feasible to do in the real world. So next time when you question your math teacher if you're going to ever use "Algebra" in the real world when you're done with your studies, you sure will especially if you pursue a career in game development.

Fluid water simulation.

Animation.

Algorithms.

Game engine architecture.

Gameplay scripting. (walking, shooting, jumping)

Analytics and data mining. (analyzing players interaction)

Timers programming (delta time, etc).

Physics programming (inertia, friction, etc).

Graphics/Shaders programming (matrices,etc).

Path finding/AI.

Procedural level design.

Handling Polygon rendering.

And much much more.

Here are some books I recommend reading.
The things listed above are only but a fraction of what math is able to help out with in game development and game design.
More questions:
This question originally appeared on Quora. Ask a question, get a great answer. Learn from experts and access insider knowledge. You can follow Quora on Twitter, Facebook, and Google+.

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How is math used in video game designing and programming? originally appeared on Quora: the knowledge sharing network where compelling questions are answered by people with unique insights. Answer by Matthew S. Stenquist, video game developer, on Quora: Math is an absolute fundamental foundation to successful game development and game design.

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Resources and guidance to support Black, LatinX, and Multilingual students to thrive in grades 6-8 A Pathway to Equitable Math Instruction is an integrated approach to mathematics that centers Black, Latinx, and Multilingual students in grades 6-8, addresses barriers to math equity, and aligns instruction to grade-level priority standards.

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User Guide: The User Guide for each assessment explains what it assesses, how the foundational work is related to the grade level work, guidance for when to use the use the assessment and how to analyze student responses.

Teacher Guide: Each item in the assessment has an answer key, standards alignment, look fors, and specific resources to support teachers as they address unfinished learning.

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SCOE Readiness Assessments for Math Project - About the Resources

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What's In This Resource? Short formative assessments that assess foundational learning for the major work of each grade level with teacher support Alignment of assessments to the scope and sequence of the Eureka Math curriculum: K-5 6-8 Three components for each assessment:

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Moving Forward with Math in the Pandemic

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Moving Forward with Math in the Pandemic

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Photo: Kiana Liu

In a school year when in-person instruction is already limited, California math teachers are making up for lost time on the fly.

Since school campuses closed in March due to the pandemic, education experts have sounded the alarm that certain groups, such as low-income and special education students, could fall further behind academically than their peers. And now test scores show that students are struggling in math more during the pandemic than in previous years.

But exactly how school districts have planned to mitigate learning gaps looks different depending on the district and even classrooms within a school.

One of California's largest school districts, San Diego Unified, is pushing ahead with grade-level math content and addressing questions and gaps in learning as they come up during lessons. That contrasts with past approaches to so-called learning loss - when students lose academic skills and knowledge over a period of time - that have involved testing students at the beginning of the year to determine where they need extra help and offer remediation based on the results.

"Over the summer, we kept hearing 'Shouldn't we have a diagnostic exam because they missed so much?'" said Aly Martinez, the instructional coordinator of mathematics for San Diego Unified.

While there was no question that students missed critical class time, she and others had major qualms with the diagnostic approach. One of the biggest concerns was putting students in a position where they feel inept at the start of an already chaotic school year.

"The diagnostic test is an emotional task. It's designed to find where students don't know the answer," Martinez said. "My third-grade son had to take a test at the end of the school year in distance learning, and it took nearly five days, and he cried every day. For me, it was a culminating moment about how we are influencing and shaping their math identity when we start by saying, 'Look at all the things you don't know and you missed.'"

This fall, the district is encouraging teachers to keep on pace with grade-level content in math and address questions from students as they come up in a method referred to as "just-in-time teaching." For example, while teaching multiplying and dividing fractions in sixth grade, some students might need a refresher on fractions from fourth grade. Instead of reviewing fourth-grade fraction lessons for a few weeks at the start of the term, the idea is to incorporate a quick lesson or activity that offered some review of the material needed to master the grade-level standard.

San Diego Unified's approach stems from guidance shared by education groups, such as the National Council of Teachers of Mathematics, which this summer released a toolkit with guidance on how schools should treat math education as the pandemic continues. Among the top suggestions was that schools should avoid front-loading the fall term with testing and review, and instead move straight into grade-level content and regularly check for gaps that need to be addressed.

"We acknowledge that students have unfinished learning. That's always been the case," said Patrick Callahan, a mathematician and consultant who has been working with San Diego Unified on its plan for distance learning. "And, yes, it might have been amplified by school closures. But the answer was not to hold kids back and delay access."

To develop the plan for this fall, Callahan and Martinez looked to research that found diagnostic testing and individual remediation didn't lead to significant student growth for New Orleans schools following Hurricane Katrina. They also pointed to studies that have shown holding students back in courses such as Algebra 1 rarely leaded to improve outcomes the second time they took the course.

"We wanted to ensure students had more opportunities to work together and with each other. If you give a diagnostic, you identify different gaps for different kids," he said. "Diagnostics delay access to grade-level math and discourage students working together collaboratively."

Over the summer, the district-level math leadership team at San Diego Unified created a set of academic priorities for each grade level to adapt to distance learning. That included a suite of review activities based on common problem areas that teachers can easily turn to if students show signs of struggle or are missing a skill necessary for the lesson.

"We created just-in-time resources for every single unit so teachers don't have to go searching for it at that moment," Martinez said. "We did the work to anticipate popular unfinished learning opportunities."

Diagnostic exams can be useful measures to gauge what students know. Many districts require these kinds of assessments at the beginning of and throughout the year to track progress. Plus, some regression or unfinished learning is typical of any school year, especially after students return to school from an extended break.

But in the era of distance learning, when students have limited and unequal amounts of time with teachers, even larger gaps in learning have been anticipated since schools closed last spring.

Early data is showing that those fears were valid - in math at least. Compared with 2019, about twice the number of students nationwide had a significant decline in math scores, falling at least 20 percentile points from last spring to this fall, test results from the Portland-based nonprofit NWEA showed. The exam tested 4.4 million students in grades 3 through 8 nationwide. Reading scores on the test have remained about the same since last year, however.

Molly Keimach, a ninth-grade math teacher at Kearny High School in San Diego Unified, said she "definitely felt like this year started off with more of a struggle than in past years content-wise." But she isn't sure whether that's been because students fell behind last spring, or simply because of the difficulties of keeping students engaged in an online environment this fall

"At the beginning of the school year, almost a third of my ninth-graders were failing. It's not uncommon to have a high failure rate for that class, but this was higher than I had ever experienced," Keimach said, referring to the Integrated 1 math course she teaches.

The model San Diego Unified is pushing is familiar to Keimach. In any given year, many of her students come to high school from middle school with learning gaps. She previously had students take pre-tests and other assessments, but after a few years began detecting patterns in the areas that students needed review on, like the distributive property, an algebra concept that many students struggle with, she said.

Now, she incorporates review activities into her lessons based on what students have needed help with before, plus what she finds they need help with from their current work, and skips the diagnostic.

"Just-in-time teaching and learning is essential during distance learning," Keimach said. "We have half of the time normally and even in normal years there isn't enough. My bigger concern is not if they learned this before, but are they engaging in online learning now? That's the biggest struggle."

Experts like National Council of Teachers of Mathematics President Trena Wilkerson fear that testing and remediation could lead to segregating students into different groups based on their perceived abilities. Some studies and reports have shown that tracking in mathematics can lead to segregation among students along racial and economic lines.

While students can also be separated by skill level in English and science, math is one of the few subjects where students may be assigned a course track as early as fifth grade that continues through middle high school, which in turn can affect their eligibility for college.

"You don't want to fall into separating students and get into tracking," Wilkerson said. "If we start separating them, we are facilitating inequities when really students just didn't have the same opportunity."

Sara Feiteria, a sixth-grade math and science teacher at Farb Middle School in San Diego Unified, didn't notice an increase in learning gaps this fall compared with any previous year. But the added challenges of online learning - like not being able to see students who have their cameras off, for example - has made it difficult to maintain her usual teaching strategies.

The district's pre-made resources have helped her manage class time, she said. And more importantly, they have freed up time for her to focus on building trust with her students in a strange new learning environment.

"The priority is the emotional wellbeing of these kids right now," she said. "Before even thinking about problem-solving or critical thinking, you need to think about these human beings who need relationships. No priority is going to be met before that."
To get more reports like this one, click here to sign up for EdSource's no-cost daily email on latest developments in education.

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How one California school district is moving forward with math in the pandemic

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Photo: Kiana Liu In a school year when in-person instruction is already limited, California math teachers are making up for lost time on the fly. Since school campuses closed in March due to the pandemic, education experts have sounded the alarm that certain groups, such as low-income and special education students, could fall further behind academically than their peers.

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NCTM Tasks aligned to Effective Teaching Practices

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NCTM Tasks aligned to Effective Teaching Practices

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Principles to Actions Professional Learning Toolkit - National Council of Teachers of Mathematics

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These grade band specific professional learning modules are focused on the Effective Teaching Practices and Guiding Principles from Principles to Actions Ensuring Mathematical Success for All. Presentation, presenter notes, and required materials are provided in each module to support professional learning with

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Read like a Mathematician:  3-Reads strategy

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Read like a Mathematician:  3-Reads strategy

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Achieve The Core Priority Considerations 2020-2021

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Achieve The Core Priority Considerations 2020-2021

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These documents name instructional content priorities in mathematics (K-8, high school) and ELA/literacy (K-12). These were developed for the 2020-21 academic year in response to the disruption of the global pandemic of COVID-19.* They provide guidance for the field about the content priorities by leveraging the structure and emphases of college- and career-ready mathematics and ELA/literacy standards. They are intended to help publishers, other designers of instructional materials, and instructional leaders find new efficiencies in the curriculum that are critical for the unique challenges that have resulted from school closures and anticipated disruptions in the year ahead, keeping at the forefront principles of equitable instruction.

All of the guidance is designed to support planning and decision making. Due to the structural differences between the grade-specific (K-8 mathematics, K-12 ELA/literacy) and course-specific (high school mathematics) guidance, the high school mathematics resource was developed separately. The high school mathematics content was designed in close partnership with Asia Franks and Jaliyla Fraser.
*Note: Send Feedback While these documents were created for the 2020-21 academic year, they remain helpful for those setting academic priorities for the 2021-22 school year. Given the incredible variability of the 2020-21 school year, to maximize the effectiveness of this guidance, the recommendations should be examined and adjusted based on the specific knowledge educators have about what students were able to accomplish and what may need additional attention. In the 2021-22 school year, educators must take into account the unique needs of students and continue to use strong formative assessment practices to understand where there is unfinished learning and to support students in engaging with grade-level content. For more information on academic acceleration and prioritization, integrated scaffolds and support, human-centered learning environments, culturally relevant pedagogy, and methods for understanding student progress, see our Priorities for Equitable Instruction: 2021 & Beyond page.

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Priority Instructional Content in English Language Arts/Literacy and Mathematics

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These documents name instructional content priorities in mathematics (K-8, high school) and ELA/literacy (K-12). These were developed for the 2020-21 academic year in response to the disruption of the global pandemic of COVID-19.* They provide guidance for the field about the content priorities by leveraging the structure and emphases of college- and career-ready mathematics and ELA/literacy standards.

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Synchronous Online Teaching Strategies and all material on this website by Theresa Wills is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Based on a work at theresawills.com.Permissions beyond the scope of this license may be available at theresawills.com/permissions.

Interactive slides for any content area

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Templates - Where THERE'S A WILLS, there's a way

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Synchronous Online Teaching Strategies and all material on this website by Theresa Wills is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Based on a work at theresawills.com.Permissions beyond the scope of this license may be available at theresawills.com/permissions.

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Smarter Balanced tests are built to provide verifiable, accurate, and representative data that helps states, districts, and schools see learning trends from multiple vantage points. Our goal is to provide educators and families with the information they need to make decisions about next steps in a student's learning journey. Learn more about our technical research, reports, and research efforts to better understand how the test works to deliver valuable information about student learning.

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Development and Design - SmarterBalanced

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SMARTER ASSESSMENTS > DEVELOPMENT AND DESIGN Development and Design Smarter Balanced is committed to an unprecedented level of transparency, so that anyone who is interested can see exactly how tests are developed and designed. Smarter Content Explorer Assessing the range of knowledge and skills is important for college and career readiness.

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Smarter Tools for Teachers. Discover classroom resources you can use today. Educator-created lessons, activities, strategies, and professional development to help tailor instruction and boost learning.

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Planning with the Interim's in mind HyperDoc

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Planning with the Interim's in mind HyperDoc

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SFUSD Elementary Math Distance Learning Overview and Scope and Sequence Documents

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Our curriculum materials have been developed and curated by expert teachers, tested and refined in classrooms over many years.

Select a subject and a grade to begin exploring!

500K+ Educators worldwide use Fishtank Learning

Here's what they have to say.

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Our curriculum materials have been developed and curated by expert teachers, tested and refined in classrooms over many years. Select a subject and a grade to begin exploring! 500K+ Educators worldwide use Fishtank Learning Here's what they have to say.

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Student Achivement Partners is committed to creating spaces for educator collaboration and shared learning led by Core Advocates from across the country. Members of the Core Advocate Network have been featured in monthly webinars and newsletters on a variety of topics related to college- and career-ready standards.

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Make a Copy

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2021 Draft Framework, Now in the public review period!

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2021 Draft Framework, Now in the public review period!

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2023 Mathematics Framework

At its meeting on July 12, 2023, the State Board of Education (SBE) adopted the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve ( Mathematics Framework). The framework is important guidance designed to help educators align classroom teaching with California's rigorous math learning standards.

The Mathematics Framework reflects input from California parents, educators, students, and others who commented during the two 60-day field review periods that were held in 2021 and 2022.

California is committed to achieving excellence in math teaching and learning through curriculum and instructional approaches grounded in research and reflective of best practices across the globe. The Mathematics Framework provides guidance for mathematics learning for all students at all levels of math-including calculus-and ensures students have a wide variety of options including pursuing Science, Technology, Engineering, and Mathematics (STEM) in college and career.

Frequently Asked Questions
Information about the draftMathematics Framework.

Schedule of Significant Events for the Revision of the Mathematics Framework
At its meeting on July 13, 2022, SBE revised the Schedule of Significant Events (Timeline) for the Revision ofMathematics Framework. The Timeline was originally approved by the SBE on May 8, 2019, and was previously revised on September 11, 2019, May 7, 2020, July 14, 2021, and November 3, 2021.

A professionally-edited and designed PDF version of the framework will be posted at a later date. The content will not substantively change from the version posted below.

Curriculum Framework and Evaluation Criteria Committee

At their January 08, 2020, meeting the State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework.

The Mathematics CFCC Meetings and Notices

Focus Groups

Pursuant to the California Code of Regulations, Title 5, Section 9511(c), the California Department of Education (CDE) convened four focus groups across California.

Listserv

Additional Resources

2013 Mathematics Framework

Assembly Bill 250 (Chapter 608, Statutes of 2011) called for the revision of the Mathematics Framework to align with the California Common Core State Standards for Mathematics.

Video: Overview of the Mathematics Framework (Dated 26-Feb-2015)
This video for teachers, administrators, and other educators provides an overview of the Mathematics Framework and how it supports implementation of the California Common Core State Standards for Mathematics.

Common Core State Standards for Mathematics (PDF; 3MB)
Links to the standards adopted by the California State Board of Education in August 2010 (Modified January 2013 Publication Version).

Common Core State Standards (CCSS) Initiative
The multi-state initiative released the CCSS on June 2, 2010. The initiative site includes information about the development and research behind the standards, appendices, the states that have adopted the CCSS, and frequently asked questions.

Appendix A
Designing High School Mathematics Courses Based on the CCSS.

2005 Mathematics Framework (Available on request)
The Framework was adopted by the State Board of Education on March 9, 2005.
*To order a copy of this framework please contact CDE Press.

Content Standards
Links to downloads of all Content Standards.

All Curriculum Frameworks
Links to downloads of all Curriculum Frameworks.

Questions: Curriculum Frameworks and Instructional Resources Division | CFIRD@cde.ca.gov | 916-319-0881

Last Reviewed: Friday, October 20, 2023

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Curriculum frameworks provide guidance to educators, parents, and publishers, to support implementing California content standards.

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Proportional Reasoning, Scientific Notation, Number Sense

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A garden snail's average speed is about ​0.029 mi/h. The North American X-15's top speed is about 4,520 mi/h. How much time would it take for each to travel across the United States, a...

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The trend of Bitmoji classrooms started last fall when many of us were teaching virtually, but many teachers are continuing to use them this year too. Since many teachers use a digital learning platform, Bitmoji classrooms offer interactive elements for students to click through to see assignments, documents, and websites.

Isabel P. says, "I'm still going to use it. Before the pandemic, I had been trying to incorporate more technology into my curriculum. To me, it is important for students to prepare themselves for the workforce. After all, it is the 21st century. Most businesses, hospitals, etc., use technology now and it's getting more sophisticated. I feel I need to be an example of those changes." Kelly B. agrees. "I use Bitmoji classrooms for my interactive read aloud. I love them, and I'm keeping them!"

Are you ready to join in? Looking for ideas of what to include in your Bitmoji classroom? We've got you covered with these creative ideas posted in our Facebook groups and on Instagram. And if you don't know how to get started ... we've included a tutorial below.

We Can't Stop Staring

There are so many details in this image posted by Kait C. on Facebook!

Anchor Charts & Posters

We also love the Alma Mater representation, from Amanda H. on Facebook.

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How Welcoming is This?!

And we love it!

Ready for School!

And the start of school for kindergarten!

Fun Bulletin Boards

And a book nook too!
Source: @elementree4teachers
A Colorful Classroom

Love that THINK poster.

We Love Any Book Love

With a Bitmoji classroom you can link to reading materials for the week.

AP Classes Get in the Mix

Get ready for some psych!
Source: @thesocialstudiesworldofmsj
Physical Science, Too

Fun with dinosaurs!
Source: @urbanscienceeducator
Ready for Game Day!

We love the theme for this Bitmoji classroom.
Source: @teamingupinelementary
Fun for Foreign Language Learners

Also how great is this Spanish classroom?!

Music Teachers Get in the Groove

We love the links to each grade level on the keyboards.
Source: @thek8musicteacher
Art Teachers Share Their Creativity

We love the challenge and artist of the week.
Source: @artwithmseggers
First Grade Teachers Represent!

The whole grade can showcase their Bitmojis.
Source: @libros.cafe.andteach
Create Your Own!

Want your own interactive Bitmoji classroom? Check out this video tutorial:

Here's how you link it to Google Classroom and Seesaw:

This video tutorial walks you through the steps to making a Bitmoji Google Classroom banner:

And if you'd rather see some step-by-step instructions this link helps!

Have your own Bitmoji classroom to share? Come join us in our WeAreTeachers HELPLINE group on Facebook!

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How Teachers Are Still Using Bitmoji Classrooms in 2021-22

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Looking for ideas of what to include in your Bitmoji classrooms? These teachers have posted a variety of fun elements.

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Make a copy :) created by maoki@fcoe.org. Thanks Marissa!!!

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Math Manipulatives Test - Version 2 - Google Jamboard

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The version of the browser you are using is no longer supported. Please upgrade to a supported browser. Dismiss

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by Jimmy Redger Reef Sunset Unified School District

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Ells and Students on IEPs: Digital Supports

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Additional Digital Content Available in Spanish

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EduProtocols: Teach better, work less, achieve more with easy to use lesson frames to spark student engagement.

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Rio School District Remote Learning Activities

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Rio School District Remote Learning Activities

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By Fawn Nguyen

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Mathematics K-8 Remote Learning Activities

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Created by SupportEd

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With all of the school closings and extended spring breaks due to Coronavirus, I felt the need to organize some tools in one place (#justalittleOCD). I hope that these tools and resources are helpful as we navigate these waters to keep our students and families safe while keeping the learning going!

FYI- some of these are pictures and you may have to to type in the link to go to the website. Also, I may add more to this page periodically so feel free to refresh every now and then.

Viana Armstrong, M.Ed.

Ferris ISD Bilingual & ESL Coordinator

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With all of the school closings and extended spring breaks due to Coronavirus, I felt the need to organize some tools in one place (#justalittleOCD). I hope that these tools and resources are helpful as we navigate these waters to keep our students and families safe while keeping the learning going!

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Non-comprehensive list of publishers offering free distance learning resources.
Coronavirus (COVID-19) Main Web Page
Below is a non-comprehensive list of publishers offering free distance learning resources. At the URL listed, users can learn about the specific resources available as publishers continue to expand their offerings. Districts are not mandated to utilize only state-adopted instructional materials, and many classrooms utilize a network of resources. In this list below, educators and parents/guardians may discover the individual resources they want for a particular need.

Please note that this list is comprised of publishers who have offered their site information. The California Department of Education (CDE) has not reviewed these sites and resources, nor does the CDE in any way endorse or specifically recommend these resources. Users should carefully conduct their own evaluation based upon their own specific local needs and the appropriateness of the resources offered.

Capstone Publishing
Resources available during school closures.
User Name = Engaged; Password = Learning

Zearn
Distance learning for math

Questions: Curriculum Frameworks and Instructional Resources Division | Covid19@cde.ca.gov

Last Reviewed: Friday, August 20, 2021

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Solvemoji - Free teaching resources - Emoji math puzzle, great as a primary math starter, or to give your brain an emoji game workout - great for home schooling

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Problems are randomized, allowing students multiple opportunities to get the practice and feedback they need on the road to mastery.

Go beyond right and wrong. As soon as a student submits an answer, they get a detailed age-appropriate explanation.

DeltaMath allows teachers to mix and match problem-sets, control rigor, vary due dates, and, with PLUS or INTEGRAL, create tests and problems of their own.

Use DeltaMath's modules to create high-leverage assignments and track student learning. With DeltaMath PLUS or INTEGRAL, students also get access to help videos. Create and assign tests, assign specific problem-types, even create your own problem.

Learn More

Problems solved with DeltaMath

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NCTM

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Our students need mathematics to make sense of their world and increase their opportunities. As teachers, administrators, and education leaders, each and every student is counting on us, our policies, and our practices to support them, support their learning, and develop them as doers of mathematics.

NCTM has embarked on a comprehensive look at mathematics education from K-12. This involved administrators, higher education faculty, educators, and leaders in mathematics education. The results of this work address policies, practices, and issues and include practical recommendations to help create positive change.

NCTM's Catalyzing Change series looks to help you engage in critical conversations and create positive change.

Catalyzing Change in Early Childhood and Elementary Mathematics: Initiating Critical Conversations

Students' mathematical learning at Early Childhood and Elementary often sets the stage for their education trajectory. Examine how to make a positive difference for each and every student at this level.

Learn More

Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations

The needs of young adolescents are unique and impactful. Our policies and practices must consider support and contribute to how they see themselves, see mathematics, and use their skills to make sense of the world.

Learn More

Catalyzing Change in High School Mathematics: Initiating Critical Conversations

Identify and address critical challenges in high school mathematics to ensure that each and every student has the mathematical experiences necessary to increase their opportunities for personal and professional success.

Learn More

Catalyzing Change Webinar

We all have a stake in the future of mathematics.

The Catalyzing Change  series empowers you to lead critical conversations to improve math education and student readiness.

Catalyzing Change Across All Levels: Opportunities and Challenges

May 26, 2020 7:00 p.m. EDT | Speaker: Trena Wilkerson, NCTM President and Robert Q. Berry III, NCTM Past President

The current situation sharpens our view of inconsistencies and inequities that exist within the teaching and learning of mathematics across all grade levels. NCTM's series of Catalyzing Change publications, including the recently released

Catalyzing Change in Early Childhood and Elementary Mathematics, and

Catalyzing Change in Middle School Mathematics

highlight critical issues and provide guidance areas of focus for critical conversations and decision making in this time of significant need and opportunity.
Download Webinar Chat Download Webinar Slides
Download Webinar Resource 1
Download Webinar Resource 2 Download Webinar Resource 3 Download Webinar Resource 4

Supporting Resources

News Release
NCTM Releases Two Catalyzing Change Publications to Help Transform Mathematics Education from Preschool through Middle School

In the News
Reports: Early inclusion strategies shape students' perception of math | Education Dive

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Catalyzing Change - National Council of Teachers of Mathematics

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NCTM's new publication, Catalyzing Change in High School Mathematics: Initiating Critical Conversations , is a must-read for anyone who's involved in high school mathematics education.

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Open Middle Math by Robert Kaplinsky gives middle and high school teachers the problems and planning guidance that will encourage students to see mathematics in an entirely different light. These challenging and rewarding Open Middle math problems will help you see your students build genuine conceptual understanding, perseverance, and creativity.

Implement Open Middle math problems that are simultaneously accessible for both students who are struggling and those looking for more challenge.

Select and create Open Middle math problems that will help you detect students' misconceptions and strengthen their conceptual understanding.

Prepare for and facilitate powerful classroom conversations using Open Middle math problems.

Access resources that will help you continue learning beyond this book.

With these practical and intuitive strategies, extensive resources, and Robert's own stories about his journey learning to use Open Middle math problems successfully, you will be able to support, challenge, and motivate all your students.
Go Digital with Stenhouse
We offer ebook editions for most of our print titles so you can access on your computer, tablet, or e-reader from several major retailers including Amazon and ebooks.com. View the full list of retailers here.

If you previously purchased an ebook from Stenhouse.com, they will remain available in your digital library.

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Imagine that you assign a math problem and your students, instead of getting discouraged after not solving it on the first attempt, start working harder-as if on a quest to figure out the answer. They talk to each other and enthusiastically share their discoveries. What could possibly make this fantastic scenario come true?