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Math Center Organization – Making a Manipulative Station

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Math Center Organization – Making a Manipulative Station

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Staying organized is the #1 way I have found to save time! Finding the right systems can take time, but once you have it, say hello to all of the hours you didn't know you had! Below is the math area of my classroom. Today, I'm going to break down 10 of my favorite math center organization tips that really work!

One way that I have really cut down on my math center prep is by organizing my manipulatives in a way that my students can access them independently. I find that having all of the items they at their fingertips helps them build responsibility while saving me hours of prep time every week. You can find these math bin labels [HERE] or newly as part of my CLASSROOM LABEL BUNDLE [HERE]!

As you can see, they are clearly labeled with pictures, and are on a low shelf that they can easily reach. In some cases, I have organization built in to each bin. For example, each bin of unified cubes is pre-sorted into two different colors. This means that students can just take a bin to their table and already have that part taken care of (and no additional colors to distract them!) We use these to help visually represent composing and decomposing numbers, so two colors are essential!

I also have my dice organized within each bin. I love organizing dice in this way, because I no longer have dice flying off tables! I used baby food containers, because I'm at a point in my life where I have an excess of these in my house! You can just as easily use small serving tupperware (which you will see below.) When I taught younger grades, I also hot-glued a piece of felt to the bottom of each container to mute the sound!

I don't know about you, but I am OBSESSED with dice! I have more than I probably should, but my students love them too! After years of outgrowing my storage systems, I have finally found a system that works for me. I give you, the Dice Box!

You can use any storage toolbox from Lowes, Home Depot, or the Container Store. Now if my centers require dice beyond the standard 1-6 doled dice, my students can get them independently, eliminating one more thing I have to prep! After some requests, I have posted the labels over at my TpT Store. Find them [ HERE]

Second only to dice, I have a serious weakness for Target's Dollar Spot Erasers. I needed a way to let my students access and choose their erasers independently, so another organization system was born.I use the small square toolboxes (similar to the Dice Organizer). I do this because I have them sorted by season. For example, the Fall/Halloween erasers are in one box, while the Winter/Holiday erasers are in another. This means that I can switch them out throughout the year to keep them new and exciting for students.

I have hot-glued one eraser to the front of each drawer so students can visually see them at a glance! The only problem with this system is that I have to keep buying more storage because I just can't say no to Target!I used to cringe at how much time we lost while students got the correct amount of counters/chips they need for a game or center. To solve this problem, I decided I'd just have them pre-sorted! I used small Dollar Store containers, and filled them with counters and chips. For the translucent chips, I include two different colors so that they can be used for partner games.

Another organization hack are my Kaboom storage containers. If you don't know about Kaboom! you need to read about my favorite center [ HERE!] Popsicle sticks are really hard to store, because they're an awkward shape. I used to have them in open cups, but that made them hard to pack up at the end of the year.

Now, I just use empty Crystal Light powder containers. I don't personally drink it, but my family is very good about supporting their teacher niece/daughter/cousin/sister. I just place a piece of construction inside to cover the bottom half of the container, and it's all ready to go! Instant center!

For years I struggled with finding a way to organize the piles of coins in my classroom. A tray was great, but not stackable. Cash registers were fun, but only good for one table at a time. Sorting them for individual centers made me want to rip my hair out! What a time suck! Finally, I figured out something that really works!

These individual student banks have been a life saver! They're quick to pull out for centers, students can independently sort and put them away when they're done, and they're small and stackable (and when you have minimal space, that's a MUST!) You can grab these individual student bank labels for FREE [ HERE!]

My Math Word Wall is another organizational tool that I use year after year. I only laminate them once, and they're good to go FOREVER! They keep our vocabulary organized, and when I need visuals for a lesson, they're right there ready to go! My students refer to this focus wall Every.Single.Day. I put magnetic tape on the back of each card, so my kids can take them down to use at their tables, and put them back up when they're done.

These Math Word Walls are available K-5, and include Australian & Canadian coins and spellings! You can find them [ HERE!]

In addition to meeting with me in my guided math groups, students also go to two activities, two games, math journals, as well as independent work in their math journals. The games and activities don't necessarily change every week, since they only go to each center once.

Their group bins are color specific, so the work board coordinates with the bins. This has really helped my students navigate their center rotations independently, which means... MORE TIME FOR YOU TO WORK WITH KIDS, which is really the most important part!

I hope this has helped give you a few new ideas for organizing your classroom. While it takes some serious effort up front, the rewards are absolutely worth it!

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10 Math Center Organization Tips to Save You Hours of Prep Work! - Teaching with Jillian Starr

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Staying organized is the #1 way I have found to save time! Finding the right systems can take time, but once you have it, say hello to all of the hours you didn't know you had! Below is the math area of my classroom. Today, I'm going to break down 10 of my favorite math [...]

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Math Manipulatives Every Classroom Should Have

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Math Manipulatives Every Classroom Should Have

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This post contains affiliate links for your convenience. View disclosure policy HERE.

Math manipulatives are small objects that help with teaching math. They are useful tools for teachers and students. They provide a hands-on way in which to explore and learn. When children are using these materials in physical ways, they are learning differently than they are when they are simply listening or watching a lesson. This tactile learning builds a deeper, personal understanding of math concepts.

Math manipulatives make math FUN! Children of all ages enjoy using these concrete tools to make sense of the problems they are given. They especially help our younger learners who are learning new math concepts for the first time. A relationship is built when shown visually how to solve problems and given opportunities to "try" something using math manipulatives. With repeated practice and "play" with manipulatives, math fluency develops.

As a teacher with many years experience incorporating math manipulatives into my lessons, I appreciate how useful they are in helping me teach different math concepts. Many items can be used in multiple ways. I enjoy watching children have "lightbulb" moments when they finally understand a concept thanks to the tools they are using. I am ecstatic when children are exploring with a tub of manipulatives and they discover something new, a pattern, or way of use.

During Lessons

I use math manipulatives for almost every math lesson I teach. When planning my lessons, I think of ways that the concepts can be taught using visuals, as well as orally or on a chart. I prep tools ahead of time so they are ready for our lessons. I vary the tools in order for students to get practice using different types. During our lessons, math manipulatives are used usually during or after the initial lesson is taught. I will explain a concept, give examples on a chart, practice orally, and demonstrate with math manipulatives. Students use those manipulatives to practice the concept or solve a problem.

Examples of Use

When teaching basic addition, I use magnetic counters that can be used on the whiteboard to illustrate a problem (i.e. 2+5=7). Students use two-sided counting chips to solve another similar problem at the carpet.

When teaching counting or identifying numbers to 100, I use a large 100's chart and a pointer. We take turns pointing to the numbers as we practice counting by 1's, 2's, 5's, and 10's. Students use small 100's charts to point and follow along as we count or they locate different numbers given orally.

When teaching geometric solids, I use large foam 3D shapes that I can hold and point out its features. Students use smaller similar shapes to find those same features, to locate similar objects in the scavenger hunt around the class, and use them to create structures.

When teaching measurement, I use many non-standard units, such as cubes, to illustrate how long, tall, wide something is. Students use the cubes to compare and measure with the cubes around the classroom (i.e. my arm is 20 cubes long).

During Independent & Group Work

Students use math manipulatives at their workspace to completed their work. We have math centers set up that incorporate manipulatives to use during their work. I also give students "free time" to grab a bin of math manipulatives to explore on their own or in small groups. This is where some of the most amazing findings happen. I occasionally put a problem on the board for students to complete with a math bin of their choosing. This encourages "real world" problem solving when they must think of the most applicable tool and try different ones out through trial and error.

Examples of Use

Before we start a lesson, students are given time to explore the tub of math manipulatives for that day. I limit my suggestions as to what they should do with them, as I want to encourage creativity and mathematical thinking.

During "free time" or math centers, I will put out a basket containing around 20, 50, or 100 small items depending and ask students to complete a task. The task could be "make groups and count to find out how many objects you have" or something that encourages thinking and problem solving.

I will put small tubs together with manipulatives and ask students to explore, create, or show me something with it. It could be a tub of pattern blocks and the instructions "use all of the blocks to create a picture" or a geoboard and the instructions "show me a picture using 8 elastic bands".

I have tubs, baskets, and containers full of math manipulatives in our math area, as well as on our math supply shelf. I use a different bin or tub to hold each type of manipulative. I suggest labeling each bin or container with a name and/or picture on it. I suggest taking photos of your students using each manipulative correctly and attaching that to the bin as an example to students.

Try to have a designated place for each type of manipulative. Have them in a place that is accessible and ready for use. Using a large storage area that holds bins for those types you use often is helpful. Teach students where they can find each type and show them how to use them and put them away properly. This will help with clean up and maintain organization.

There are many types of math manipulatives available to teachers. Many can be used in multiple ways. It's a good idea to have a variety of types available in your school or ready in your classroom to help with teaching the variety of math concepts. Below I have categorized them into must-have (those you will use often and for many things) and useful (those that you may not use everyday but are very helpful in teaching concepts. I have used all of the manipulatives provided below and I recommend them for primary teachers (with Amazon Affiliate links).

Must-Have Manipulatives

Dice are a great tool to have on hand for math games and activities. There are many types available today, such as these dice in many colors. There are also different sized dice available, such as these large foam dice. Jumbo dice are great for rolling during a class game or for "flashing" to kids to have them call out the number shown. I suggest putting pairs of dice into small clear containers that students can quickly grab and shake while playing games. My favorite type of dice for teaching addition and playing games are the dice in dice.
Playing Cards
Playing cards make useful math tools because they have numbers on them. They can be used to teach addition and subtraction through games like addition "war" and subtraction "war". Playing cards, like these, come in traditional decks that you can find at most stores or dollar stores. Buying them in bulk playing card sets and having a deck for each student is helpful. Teachers would benefit from a set of jumbo playing cards to use for lessons and demonstrations as they provide a large visual for kids.

Unifix cubes are the colored cubes that connect in one way and snap cubes are colored cubes that can connect in different ways. Both can be used in many ways to teach many math concepts, such as patterning, place value, and measurement. Snap cubes are one of the most used math manipulatives. They visually demonstrate many number concepts, such as counting, grouping, adding, and taking away. Children love snapping the cubes together to make number "trains".

Another must-have manipulative are the two-color (red and yellow) counters. They have many uses and help little learners learn to count, make patterns, add, and subtract. They are an essential tool for teaching addition that I use frequently. Students use them for independent practice and help in solving addition and subtraction problems. I keep sets of 20 these colored counters in small containers students to use when needed. This set of ten frames with magnetic counters would be great for many number concepts.
Number Lines
Pattern blocks are small shaped blocks that can be used in multiple ways. They make great learning tools because they are consistent in shape and color. They work for teaching sorting, patterning, fractions, geometry, and more. They promote creativity and encourage students to create unique designs. I keep pattern blocks in a few large tubs for students to grab and explore with during math centers. Sets like the one below are available that include activity cards for students to complete.

Place value blocks are very helpful in teaching counting, number concepts, double-digit addition and subtraction. Place value concepts are more difficult to grasp and using these concrete manipulatives helps build understanding. I suggest have a large bin of of place value blocks similar to those below with enough for each student to represent the numbers you are learning. The magnetic set would be helpful for whole class demonstrations on a whiteboard. If you are teaching PreK or Kindergarten, consider introducing place value during calendar time with this counting pocket chart and straws.

Useful Manipulatives

Dominoes are a fun math manipulative to have available for games and other activities, such as matching numbers together. There are endless options for use, but my favorite for little learners is to use them to practice addition and subtraction. Give students a small pile of dominoes and have them record a number sentence and solve by counting. You can find dominoes at most dollar stores, but I love these colored dominoes for the classroom.

Magnetic numbers are great to have in a math center for children to play with. Children love to stick magnets on anything! They are helpful during lessons when counting, ordering, and number identification is taught. You can find plastic ones, foam ones, and wooden ones and they are available at most dollar stores and teacher supply stores. I like these foam magnetic numbers because they make less noise when they are played with or fall on the ground. These jumbo magnetic numbers would be helpful for teachers during lessons.

Shape counters are fun to use in a math center for little learners. Encourage them to sort the shapes by color, size, type, and create different patterns with them. They are also great for teaching beginning addition and subtraction (i.e. I have five bears and I take one bear away). Shape counters come in many fun shapes, such as bear counters, animal counters, bug counters, and transportation counters.

Large Teaching Clock & Mini Clocks
Geoboards
Geoboards are great for building shapes and learning about different geometry concepts. They make a great math center for children to explore. You could give children pictures to copy or specific tasks to complete with a geoboard. Teaching proper care and safety with the elastic bands is important. Check out this set of small plastic geoboards.

Play Money & Cash Register
Teaching financial literacy at an early age is important. Encouraging children to shop at a class made store and exchange items for money. Use a cash register like this and kid wallets like this to hold the pretend money. Play money games where coins and bills are used. Teach lessons and have children practice sorting coins, ordering coins by size and quantity, and creating different quantities. This deluxe coins & bills set includes tons of play money for all your activities.

Bucket balances are helpful tools in comparing different objects and volumes of liquid. In primary grades, we often use them to observe and estimate which of two objects is the heaviest. I like this balance scale because items can be easily put in and taken out by children during their exploration.

Mini Whiteboards & Markers

Mini whiteboards are amazing items that I use daily. I store a class set of boards, markers, and erasers in a basket at the carpet with our other math items. They make those quick moments when you want students to record their findings or solve a problem easy. We use ours daily during our number of the day activities (read HERE). Check out this class pack of whiteboards to go along with my go-to dry erase markers that last the longest ( these Expo markers).

While teacher supply stores have great quality math manipulatives, they are often expensive. If you can get your school to fund your classroom supply, then go this route. Lakeshore Learning has endless types and varieties of manipulatives and wonderful games that would fulfill your needs.

I suggest buying the majority of your items when they go on sale or when you can purchase them at affordable prices through Amazon. Each type of manipulative listed above is linked to Amazon to help you create your classroom wishlist. You can sign up for Amazon Prime and get all of your materials quickly, no matter what the weight of your package. Awesome! Make sure to enter the Math Manipulatives Every Classroom Should Have GIVEAWAY below.

There are many places to purchase math manipulatives. Get creative and have fun searching for materials in your home or find them for cheap at the dollar store. Read about free and affordable math manipulatives from Stir the Wonder.

Teachers Pay Teachers is another wonderful option for finding math resources, games, centers, and printable manipulatives for your classroom.

ComprehensiveMath Curriculum

TIPS FOR BUILDING MATH FLUENCY

Guide to the BEST Children's Books for Teaching Math

TOP TIPS FOR MATH

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Math Manipulatives Every Classroom Should Have

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This post contains affiliate links for your convenience. View disclosure policy HERE. Math manipulatives are small objects that help with teaching math. They are useful tools for teachers and students. They provide a hands-on way in which to explore and learn.

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To learn more about the standards, click here. To learn more about the NGSS Appendices,click here.

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Greis Leiva Before During After Lesson Plan Template

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Greis Leiva Math Assessment Commentary Assignment

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SCIENCE: Teacher Workbooks/Graphic Organizer 

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SCIENCE: Teacher Workbooks/Graphic Organizer 

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Support Reading Comprehension with Activity Worksheets for Organizing Information

Science A-Z Graphic Organizers support content-area learning and reading comprehension as students read fiction and nonfiction science texts. The Graphic Organizer collections are arranged by primary (grades K-2) and intermediate (grades 3-6) as well as by nonfiction and fiction. Select appropriate sheets for informational texts or literary texts to support students who are learning at different developmental levels and reading for various purposes.

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Science A-Z Graphic Organizers support content-area learning and reading comprehension as students read fiction and nonfiction science texts. The Graphic Organizer collections are arranged by primary (grades K-2) and intermediate (grades 3-6) as well as by nonfiction and fiction.

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Free Science Graphic Organizers/Teachers Pay Teachers

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Free Science Graphic Organizers/Teachers Pay Teachers

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Find Science resources | TPT

Importance of learning science

Learning science is particularly important for students as it equips them with the essential knowledge and skills to make sense of the world around them. Science education is not just about memorizing facts. It fosters critical thinking, inquiry, and problem-solving abilities. These skills are not only useful in school but also in everyday life beyond the classroom.

Benefits of learning science

Learning science offers many benefits to students both in school and beyond. In fact, it helps students:

Question the world around them and seek evidence-based explanations

Cultivate their ability to observe, experiment, and analyze data

Nurture a sense of curiosity, awe, and wonder about the natural world

Understand natural phenomena and the laws that govern the universe

With a solid foundation in science, teachers can help empower students to think critically, solve problems, make informed decisions, and engage with the world around them in meaningful ways.

Teaching with science resources

One of the best parts about science class is all of the possibilities for hands-on, collaborative learning! Think: labs, experiments, inquiry-based activities, and design challenges. These activities encourage students to explore scientific concepts by observing, asking questions, and conducting investigations. Additionally, with small group centers, students can engage in group experiments, discussions, and projects that require them to collaborate, share ideas, and solve problems together.

Discover printable and digital science resources

If you're a teacher or parent looking for printable or digital science resources, TPT has an extensive array of instructional materials for every learning need, topic, or grade level. Whether you're learning about plant parts or butterfly life cycles, or exploring advanced topics like the anatomy of a cell or Newton's laws of motion, we've got you covered.

On TPT, science resources come in various forms: from labs and worksheets to craftivities and doodle notes. They can be used to enhance learning, assess a student's mastery of science concepts, or to reteach a tricky topic. With plenty of TPT resources at your fingertips, teaching and learning science will be so much easier. Plus, you can expand students' knowledge even further by exploring TPT math resources, which are frequently paired with science lessons.

Frequently asked questions about teaching science

What types of science lessons are available on TPT?

There are many different types of science resources sold by Sellers on TPT. Some popular science lessons include biology, earth sciences, chemistry, environment, engineering, and anatomy.

How do I find science lessons on TPT?

Educators can save time preparing science lessons with resources created by experienced teachers. Simply start a search for science resources on the TPT marketplace, and filter by grade level, price, and/or resource type to find materials that've been proven to work in classrooms like yours. No matter what you're teaching, there are plenty of science lessons and activities sold by Sellers on TPT that are tailored to meet your students' skill levels.

How can I make my science lessons fun and engaging?

Students learn best when they're engaged! Sprinkle a little fun into your science lessons and make them feel like real scientists by investigating everyday objects, exploring the world outside the classroom, and doing hands-on and collaborative experiments and design challenges.

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Browse free science graphic organizers on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources.

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Common Core Instruction: Exploring Dividing Decimals to the Hundredths

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First Grade Math Lesson Time To The Half Hour On An Analog Clock

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Time for Class - Mr. Adler Science Lesson

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Academic Language Function for English Learners

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Academic Language Function for English Learners

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Update 2022: For a recent article on how to talk about math, click here.
Think about the questions that you ask in your math classroom. Can they be answered with a simple "yes" or "no," or do they open a door for students to really share their knowledge in a way that highlights their true understanding and uncovers their misunderstandings? Asking better questions can open new doors for students, helping to promote mathematical thinking and encouraging classroom discourse. Such questions help students:

Work together to make sense of mathematics.

Rely more on themselves to determine whether something is mathematically correct.

Learn to reason mathematically.

Evaluate their own processes and engage in productive peer interaction.

Discover and seek help with problems in their comprehension.

Learn to conjecture, invent and solve problems.

Learn to connect mathematics, its ideas and its applications.

Focus on the mathematical skills embedded within activities.

Below are 100 questions from mathematics expert Dr. Gladis Kersaint to help you address these core areas and promote mathematical thinking and discourse in the classroom. Want these questions visible in your classroom? Curriculum Associates has released an infographic that you can print and have at your desk or in your class for quick access! Here's a preview:

For more, please download Dr. Kersaint's new whitepaper:Orchestrating Mathematical Discourse to Enhance Student Learning.
Dr. Gladis Kersaint
Help students work together to make sense of mathematics

1. What strategy did you use?

2. Do you agree?

3. Do you disagree?

4. Would you ask the rest of the class that question?

5. Could you share your method with the class?

6. What part of what he said do you understand?

7. Would someone like to share ___?

8. Can you convince the rest of us that that makes sense?

9. What do others think about what [student] said?

10. Can someone retell or restate [student]'s explanation?

11. Did you work together? In what way?

12. Would anyone like to add to this?

13. Have you discussed this with your group? With others?

14. Did anyone get a different answer?

15. Where would you go for help?

16. Did everybody get a fair chance to talk, to use the manipulatives, or to be recorded?

17. How could you help another student without telling the answer?

18. How would you explain ___ to someone who missed class today?

Refer questions raised by students back to the class.

Help students rely more on themselves to determine whether something is mathematically correct

1. Is this a reasonable answer?

2. Does that make sense?

3. Why do you think that? Why is that true?

4. Can you draw a picture or make a model to show that?

5. How did you reach that conclusion?

6. Does anyone want to revise his or her answer?

7. How were you sure your answer was right?

Help students learn to reason mathematically

1. How did you begin to think about this problem?

2. What is another way you could solve this problem?

3. How could you prove that?

4. Can you explain how your answer is different from or the same as [student]'s?

5. Let's see if we can break it down. What would the parts be?

6. Can you explain this part more specifically?

7. Does that always work?

8. Is that true for all cases?

9. How did you organize your information? Your thinking?

Help students evaluate their own processes and engage in productive peer interaction

1. What do you need to do next?

2. What have you accomplished?

3. What are your strengths and weaknesses?

4. Was your group participation appropriate and helpful?

Help students with problem comprehension

1. What is this problem about? What can you tell me about it?

2. Do you need to define or set limits for the problem?

3. How would you interpret that?

4. Would you please reword that in simpler terms?

5. Is there something that can be eliminated or that is missing?

6. Would you please explain that in your own words?

7. What assumptions do you have to make?

8. What do you know about this part?

9. Which words were most important? Why?

Help students learn to conjecture, invent and solve problems

1. What would happen if ___? What if not?

2. Do you see a pattern?

3. What are some possibilities here?

4. Where could you find the information you need?

5. How would you check your steps or your answer?

6. What did not work?

7. How is your solution method the same as or different from [student]'s?

8. Other than retracing your steps, how can you determine if your answers are appropriate?

9. What decision do you think he or she should make?

10. How did you organize the information? Do you have a record?

11. How could you solve this using (tables, trees, lists, diagrams, etc.)?

12. What have you tried? What steps did you take?

13. How would it look if you used these materials?

14. How would you draw a diagram or make a sketch to solve the problem?

15. Is there another possible answer? If so, explain.

16. How would you research that?

17. Is there anything you've overlooked?

18. How did you think about the problem?

19. What was your estimate or prediction?

20. How confident are you in your answer?

21. What else would you like to know?

22. What do you think comes next?

23. Is the solution reasonable, considering the context?

24. Did you have a system? Explain it.

25. Did you have a strategy? Explain it.

26. Did you have a design? Explain it.

Help students learn to connect mathematics, its ideas and its application

1. What is the relationship of this to that?

2. Have we ever solved a problem like this before?

3. What uses of mathematics did you find in the newspaper last night?

4. What is the same?

5. What is different?

6. Did you use skills or build on concepts that were not necessarily mathematical?

7. Which skills or concepts did you use?

8. What ideas have we explored before that were useful in solving this problem?

9. Is there a pattern?

10. Where else would this strategy be useful?

11. How does this relate to ___?

12. Is there a general rule?

13. Is there a real-life situation where this could be used?

14. How would your method work with other problems?

15. What other problem does this seem to lead to?

Help students persevere

1. Have you tried making a guess?

2. What else have you tried?

3. Would another recording method work as well or better?

4. Is there another way to (draw, explain, say) that?

5. Give me another related problem. Is there an easier problem?

6. How would you explain what you know right now?

Help students focus on the mathematics from activities

1. What was one thing you learned (or two, or more)?

2. Where would this problem fit on our mathematics chart?

3. How many kinds of mathematics were used in this investigation?

4. What were the mathematical ideas in this problem?

5. What is the mathematically different about these two situations?

6. What are the variables in this problem? What stays constant?

Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. In the next and final blog in this series, we will dive into the specific strategies that teachers can use to foster meaningful conversations about what students are thinking, doing and learning.

This blog is part of a three-post series on the importance of mathematical discourse from Curriculum Associates and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy .
For more on mathematical discourse and Curriculum Associates, check out:
Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of Connecticut. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. This post includes mentions of a Getting Smart partner. For a full list of partners, affiliate organizations and all other disclosures please see our Partner page

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Talking Math: 100 Questions That Help Promote Mathematical Discourse

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By Gladis Kersaint - 100 questions from a mathematics expert to help promote mathematical thinking and discourse in the classroom.

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Lead in Literacy - Resources For Kindergarten, 1st & 2nd Grade

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Let’s Talk Math! Implementing Math Talk in the Classroom

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Math Talk discussions are an effective way for students to develop strong communication skills and deepen their understanding of mathematical content. Make sure to download the free math talk posters in the post! Hello Friend!

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Backwards Planning for School Year Success Part 3

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School year curriculum mapping and planning for school year success is an essential part of being organized and making your teacher life easier. Part 3

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How to Read the Next Generation Science Standards

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How to Read the Next Generation Science Standards

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NGSS Elementary School Science Classroom Activity

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NGSS Elementary School Science Classroom Activity

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

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The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

The progressions can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics. They would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks. Progressions documents also provide a transmission mechanism between mathematics education research and standards.

For more information on the project, please visit the project website.

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Progressions Documents for the Common Core State Standards for Mathematics

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The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

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6 Ways to Merge Math and Literacy - Article

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6 Ways to Merge Math and Literacy - Article

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When teachers find creative ways to integrate reading and writing with math curricula, it humanizes the subject matter and allows kids to process unfamiliar material linguistically.

Research has long linked strong reading skills with improved math achievement -which may seem obvious when it comes to typical math tasks like understanding directions on a test, or parsing word problems.

But literacy skills also support and deepen math understanding in unique and powerful ways.

"Reading and writing are complex, fundamental, integrative learning skills that should be used to their full potential in math class," writes Alessandra King, a middle school math teacher in Bethesda, Maryland. For all students, and especially those who "enjoy reading and writing more than the computational side of math," King says that finding ways to fold literacy into math class gives them "a deeper understanding and stronger appreciation of the usefulness and effectiveness of mathematics."

Blending the disciplines, when the lesson allows for it, also sets students up to "engage with math in a new-and often far more inviting-way," explains educator and tutor Chelsea Miro in an article about math read-alouds. "Kids who have struggled with geometry may love the opportunity to write a shape story, for instance-and it might even help them to remember that a square is a type of rectangle but a rectangle is not a type of square."

Here are six ideas, sourced from teachers and recent research, for merging math and literacy in ways that challenge students' abstract reasoning and build critical thinking and collaborative learning skills.

Explore Picture Books

Early-grade math problems tend to be straightforward and linear-much like the picture books that introduce them to literacy concepts. These shared properties make mathematical reasoning fertile ground for early-grade book authors.

But not all children's books that feature math are created equal. Just like in language arts classes, text selection is important, say educators Kathleen Crawford-McKinney and Asli Özgün-Koca. The trick is to find options that present a rich mathematical problem that students can work through alone or in groups, and then compare their answers to the solution in the book.

In one of their favorite examples, Molly Bang's When Sophie Thinks She Can't, main character Sophie is challenged to form as many different rectangles as possible using 12 tiles. It's a low-threshold, high-ceiling problem, offering a challenge for students across a range of skill levels. For some kids, a related exercise might involve creating their own rectangles using manipulatives and comparing solutions as a class; a more advanced exercise could involve asking them to create squares instead and discussing the differences between shapes.

When designing lessons around picture books, Crawford-McKinney and Özgün-Koca suggest creating content specific questions for students to answer, which will vary by book. But they also favor asking general questions about how math concepts shape the story and how the author establishes this understanding-which can teach students to think more like mathematicians.

For more book ideas, see former elementary school teacher Chelsea Miro's list of favorite books for math read-alouds, including more abstract titles like Kate Hosford's Infinity and Me.

Connect Thinking Through Math Journals

Teachers in subjects like English and science often use journals or logbooks to give students space to record their learning progress, make observations, and brainstorm solutions in a low-stakes format.

In math class, however, the journals might look a little different, explains former high school math teacher Nell McAnelly, who used them often with her students. "It is a record of personal experience showing what a student tried, what worked and what didn't, what practices should be continued, and what improvements a student should focus on going forward," she says. "Consequently, journals can promote initiative and confidence, which we know are gateways to learning."

There's still space for written reflections, but also for illustrations, diagrams and charts-making math journals more formal than scrap paper but less polished than an exam paper.

In her experience, students use them to make connections across mathematical ideas and delve into the reasoning behind their answers-much like they might use a journal to analyze a poem or text in language arts. Entries can also be used as discussion prompts for group work, where students can learn directly from one another as they explore new strategies.

Design Math Magazines That Relate to Real-World Topics

In Alessandra King's math classroom, while writing prompt activities are helpful, she prefers assignments that create strong connections between what students are learning in math class and the real world. "Reading and writing are particularly effective in developing a quantitative understanding of the world around us because they can be used to lead students to reflect on everyday experiences," King writes.

To harness the benefits of reading and writing, King has students create math magazines, collaborative publications that they compile with summaries they've written of math-related articles and images from publications like Scientific American, The Economist, the New York Times' Upshot section, and the Atlantic. It's one of her most popular assignments of the year.

King keeps a thick file of articles she's clipped or printed out that touch on math-related topics-from political gerrymandering to fractals in modern art and using machine learning to predict March Madness upsets-and lets students choose ones that pique their interest. They compose a page-long summary of the piece with special emphasis on the math concepts discussed and package their work with related charts or graphics.

At the end of the assignment, everyone's contributions are compiled into a magazine, and King uses a simple rubric to assess their content understanding, clarity of communication, editing, critical thinking, initiative, and creativity.

Identify and Teach Math Vocabulary

When fifth-grade math teacher Kathleen Palmieri discovered that only about 40 percent of her students could accurately define key math vocabulary (of various levels of complexity), she realized she needed to make learning math terms a regular part of her instruction, Palmieri writes in an article for MiddleWeb.

But rather than simply memorizing a list of words, she found that students needed to understand how the mathematical concept worked before the term itself would stick. In other words, if her students didn't know how fractions work, learning the definition probably wouldn't mean much. Additionally, math concepts typically make the most sense when learned in sequential order.

Drawing on ELA vocabulary building skills, Palmieri began asking students to pull out key terms they don't understand at the beginning of a unit for a math glossary that they add to as they learn each concept. Students also used colorful Post-its to create a math word wall that they add to as they learn new words-and can refer to at any time. Lastly, the class regularly decides on a word of the day or even a word of the week, with students responsible for tallying every time they see the word and describing how it's used.

Identify Patterns and Connections Via Word Sorts

Another strategy inspired by ELA instruction, word sorts can easily be adapted to math class to help students recognize patterns and relationships between words. Working alone or in groups, students identify each term in a given vocabulary list and sort terms into categories-either ones created by the teacher (known as closed sorts) or that they come up with themselves (open sorts).

Word sorts can be implemented using mathematical terms, symbols, or even expressions. Students can sort these based on various attributes-say, operation type (addition, subtraction, multiplication, division), geometric shapes (circle, triangle, square), or algebraic properties (commutative, associative, distributive).

To sort a list of mathematical expressions, kids might separate them based on whether they involve addition, multiplication, or both (e.g., the expression 5𝑥+ 3).

Younger students might perform a similar sort by placing the word "rhombus" into multiple categories, including parallelogram, quadrilateral, and two-dimensional, write Miranda L. Sigmon, Kavin Ming, and Daniel Herring-the authors of a 2022 piece on word sorts for the journal Mathematical Teacher.

To drive meaning home, the authors suggest using sentence stems, such as "I think (insert term) goes under the (category name) category because . . ." -which gets students thinking more about the choices they're making. Model a few examples yourself and split students into small groups to encourage genuine discussion and comprehension.

Encourage Collaboration With Math Circles

Inspired by literature circles, a common practice in ELA, history, and occasionally even science classes, math circles involve assigning roles to students that they perform as part of collaborative work in small groups. The goal is to foster math-related group learning, discussion, and advanced collaboration skills like leadership and flexible thinking.

In Patricia Kridler's middle school math classroom, student roles include Situation Summarizer, Vocabulary Master, Idea Guy/Gal, Model Maker, and Computation Kid, Kridler writes in the journal Mathematics Teaching in the Middle School. Since math topics can vary greatly, she often creates new roles depending on the assignment, and asks groups to complete a role worksheet that includes space for every student to share their contributions. After every cycle, she asks students to swap roles.

At first, she assigns simple word problems and lets students take turns in their roles before moving to more complicated or abstract projects that could take several class periods to complete. Typically, students use the role sheets to explain their thinking and their mathematical reasoning in depth, and the Situation Summarizer presents the findings to the entire class.

Math circles allow Kridler to structure a math task "so that all students get to focus on different aspects of how to solve a problem," she writes. "Students also develop the skills necessary to become better independent thinkers. In the process, I am learning much about how students think through problems."

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6 Ways to Merge Literacy With Mathematics

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When teachers find creative ways to integrate reading and writing with math curricula, it humanizes the subject matter and allows kids to process unfamiliar material linguistically.

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Toy Theater is your source for free educational games specially designed for elementary-aged students. It's available on all desktop computers, tablets, and mobile devices, ensuring learning is never out of reach. If you are a fan of our site, we encourage you to share Toy Theater on your social media or website.

Explore Toy Theater

Here's a sneak peek into what Toy Theater has in store:

Math Games: Ranging from counting and numeral recognition to division and telling time, there's a vast assortment of interactive math games.

Language Arts: Students can work on spelling, letter recognition, and even practice reading with online books.

Art and Music : From teaching students to play simple songs on a keyboard to exploring symmetry via art games, the platform fosters creativity alongside learning.

Puzzles and Games: Ideal for early finishers or indoor recess, their online educational puzzles and games promise fun-filled learning.

Teacher Tools: Need a fun timer or a spinner? Or perhaps a simple way to evaluate basic math skills? Their virtual teacher tools have got you covered.

Whether you project Toy Theater games and interactive tools on your smartboard for the whole class to see or use them during small group work, you're sure to love them!

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Toy Theater | Fun Online Educational Games for Kids

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Make learning a blast! Toy Theater is chock full of interactive online art, reading & math games for kids. Designed with the needs of kindergarten through third grade classrooms in mind, these free games are trusted by teachers around the world to provide real educational value.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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Practice addition, multiplication, fractions and algebraic reasoning with our popular math games. Discover fun learning games kids love to play.

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Solve problems and explain your thinking in a digital math workspace.

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A beautiful, free online scientific calculator with advanced features for evaluating percentages, fractions, exponential functions, logarithms, trigonometry, statistics, and more.

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Before, During, After. Three Phase Lesson Structure 

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Before, During, After. Three Phase Lesson Structure 

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NGSS Standards

On September 4, 2013, the SBE adopted the Next Generation Science Standards for California Public Schools, Kindergarten through Grade Twelve (CA NGSS) as required by California Education Code 60605.85. The NGSS Appendices A-M were also adopted to assist teachers in the implementation of the new science standards and to aid in the development of the new science curriculum framework.

The SBE-adopted California Next Generation Science Standards (CA NGSS) can be viewed below by grade level Disciplinary Core Ideas (DCI): Life Sciences, Earth and Space Sciences, and Physical Sciences or by grade level Topic (e.g., Chemical Reactions, Structure and Function, or Space Systems).

For information on how to read the standards and implement the standards, please read How to Read CA NGSS (PDF) or consult the 2016 Science Framework or visit the Adopting and Implementing NGSS page. For questions about the CA NGSS and 2016 Science Framework, contact the Curriculum Frameworks and Instructional Resources Division (CFIRD) at cfird@cde.ca.gov or 916-319-0881.

Kindergarten through Grade Five Standards

Standards Arranged by Disciplinary Core Ideas (Life, Earth and Space, and Physical Science)

Grades Six through Eight Standards

On November 6, 2013, the SBE approved the Science Expert Panel's (SEP) recommended Integrated Learning Progression model as the preferred model for middle grades six through eight. At the same November meeting, the SBE approved a recommendation by the SSPI to reconvene the SEP in order "to develop ... as an alternative model ... a discipline specific model" for the grade span of six through eight based on Achieve's domains model in Appendix K.

In December 2013, the SEP reconvened to develop an alternative domain specific course model.

The documents below provide middle school educators the rationale for the CA NGSS Integrated Learning Progression Course for middle grades six through eight and the Alternative Discipline Specific Course for grades six through eight. The documents also describe learning progressions for each grade level.

Integrated Learning Progression Model (PDF)
This document provides middle school educators the rationale for the Integrated Learning Progression Course arrangement of standards developed by the California Science Expert Panel. Documents containing the standards for each grade level are below.

Discipline Specific Model (PDF)
This document provides middle school educators the rationale for the Discipline Specific Course arrangement. Documents containing the standards for each grade level are below.

Integrated Model Standards Arranged by Disciplinary Core Ideas

Discipline Specific Model Standards

Grades Nine through Twelve Standards

Standards Arranged by Disciplinary Core Ideas (Life, Earth and Space, and Physical Science)

NGSS Appendices A-M

The NGSS Appendices A-M were adopted to assist teachers in the implementation of NGSS and in the development of the new science curriculum framework.

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

Last Reviewed: Wednesday, June 12, 2024

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NGSS for California Public Schools, K-12

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In 2013, the State Board of Education (SBE) adopted the Next Generation Science Standards for California Public Schools, Kindergarten through Grade Twelve.

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CALIFORNIA STANDARDS FOR THE TEACHING PROFESSION (CSTP)

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CALIFORNIA STANDARDS FOR THE TEACHING PROFESSION (CSTP)

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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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Common Core State Standards for Mathematics

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Common Core State Standards for Mathematics

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California Common Core State Standards for Mathematics
Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

1. Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.Students build proofs by induction and proofs by contradiction. CA 3.1 (for higher mathematics only).

4. Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x^2 + x + 1), and (x - 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word "understand" are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.

In this respect, those content standards which set an expectation of understanding are potential "points of intersection" between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.

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

Last Reviewed: Tuesday, July 25, 2023

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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

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Science Content Standards for California Public Schools

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Science Content Standards for California Public Schools

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Scientific and Engineering Practices SEP

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Scientific and Engineering Practices SEP

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An inquiry-focused method gives students a way to connect scientific ideas to their experiences and apply their learning.

Try to recall the last science class you taught. It probably had many components over the course of 50 minutes, such as a video, a mini-lecture, an assessment, discussion, or a demonstration. What were all the components? Did your students discuss a question in small groups? Was it a whole-class discussion? Did you introduce a new concept? In what order did you introduce these components? How did you decide what came first? What is the optimal order of activities in an inquiry-based science classroom?

Engage Students' Curiosity

Teaching science using an inquiry approach requires instructional planning that encourages students to engage their curiosity to ask questions, explore solutions to socio-scientific issues, use evidence-based explanations to justify their reasoning, elaborate on possible effects, evaluate their findings, and predict potential outcomes based on different variables. In inquiry science, students are cognitively challenged as they engage in authentic problems while learning content, practicing reasoning skills, and communicating their ideas.

One approach to inquiry science is the 5E instructional model (Engage, Explore, Explain, Elaborate, Evaluate). The 5E model is a planning tool for inquiry teaching that provides a structure for students to connect science ideas with their experiences and apply their learning to new contexts. The 5E model comprises five phases that help teachers build a sequence of coherent and engaging learning experiences for students.

How the 5E Model Works

1. Engage. The teacher uses short activities to promote curiosity. The activity must connect prior knowledge to new learning experiences in order to expose any misconceptions and prepare students for new learning.

Novel questions, discrepant events, demonstrations, or a powerful visual are ideal ways to engage students and ascertain their prior knowledge or any misconceptions that might interfere with constructing new knowledge. For new concepts to become meaningful, students use their prior knowledge to connect their past and present learning experiences.The engagement phase doesn't have to be part of the class time. It can be structured as a homework assignment where students can read an article related to the new topic to be introduced, explore a website, watch a video, or answer a question related to their prior knowledge.

For example: Why are acidic drinks stored in a cold place?

2. Explore. A lab investigation or hands-on activities are usually introduced in this phase as students attempt to investigate a problem. Conflicting ideas, questions, and confusion are common and help students identify what they need to know before new terms or concepts are introduced in the Explain phase.

What is the problem I am trying to solve?

What do I need to find out?

What do I know already?

Students are provided with two identical soda cans, a bottle opener, hot water, and an ice bath. Students perform the activity in pairs or groups, write down their observations, and discuss their results in the group.
Encourage students to think of the following questions:

For example: Which soda, the warm or the cold one, had more dissolved carbon dioxide? List all the ways that you know.

3. Explain. With the teacher's guidance, students explain the concepts they explored in the previous phase and demonstrate their understanding of the new terms that were introduced. Depending on the topic and the grade level, teacher-led instruction might be necessary to address any confusion and questions that came up in the Explore phase. Questions can make learning more meaningful, interactive, and participatory.

Students provide a tentative explanation as they present their results to the whole class. The teacher may pose additional questions to support the discussion. It is recommended that the teacher introduce a formative assessment in this phase to identify if the students are ready to start the Elaborate phase and determine if additional instruction or assistance is needed.

For example: What is the best way to store an opened bottle of soda so that it doesn't go flat quickly?

4. Elaborate. Students apply their knowledge to new experiences and extend their conceptual understanding as they solve a problem in a new context before evaluation in the last phase of the 5E model. Elaboration activities can take place during classroom time, or they can be a homework assignment.

For example: Decompression sickness (DCS) occurs when divers swim to the surface too quickly (rapid ascent). What causes DCS to occur?

5. Evaluate. Students evaluate their learning and demonstrate their understanding and mastery of key concepts. Evaluation doesn't have to be limited to a quiz or test. It can be a product such as a presentation, a poster, a pamphlet, a journal article, or a final paper.
Many power plants condense steam by pumping cool river or lake water around the steam pipes. The steam cools and condenses as its heat is transferred to the water, which is then returned to the river or lake. What impact does this warm water have on the fish in the lake or river?
For example: In your opinion, why do fish wash ashore on hot summer days?

You may already be using these elements without being familiar with the 5E model's formal structure. Consider the phases discussed above and reflect on the activities you planned for the last science lesson you taught. Which component would you classify as an Engage activity? Explore? Explain? How well does the order you have planned reflect the 5E model?

The goal isn't to plan every science lesson according to the 5E model-it's to consider the order and sequence of activities to align with the model to maximize student learning.

Here are some final suggestions:

Start small. You might design a lesson with only two components of the 5E model. If your lesson already has a hands-on activity, you may want to start with Engage to get the students thinking about the hands-on activity they're going to complete in the Explore phase. A simple 3- to 5-minute activity such as a current events story, a video, an advertisement, a problem scenario, or a challenge statement based on a common misconception can engage students.

Explore before Explain. Lab investigations or hands-on activities in the Explore phase, no matter how simple, may be time-consuming. Yet, you can allow at least some exploration before explanation to prepare students to receive new information. They might attempt to solve a problem, make a prediction about an experiment or demonstration, or answer a complex question. Consider starting instruction (Explain) in the middle of the class session, as opposed to the beginning, after students have had time to do some exploration.

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How to Use the 5E Model in Your Science Classroom

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An inquiry-focused method gives students a way to connect scientific ideas to their experiences and apply their learning.

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Identifying and Addressing Student Errors

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Identifying and Addressing Student Errors

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How do you identify students' strengths and areas of growth in math? How do you meet this big range of needs? Having a math diagnostic assessment that's easy to use AND provides data that's easy to understand is key. You'll also want the information to be transferred into clear, actionable steps.

In this post, I'll go through a free math diagnostic assessment I offer. I'll explain how to use it, the different components, and most importantly, what to do with the information once you're done.

What Is A Math Diagnostic Assessment?

A math diagnostic assessment is used to "diagnose" or identify the strengths and areas of growth of students in your classroom. The assessment should help you determine exactly what math skills students are proficient in. Then, based on each student's results, you can identify math skills students already know, as well as skill gaps.

This is incredibly valuable because the results will give you the exact next steps to help kids move ahead in math!

This free math diagnostic includes an assessment for Kindergarten, 1st grade, and 2nd grade.
Here are the broader categories covered in the Kindergarten, 1st grade, and 2nd grade assessments:

Operations & Algebraic Thinking

Number & Operations in Base Ten

Measurement & Data

Geometry

**Kindergarten also covers the category of "Counting & Cardinality."

For every section, there are teacher directions so that you can plan accordingly:

Then, of course, there are materials for students to complete as they are being assessed! Here are some examples from the Kindergarten, 1st grade, and 2nd grade assessments:

Many of the components can be given in a large or small group setting (such as circling which group of items has more/less), whereas some components should be administered in a one-on-one setting so that you can get accurate data for individuals.

Collecting Data

There are a variety of ways you could use this free resource. Use the math diagnostic assessment:

as a pretest to see what skills students have before teaching a unit

as a summative assessment at the end of a unit

at the end of the school year to see what skills students have mastered or are still developing

at the beginning of the year to see which skills students have mastered/need support with for the upcoming school year **(For this option - if you are a 1st grade teacher, for example, you'd probably want to use the Kindergarten assessment to get an accurate picture of what students have already mastered, since students wouldn't have been taught the 1st grade skills yet.)

This resource has options for teachers to mark students' answers on either a single assessment scoring sheet or a multi-student assessment scoring sheet. See examples of each here:

Some teachers prefer one or the other. Some even like to start with the single and then transfer to the multiple, so I wanted to offer both options!

You've Completed The Diagnostic - Now What?

After completing the math assessment for your student(s), you'll have lots of information at your fingertips! You'll see things that students were able to do, but also most likely skills that students aren't familiar with.

We can look at this data through a waterfall analogy. We can start big picture, trickle down to group trends, and then end with individual takeaways. Here's a list of questions you should ask yourself (and write down answers to) when reflecting on the data:

What are some strengths our class has as a whole? (at least 2/3 of the class was able to do)

What are some areas of growth our class has as a whole (at least 2/3 of the class wasn't able to do)

Are there certain skills that a group of students is really advanced in? (i.e. five Kindergarten students were able to compose teen numbers)

Are there certain skills that a group of students had trouble with? (i.e. six 1st grade students weren't able to count a group of objects up to 10)

Are there individual students who are advanced in particular skills? (i.e. one Kindergarten student could add/subtract two digit numbers)

Are there individual students who are fairly behind in certain areas? (i.e. one 2nd grade student who can't identify 2-D shapes)

Answers to these questions will help you determine which type of instruction you should do in whole group, small group, and 1:1.

If a majority of your class is at (more or less) the same starting point, you'll be able to do a lot of your instruction whole group. This will help maximize the instructional time your students are getting to cover the same skills.

However, if your class has a pretty wide variety of skill levels, you'll most likely want to be doing a lot of (but not necessarily all of) your math instruction in a small group setting. This will allow you to tailor each small group lesson around a different skill that matches the ability level of the group.

If you're seeing some individual outliers (high and low), you'll want to make notes of how you can incorporate this one-on-one instruction throughout the day/week. Maybe you can provide differentiated materials to this student during math time. If you have an aide, they can pull the student to work on the specific skills.

Materials To Use For Instruction

Trying to find or create materials for a vast array of abilities can be difficult and time-consuming! That's why I developed my Math Library. The categories covered in the Math Library mimic the skills addressed in the math diagnostic. Each Math Library is organized into different categories (like "Addition and Subtraction") for easy downloading.

There are tons of different types of resources in each of the Kindergarten, 1st grade, and 2nd grade libraries- worksheets, games, hands-on materials, Google slides, etc! New activities are added each month, and you'll receive an email letting you know that fresh materials are ready for you!

Conclusion

Having a math assessment will provide you with the necessary tools to identify student strengths and areas of growth. Click here to get access to my FREE math diagnostic assessment!

Happy teaching!

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Use This Math Diagnostic Assessment to Identify Strengths and Areas of Growth - Learning at the Primary Pond

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Having a math diagnostic assessment that's easy to use AND provides data that's easy to understand is key. In this post, I'll go through a free math diagnostic assessment to identify student strengths and areas of growth.

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This article discusses different math formative assessment examples to inform both your teaching and your students’ learning.

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Page 1: Formative Assessment

Whether we are conscious of it or not, mathematics is key to many of our most common daily activities and routines. When we shop, cook meals, balance our finances, or conduct home repairs, we are using mathematics. Further, a growing number of jobs in STEM-related fields (science, technology, engineering, and mathematics) require proficiency in math and science. If they are to be college- and career-ready, today's students must begin to develop essential math skills and understand mathematic concepts at an early age. Educators can help them to do so by implementing high-quality mathematics instruction.

Although perhaps not immediately intuitive, assessment is an integral part of this instruction. In general, assessment is the process of gathering information through methods both formal and informal to measure student performance. Used effectively, classroom assessment informs the ways in which teachers approach and deliver instruction. Though some teachers are concerned that assessments will take time away from instructional activities, in fact the opposite is the case. Classroom assessment can help teachers plan instruction that more efficiently and effectively targets specific student needs, subsequently improving learning outcomes. The table below outlines the three most common types of assessment.

Diagnostic assessment*

Often referred to as pre-assessment, it can be used by teachers before instruction to:

Assess students' current level of knowledge and skills

Identify misperceptions

Plan whole-class instruction

Essays

Work samples

Informal mathematics assessments

Formative assessment

This ongoing evaluation of student learning during instruction can be used to:

Provide continuous feedback about performance to both learners and instructors

Inform or guide instruction

Exit tickets

Pop quizzes

Informal teacher questioning

Progress monitoring measures

Exit ticket
A tool for assessing student understanding of a topic or skill introduced in class; sometimes referred to as an exit card.

Summative assessment

This evaluation administered after instruction is used to:

Measure student mastery of content or skills

Year-end standardized tests

Unit tests

Research papers

* This type of diagnostic assessment is not to be confused with individualized diagnostic assessment implemented after instruction with struggling learners or students with disabilities. This diagnostic assessment is used to understand why these students are not making adequate progress in certain skills and to subsequently inform the teacher's instruction.

Did You Know?

Federal laws, such as the Every Student Succeeds Act (ESSA) and the Individuals with Disabilities Education Act (IDEA), encourage the use of formative assessment to improve student outcomes and to narrow learning gaps.
Every Student Succeeds Act (ESSA)
Each of the assessments described above serves an important, albeit a very different, function in the instructional process. Read on to learn more.

Diagnostic assessments allow teachers to collect information about a student's strengths or weaknesses in a content or skill area prior to instruction. Teachers can then use this information to more effectively plan instruction, making sure to address misunderstandings and to focus on skills or content the students have not mastered while avoiding covering topics with which they have already gained proficiency.

Summative assessments, which are usually one-time evaluations, allow teachers to evaluate whether students have learned previously taught content or skills. On one end of the spectrum are common classroom assessments typically used for grading purposes (e.g., chapter tests, unit tests, research papers). At the other end of the spectrum are year-end achievement tests, which are given once a year, near the end of the school year. Although the results are usually not available for many weeks or months following administration, they provide an indication of a student's overall progress for the year. As is typically the case for any type of summative assessment, teachers do not have enough remaining time to implement instructional changes to remediate skills if they find that students did not perform well.

Formative assessments, which occur during instruction, allow teachers to determine whether students are learning as the material is being taught. This deliberate process of assessing as learning is occurring allows teachers to adjust instruction as needed to meet the learning needs of their students. More specifically, formative assessment:

Provides useful information about a student's progress toward certain learning objectives, her understanding of the skills or content being taught, and any misconceptions she may have

Allows teachers to make informed decisions about when to review or reteach content or skills or to adapt instruction

Helps identify students who are consistently struggling

As you learned in the Challenge, Ms. Wu is interested in using assessments-like she did in reading-to inform her instruction in mathematics and to help identify students who need additional support. This module will focus on formative assessment, something that will help Ms. Wu to accomplish her goal.

Research Shows

Formative assessment has been proven effective through many years of research and practical application.

Seminal research and subsequent reviews of research indicate that students whose teachers use formative assessment perform better on a variety of achievement indicators (including mathematics) than their peers whose teachers did not.
(Klute, Apthorp, Harlacher, & Reale, 2017; Hanover Research, 2014; Black & Wiliam, 1998; Kingston & Nash, 2011)

Formative assessment has been shown to improve the learning outcomes of students with disabilities, struggling students, and English learners.
(Madison-Harris & Muoneke, 2012)

Feedback to teachers via formative assessment had a significant impact on students' academic performance in mathematics.
(Gersten, Chard, Jayanthi, Baker, Morphy, & Flojo, 2009)

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Whether we are conscious of it or not, mathematics is key to many of our most common daily activities and routines. When we shop, cook meals, balance our finances, or conduct home repairs, we are using mathematics. Further, a growing number of jobs in STEM-related fields (science, technology, engineering, and mathematics) require proficiency in math and science.

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The Cycle of Formative Assessment Benefits

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The Cycle of Formative Assessment Benefits

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Digital Engineering & Technology | Elearning Solutions | Digital Content Solutions

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The Role of Data Analytics & Formative Assessments in Shaping the Future of Higher Education

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Formative assessment transforms higher education with real-time feedback and insights, enhancing learning outcomes and shaping the future.

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SplashLearn Blog - Educational Resources for Parents, Teachers & Kids

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difference between summative assessment & formative assessment

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What Makes Summative Assessment a Powerful Tool for Teachers

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Read to know all about summative assessment - examples, benefits, limitations, etc. Also, know the differences between formative & summative assessments.