# data[].attributes.attachment_link.readable_text
This printable pre-assessment assesses key second grade skills in the four domains of the Math Common Core State Standards: Operations & Algebraic Thinking, Number & Operations in Base Ten, Measurement & Data, and Geometry. It has a total of 30 questions. This assessment can also be used at the end of the year with second graders as a summative assessment.

It is designed to help teachers determine how much incoming third graders remember second grade math standards at the beginning of the year. I know most teachers receive state test scores before the school year starts, but I find that many students fall victim to the "summer slide" and forget much of what they had learned the previous year.

Therefore, I give this pre-test the very first week of school before I start math instruction, so I can gauge where my students are. From the results, I can create math groups, know my students' strengths and weaknesses, and better adjust my instruction to meet the needs of my students. It is also great data to show parents during conferences.

It assesses key second grade math skills and concepts that can give you data on students' readiness for third grade math. A data sheet is also included, so teachers can record the students' scores. An answer key is also included.

If you teach multiple grades, you can also purchase this pre-assessment as part of a bundle:

⭐ Math Pre-Assessment Bundle

If you're looking for the DIGITAL VERSION of this assessment, click below:
3rd Grade Math Pre-Assessment Digital Version
Here is the breakdown of the test:
Operations & Algebraic Thinking (7 points)

Solve two-step word problems within 100

Fluently add and subtract within 20 using mental strategies

Determine whether a group of objects (up to 20) is odd or even

Find the total number of objects arranged in rectangular arrays and write an equation to express the total

Number & Operations in Base Ten (12 points)

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones

Skip-count by 5s

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form

Compare two three-digit whole numbers

Fluently add and subtract within 1000

Add up to four two-digit numbers

Mentally add 10 or 100 to a given number 100-900

Measurement & Data (7 points)

Select an appropriate tool for measuring the length of an object

Estimate lengths using units of inches, feet, centimeters, and meters

Solve word problems involving lengths

Write and tell time from an analog clock

Solve word problems involving money

Solve word problems using a picture graph

Geometry (4 points)

Identify shapes based on number of angles and sides

Identify polygons

Describe rectangles partitioned into equal shares

If you like this resource, please check out my other products:
⭐ Math Resources

⭐ Math Puzzle Matching Games

⭐ 4th & 5th Grade Task Cards

Click HERE to follow my store!

Purchasing this resource gives you the license to use in YOUR CLASSROOM only. If you want to share with other teachers, please purchase additional licenses upon checkout or after purchasing. Multiple licenses are offered at a discount for your convenience. Because I spend countless hours creating resources, I simply ask that you respect the time and effort that I put into them.

Don't forget to LEAVE FEEDBACK, which earns you credit toward future TpT purchases. Thank you!

# data[].attributes.attachment_link.title
Beginning of Year 3rd Grade Diagnostic Math Pre-Assessment Pretest

# data[].attributes.attachment_link.description
This printable pre-assessment assesses key second grade skills in the four domains of the Math Common Core State Standards: Operations & Algebraic Thinking, Number & Operations in Base Ten, Measurement & Data, and Geometry. It has a total of 30 questions. This assessment can also be used...

# data[].attributes.attachment_link.readable_text
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!

# data[].attributes.attachment_link.title
10 Math Center Organization Tips to Save You Hours of Prep Work! - Teaching with Jillian Starr

# data[].attributes.attachment_link.description
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 [...]

# data[].attributes.attachment_link.readable_text
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

(Visited 1 times, 85 visits today)

# data[].attributes.attachment_link.title
Math Manipulatives Every Classroom Should Have

# data[].attributes.attachment_link.description
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.

# data[].attributes.attachment_link.title
EDU 505 Math Assessment Commentary Assignment

# data[].attributes.attachment_link.title
Common Core Instruction: Exploring Dividing Decimals to the Hundredths

# data[].attributes.attachment_link.title
The 8 Standards for Mathematical Practice

# data[].attributes.attachment_link.title
Time for Class - Mr. Adler Science Lesson

# data[].attributes.attachment_link.description
The Coherence Map shows the connections between Common Core State Standards for Mathematics.

# data[].attributes.attachment_link.readable_text
Did you know that not all vocabulary words are created equally? This is especially true when it comes to classroom instruction. The type of words we focus on can make a big impact on students' vocabulary progress. Within this blog post, we'll chat about the three tiers of vocabulary. We'll also discuss what each vocabulary tier consists of, examples of words for each tier, and how we can use this information as teachers. Let's get started!

What are the Three Tiers of Vocabulary?

For instructional purposes, vocabulary words are sorted into three tiers: Tier 1, Tier 2, and Tier 3. The illustration below shows the three tiers of vocabulary. As you can see, we move from Tier 1 on the bottom of the triangle up to Tier 3 at the top of the triangle.

What is the difference between each vocabulary tier? The image below gives a quick, concise explanation of each tier. I will break down each tier for you and give examples of words for each tier.

As you can see in the image above, each tier consists of a very different type of word list. Let's break down each vocabulary tier and discuss what it means for us as classroom teachers and the focus for our instruction.

Tier 1 Vocabulary

Tier 1 vocabulary words consist of basic, familiar words. These words are commonly used by most students in everyday conversation. Students have the highest exposure with Tier 1 words. In fact, children are exposed to Tier 1 words from an early age, and as a result, they become easily familiar with this set of words. Perhaps the easiest way to think about Tier 1 words is to remember that the words are often used in oral conversations and familiar in speech. Examples of Tier 1 words are shown in the image below.

Tier 1 word examples in the image above include: sad, walk, elephant, baby, red, bus, clock, phone, and rain. Tier 1 vocabulary words are words students come to school knowing and using the most. In fact, Beck, McKeown, and Kucan explain in their book, Bringing Words to Life, that students are likely able to learn Tier 1 words naturally and independently!

Tier 2 Vocabulary

Tier 2 vocabulary words are robust, high-frequency words that students encounter across the content areas. They are not widely used in speech and daily conversation. Unlike Tier 1 words, Tier 2 words are not usually learned naturally or independently because students do not hear or use them in conversation. A key point to understand is that Tier 2 words are often used and found in books and written text. Tier 2 vocabulary words often have multiple meanings. This tier can also be referred to as academic vocabulary words. Examples of Tier 2 vocabulary words are listed in the image below.

Examples of Tier 2 vocabulary words are bolt, fine, amiable, rare, harmony, blush, astute, and valuable. As you can see, these words have multiple meanings and are not typically used in everyday, causal conversation. However, it is Tier 2 words that students will encounter frequently in written texts. Tier 2 words will have an important impact on your students' comprehension skills.
(Pssst! Guess what?! If you use any of my Vocabulary Curriculum Sets already in your kindergarten, first grade, or second grade classroom, you are already a ROCKSTAR at explicitly teaching Tier 2 words! Go you!)
Tier 3 Vocabulary

Tier 3 vocabulary words are low-frequency words. These words are content specific and have distinct meanings and purposes. Examples of Tier 3 words are listed in the image below.

Tier 3 words like pterodactyl, aorta, thesis, isosceles, osmosis, electrolyte, photosynthesis, and igneous are not words we often use in everyday conversations. These words have a distinct purpose and we use them only when they relate to a specific topic or domain. When we use a Tier 3 word, there is a specific reason to do so, such as when we are learning about plants in a science unit or triangles during math class.

Which Tier Should We Focus Instruction On?

Let's recap what we learned about the three tiers of vocabulary. We learned that Tier 1 vocabulary words are words students come to school knowing and using the most. Therefore, as teachers, we naturally do not (and should not) spend the bulk of our time explicitly teaching the meanings of Tier 1 words. Remember, most students can naturally and independently learn Tier 1 words. For example, if the word "dinosaur" is part of your district's reading curriculum, I think it's safe to say that most first graders have heard of the word dinosaur before. They know what a dinosaur is and what it looks like! A quick review or picture card would probably be all they need to remind them of what a dinosaur is. Spending a week on the word dinosaur is not an effective use of instructional time!

Students will need to know Tier 3 words, however, Tier 3 words will not make up the bulk of the words they encounter in written text. For example, if your students are reading a chapter series, the frequency of the word "mitosis" in each book is going to be really low! Furthermore, Tier 3 words typically do not have synonyms and antonyms, so learning the definition to a Tier 3 word is usually pretty "cut and dry". Students only need to learn Tier 3 words when a specific need is present.

So, did a lightbulb go off for you yet?! Do you know which vocabulary tier we want to spent the most time on each week? If you answered Tier 2, you are correct!

As teachers, we will get the most "bang for our buck" if we spend the bulk of our vocabulary instruction on Tier 2 words. These are words that are found and used across variety of topics, domains, areas, and content. Since MANY Tier 2 words have multiple meanings, they are more difficult to learn because students need to understand the word within multiple contexts, as well as understand the connection between the words' synonyms and antonyms.

Having a robust vocabulary and knowledge of Tier 2 words directly impacts our students' reading comprehension skills.

Ways To Focus on Tier 2 Vocabulary

Now that we know the importance of Tier 2 vocabulary words, let's chat about ways to incorporate these words into our daily routine! Several years ago, I created an engaging and easy-to-follow vocabulary routine for kindergarten, first-grade, and second-grade teachers! I often get asked, "Where did the words in each set come from?" The words I chose for my curriculum are Tier 2 words that often have multiple meanings and can be seen in written text, across multiple contents, topics, and domains! Sounds pretty spot-on to what we just learned about in this post, right?! Take a look at some of the word lists below. These Tier 2 words are words that students will not typically learn independently. It's important we have a routine and a plan for explicitly teaching Tier 2 vocabulary in our classrooms.

Synonyms and Shades of Meaning

We can expose students to multiple Tier 2 words by spending time on the synonyms and antonyms for Tier 2 words. When we teach our students even three to five Tier 2 words, we can actually expose them to up to TWENTY Tier 2 words throughout the week by discussing the synonyms associated with these words, and their shades of meaning. The image below shows you an easy routine for teaching and exposing your students to a variety of Tier 2 words:

Multiple Meanings and Multiple Contexts

As we learned in this post, many Tier 2 words have multiple meanings. It's important to explicitly point out these multiple meanings and help students understand how they are used in various contexts. Each week's vocabulary lessons in my curriculum includes a passage AND a read aloud! The read aloud (often presented on Day 2 each week) uses the Tier 2 words in a different context than the passage on Day 1. Exposing our students to various contexts and situations helps them to better understand the word and see it used in various ways! ( Bonus: Each read aloud comes in a printable version AND a digital version!)

Tier 2 Vocabulary Word Play

Pointing Tier 2 words out in the books you read and allowing students to "play" with words is also an important part of vocabulary instruction. We want our students to have a lot of opportunities for word play and practice using the words in their daily discussions. Examples of word play games include:

One of the best parts of my vocabulary sets are the included word play games for each week's Tier 2 words! You can see the table of contents in image above, and a page out of the word play section called Sing-Along Antonyms! Each word play activity has a teacher direction page and if required, the printable materials that are needed. You can read more about Vocabulary Word Play ideas in another blog post I wrote by clicking HERE.

Learn More About Vocabulary Instruction

That was ALOT of information on the three tiers of vocabulary, and some various activities and ideas for teaching Tier 2 words within your classroom! If you'd like to learn more about my simple, already-done-for-you vocabulary routine click HERE to check out my vocabulary curriculum blog post! In this post, I go into depth on even more vocabulary research and why it is so important to have an explicit plan in place for your vocabulary instruction.

You can check out my vocabulary curriculum bundles by clicking on your grade level below. The vocabulary bundles are also sold as individual sets, too!

If you'd like to refer back to this post, or share it with a colleague, feel free to pin the image below to your Pinterest page! Thank you so much for hanging out with me and learning about the three tiers of vocabulary and how they impact our classroom instruction. Don't forget to make sure you are following me on Instagram @missdecarbo for weekly tips, ideas, activities, resources, and freebies!

# data[].attributes.attachment_link.title
The 3 Tiers of Vocabulary for Classroom Instruction - Miss DeCarbo

# data[].attributes.attachment_link.description
Learn about the 3 tiers of vocabulary for the classroom and lesson planning. Discover how to choose your vocabulary words, and which ones matter!

# data[].attributes.attachment_link.title
Bloom’s Taxonomy _ Center for Teaching _ Vanderbilt University.pdf

# data[].attributes.attachment_link.description
Bloom’s Taxonomy _ Center for Teaching _ Vanderbilt University.pdf - Download as a PDF or view online for free

# data[].attributes.attachment_link.title
Bloom’s Taxonomy - Center for Instructional Technology and Training - University of Florida

# data[].attributes.attachment_link.description
The original Taxonomy of Educational Objectives, commonly referred to as Bloom’s Taxonomy, was created by Benjamin Bloom in 1956, and later revised in 2001. Bloom categorized and classified the cognitive domain of learning into varying levels according to complexity and richness. As you travel up th…

# data[].attributes.attachment_link.title
Math Talk Mathematical Discourse Sentence Stem Posters by Trisha Blalack

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Science Sentence Stem Cards: Accountable Talk by Gifted Teacher 305

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.readable_text
The DoK Levels added to questions will be reflected in reports. Teachers can easily track and show growth of students understanding in an individual assignment from start to end.

What do individual DoK Levels help you assess?

Level 1: Recall - Focus here is on specific facts, information, details, and procedures e.g specific definitions, details, applies simple steps.

Level 2: Skills and Concepts - Processing of conceptual knowledge, comparing and contrasting, extracting main points, interpreting facts etc. More content knowledge required here than Level 1. Actions require more than one step.

Level 3: Strategic Thinking - Focus is on reasoning based on deep knowledge: which include understanding and rationalizing thoughts, manifesting them into achievable steps. E.g Drawing conclusions from Examples, citing evidence to support a logical argument, concept based explanations.

Level 4: Extended Thinking - Focus is on applying complex reasoning, experimental design, and planning over an extended period of time. It requires extended investigation (research) and time to process information and problem solving. Students are required to make multiple connections, relate ideas to specific content area(s), and select an approach from among many as a solution.

Download the PDF Depth of Knowledge Question Stems.

To learn more about the DoK framework, you can refer to Brenda Matthews' presentation:
Brenda Mathew's DoK framework
Add Depth of Knowledge Levels:

STEP 1: Select "Options" then "Add DoK"

STEP 2: Select the DoK Level you want

View a student's proficiency by DoK Level in your Student Reports [Team Plan]

This will give you real-time metrics on how your students are engaging with texts and how they are performing by DoK Levels.

# data[].attributes.attachment_link.description
The DoK Levels added to questions will be reflected in reports. Teachers can easily track and show growth of students understanding in an individual assignment from start to end. What do individual DoK Levels help you assess? Level 1: Recall - Focus here is on specific facts, information, details, and procedures e.g specific definitions, details, applies simple steps.

# data[].attributes.attachment_link.readable_text
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

# data[].attributes.attachment_link.title
Talking Math: 100 Questions That Help Promote Mathematical Discourse

# data[].attributes.attachment_link.description
By Gladis Kersaint - 100 questions from a mathematics expert to help promote mathematical thinking and discourse in the classroom.

# data[].attributes.attachment_link.readable_text
Children's books often contain valuable lessons that can help young students begin to think like mathematicians.

monkeybusinessimages / iStock

Many students and teachers view math as a subject for numbers and computation, instead of one that benefits from discussion and interpretation. Based on our experience as children's literature and mathematics teacher-educators, we've found that providing the context to mathematical problems through literature supports students' learning-children's books can be used to integrate math and literacy and to provide context for math.

For example, the books When Sophie Thinks She Can't, a story about a little girl who discovers the importance of struggle, and , a story about the history of the color blue, are great examples of books that integrate mathematical thinking into storytelling.

USING LITERATURE TO SUPPORT MATHEMATICAL THINKING

1. Selecting books to support mathematical thinking: First, find books that have a worthy math problem to discuss or a story to connect to a math problem in your curriculum. Context is one of the most important parts of choosing a book. If the problem is not challenging or accessible enough for students, think about ways to revise the problem. We advocate for low-threshold, high-ceiling problems, which allow access for all students with their previous knowledge and build more knowledge and challenge all students.

When Sophie Thinks She Can't, by Molly Bang, poses a worthwhile math task, asking Sophie and her friends to form as many different rectangles with 12 tiles as they can. Because she can't figure out the solution to the problem, her teacher says, "You can't figure it out yet," which encourages her to keep trying. This book is a perfect example of a mathematical problem that is easily seen in the context of the story and encourages the notion of the power of yet as a problem-solving technique.

In many books, the math problem is not as easily seen. As a teacher, you may not think that most books have some type of mathematical focus within them, but upon close examination, you can discover that many of them can be part of your math curriculum. For example, Blue, written by Nana Ekua Brew-Hammond and illustrated by Daniel Minter, can be connected to an examination of patterns and shapes in textile designs. Working with different shades of blue papers, students could be asked to create patterns by folding the papers and study the patterns that they created mathematically. Studying the relationships between the number of folds and partitions in the final shape would take this task to a higher ceiling.

1. Whose story is this? How might it relate to students' mathematical stories?

2. Through what point of view is this story told?

3. What mathematical concepts shape the story?

4. How are mathematical tasks and understandings established?

2. Critically examining literature: Teachers should spend time critically examining their texts; as Maria José Botelho and Masha Kabakow Rudman advise, teachers should read beyond the words in the text and make connections between local, sociopolitical, personal, and mathematical content. Teachers can ask questions like the following:

The first two questions help students relate to the issues, topics, and questions they may have about the story. The last two questions help students think like a mathematician. For example, Blue is told from a historical perspective and touches on classism throughout time. By examining the book closely, teachers can pull out the patterns in the illustrations and ask students to create mathematical patterns on their own-this is shown throughout this book and particularly on the endpapers.

This picture book provides so many historical background understandings of who cultivated the materials to make the color blue and who had access to textiles made from blue dyes. By leading the students through the questions above, teachers will help them begin to see math in all things and begin to think like mathematicians.

3. Designing a lesson to integrate literacy and mathematics: It's beneficial to think ahead about questions for both disciplines that can help students extend and guide their thinking; in previous work, we developed a full lesson with content-specific questions. Asking students to analyze or interpret their peers' mathematical work and making connections to the text would also extend students' thinking. After coming up with their own set of rectangles with 12 tiles, students can compare their rectangles with the rectangles created by their peers or by Sophie and her friends. This can lead to a discussion of how similar or different all of the rectangles are.

Circle Dogs, written by Kevin Henkes, illustrated by Dan Yaccarino. Exploring shapes through a day in the life of two dachshunds. Perfect read-aloud for a geometry unit! Pair this with Hot Dog (below) to help your students make text-to-text connections.

Bean Thirteen, written and illustrated by Matthew McElligott. This book explores the concept of division with the tribulations that the two characters encounter as they work their way through a problem. A great way to engage children in discussions of trying to work through problem-solving.

, written and illustrated by DougSalati. This 2023 Caldecott-winning book explores a day in the life of a dog as readers are taken on an adventure throughout an urban setting to find solitude for the owner and the dog in a noisy city. A wonderful way to look at mapping.

A Land of Books: Dreams of Young Mexihcah Word Painters, written and illustrated by Duncan Tonatiuh. This story focuses on the creation of books by the Indigenous people of Mexico, exploring their knowledge, culture, and history. Readers can dig deeply into the illustrations and see how precise measurement, geometry, and special relationships of mathematical concepts enhance the telling of this story.

We hope these ideas and books will support you as you provide meaningful conversations with your students by integrating mathematical understandings through children's literature.

# data[].attributes.attachment_link.title
Using Stories to Support Mathematical Thinking in Young Students

# data[].attributes.attachment_link.description
Children's books often contain valuable math lessons that can help young students begin to think like mathematicians.

# data[].attributes.attachment_link.readable_text
Improving Science Education Through Three-Dimensional Learning

Quick Search Next Generation Science Standards

THE THREE DIMENSIONS OF SCIENCE LEARNING

Within the Next Generation Science Standards (NGSS), there are three distinct and equally important dimensions to learning science. These dimensions are combined to form each standard-or performance expectation-and each dimension works with the other two to help students build a cohesive understanding of science over time.

Crosscutting Concepts help students explore connections across the four domains of science, including Physical Science, Life Science, Earth and Space Science, and Engineering Design.

When these concepts, such as "cause and effect", are made explicit for students, they can help students develop a coherent and scientifically-based view of the world around them.

Science and Engineering Practices describe what scientists do to investigate the natural world and what engineers do to design and build systems. The practices better explain and extend what is meant by "inquiry" in science and the range of cognitive, social, and physical practices that it requires. Students engage in practices to build, deepen, and apply their knowledge of core ideas and crosscutting concepts.

Disciplinary Core Ideas (DCIs) are the key ideas in science that have broad importance within or across multiple science or engineering disciplines. These core ideas build on each other as students progress through grade levels and are grouped into the following four domains: Physical Science, Life Science, Earth and Space Science, and Engineering.

More about 3D Learning

GET TO KNOW

The Next Generation Science Standards (NGSS) are K-12 science content standards. Standards set the expectations for what students should know and be able to do. The NGSS were developed by states to improve science education for all students.

A goal for developing the NGSS was to create a set of research-based, up-to-date K-12 science standards. These standards give local educators the flexibility to design classroom learning experiences that stimulate students' interests in science and prepares them for college, careers, and citizenship.

Get to Know the Standards

IMPLEMENT

The NGSS call for a three-dimensional approach to K-12 science instruction. This represents a significant transition from previous state standards. That's why effective implementation demands a great deal of collaboration and patience among states, districts, schools, teachers, and students.

Thoughtful and coordinated approaches to implementation will enable educators to inspire future generations of scientifically literate students. That is the vision of the NGSS. This website provides a range of high-quality resources that empower educators, administrators, parents, and the general public to help bring this vision to life.

Find Tools and Resources

WHY

Science-and therefore science education-is central to the lives of all Americans.

A high-quality science education means that students will develop an in-depth understanding of content and develop key skills-communication, collaboration, inquiry, problem solving, and flexibility-that will serve them throughout their educational and professional lives.

# data[].attributes.attachment_link.title
Home Page | Next Generation Science Standards

# data[].attributes.attachment_link.description
Improving Science Education Through Three-Dimensional Learning Quick Search Next Generation Science Standards Within the Next Generation Science Standards (NGSS), there are three distinct and equally important dimensions to learning science. These dimensions are combined to form each standard-or performance expectation-and each dimension works with the other two to help students build a cohesive understanding of science over time.

# data[].attributes.attachment_link.title
Math Exit Slips - 3rd Grade Exit Tickets - Printables - Digital - Worksheets

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.readable_text
The UDL Guidelines are a tool used in the implementation of Universal Design for Learning, a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn. Learn more about the Universal Design for Learning framework from CAST. The UDL Guidelines can be used by educators, curriculum developers, researchers, parents, and anyone else who wants to implement the UDL framework in a learning environment. These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Reenvisioning the UDL Guidelines

Because the UDL Guidelines are meant to be informed by feedback from the field as well as new research, they have been updated several times in the past. We are in the process of updating the Guidelines once again in our UDL Rising to Equity initiative.

This update will focus specifically on addressing systemic barriers that result in inequitable learning opportunities and outcomes. CAST aims to develop a transparent, inclusive, and community-driven process. If you are interested in collaborating and staying updated on our progress, we invite you to complete a brief survey.

# data[].attributes.attachment_link.description
The UDL Guidelines are a tool used in the implementation of Universal Design for Learning, a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn. Learn more about the Universal Design for Learning framework from CAST. The UDL Guidelines can be used by educators, curriculum developers, researchers, parents, and anyone else who wants to implement the UDL framework in a learning environment. These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.

# data[].attributes.headline
CTC CA Standards for the Teaching Profession

# data[].attributes.subject
CTC CA Standards for the Teaching Profession

# data[].attributes.attachment_link.title
CTC California Standards for the Teaching Profession

# data[].attributes.attachment_link.title
2016 Science Framework - Science Framework (CA Dept of Education)

# data[].attributes.attachment_link.description
The curriculum framework was adopted by the State Board of Education on November 3, 2016. This is the final published version.

# data[].attributes.attachment_link.title
How to Read the Next Generation Science Standards

# data[].attributes.attachment_link.title
NGSS Elementary School Science Classroom Activity

# data[].attributes.attachment_link.title
A Project-Based Approach to Teaching Elementary Science

# data[].attributes.attachment_link.readable_text
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!

# data[].attributes.attachment_link.title
Toy Theater | Fun Online Educational Games for Kids

# data[].attributes.attachment_link.description
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.

# data[].attributes.attachment_link.title
Tinkercad | From mind to design in minutes

# data[].attributes.attachment_link.description
Tinkercad is a free, easy-to-use app for 3D design, electronics, and coding.

# data[].attributes.attachment_link.description
Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

# data[].attributes.attachment_link.title
SECOND GRADE Math Summative Assessments - BUNDLE! | TPT

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
2nd Grade Math Summative Assessment (Common Core) by Second Grade Sweets

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Progress Monitoring Math Assessments (Special Education Data Collection Sheets)

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Success Criteria and Learning Intentions - Math Tasks -Operations & Algebraic...

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Math Rubrics for First Grade by Sarah Paul | TPT

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Minecraft Geometry Performance Based Assessment Activity with Rubric

# data[].attributes.attachment_link.description
This Minecraft Performance Based Assessment will truly grab the attention and engage your students! It includes lines, angles, and shapes from the 4th grade Common Core standards. Students are given the chance to employ their creativity during this end of unit assessment! This assessment also includ...

# data[].attributes.attachment_link.readable_text
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."

# data[].attributes.attachment_link.title
6 Ways to Merge Literacy With Mathematics

# data[].attributes.attachment_link.description
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.

# data[].attributes.attachment_link.description
The widely adopted ISTE Standards provide a framework for educators to create high-impact, sustainable and scalable learning experiences for all students.

# data[].attributes.attachment_link.readable_text
Ensuring that the technology we bring into math classes fosters active engagement is key.

Incorporating technology in mathematics classrooms enables educators to craft powerful collaborative learning experiences that support problem solving and flexible thinking. With strategic integration of both content-specific and content-neutral technology, students and teachers can construct their learning together in authentic ways that elevate mathematics learning.

Until recently, one of educators' primary concerns around educational technology was the lack of access that existed in many American schools. That gap has decreased, but a new digital divide has emerged: The updated 2017 National Education Technology Plan explains that in today's classrooms many students are using technology as a tool for passive learning rather than engaging in active learning experiences that promote student agency.

The Importance of Content-Specific Pedagogy

In order to create technology-infused experiences that support active mathematics learning, educators must of course have pedagogical content knowledge (PCK)-an understanding of best practices specific to mathematics.

One method a teacher can use to analyze the effectiveness of technology integration is the Technological Pedagogical Content Knowledge (TPACK) framework. This tool supports careful educator reflection on pedagogy, content, and technology not only as separate entities but as overlapping and intersecting domains.
Reproduced by permission of the publisher, ©2012 by tpack.org
For example, when planning to integrate technology into a lesson, educators can take into account the technology knowledge the students will need, the mathematics content knowledge they'll need, and the best practices for teaching both the technology and the math. This process is extremely important because without it, the technology may be integrated in a way that is pedagogically inappropriate for mathematics instruction.

Using PCK to Spot Unhealthy Apps and Websites

Teachers start from their understanding of PCK, or best practices for mathematics instruction, in choosing effective technology tools for the mathematics classroom. We know that mathematics should not be focused on speed or quick answer finding. And timed fact testing is a known trigger of math anxiety, which can lead to low mathematics achievement and mathematics avoidance. Yet math apps and websites that focus on speed and rote memorization are readily available and widely used.

This use of technology can promote fear and stress, and it also sends inaccurate messages about the purpose of mathematics. Math is about thinking deeply, discovering patterns, and making connections. Automaticity with math facts and math skills is critical, but how we get students to automaticity matters. A focus on memorization without understanding promotes a joyless, nonsensical form of mathematics that requires remembering a large amount of seemingly disconnected information.

In addition, technology that simply transfers a gradual release-the "I do, we do, you do" structure-to an online format is a form of passive learning that strips math of student agency and rigor. Although gradually releasing responsibility is an effective model in other content areas, in mathematics this model is best flipped to give students the agency to decide what strategies they want to use and how they might solve a problem.

That's because students should productively struggle with math. We need them to problem solve rather than learn to repeat a specific list of procedures given by the teacher. Problem solving skills are more valuable than memorization, and they're the true work of mathematicians. If we're integrating technology into our classrooms to engage students in real-world experiences, our students must be given opportunities to do real mathematics.

Technology That Fosters Deep Mathematical Thinking

When used appropriately, both content-specific and content-neutral technology can be effective in the math classroom. Research indicates that content-specific apps and websites that focus on math learning with the use of virtual manipulatives are highly effective, and in some cases more efficient than physical manipulatives.

The Math Learning Center, for example, provides several manipulative options, such as rekenreks, geoboards, number lines, and number frames. Apps and websites that provide these types of virtual tools are easy to use, support students with conceptual understanding, and increase student access to math tools.

Content-neutral technology includes tools such as virtual whiteboards, handheld clickers, and student collaboration apps. Virtual whiteboard and websites, such as Explain Everything, promote self reflection, enable students to make their learning visible and share and connect ideas, and have been linked with high-level student thinking and teacher questioning.

But content-neutral technology that promotes fast answering, such as handheld clickers, is associated with decreased cognitive demand, most likely due to the likelihood of being used with minimal student discourse.

Being a Critical Consumer of Technology

The educational technology market is flooded with new apps, tech tools, and gadgets, and in some instances, teachers are commended for increased technology use whether it supports healthy math learning or not. Technology can have a truly positive impact on student learning, but it should not replace teaching or ignore research-based best practices for math instruction.

If we believe that students of mathematics need opportunities for discussing math, creating and connecting visuals, analyzing models, discovering patterns, and making generalizations, the technology that we introduce into our classrooms should match those values.

There was a time when simply getting technology into the hands of our students was a goal, but the time has come to slow down and plan for technology integration that truly supports healthy and productive mathematics learning.

# data[].attributes.attachment_link.description
Ensuring that the technology we bring into math classes fosters active engagement is key.

# data[].attributes.attachment_link.readable_text
Digital learning experiences can be used to mirror the work of real scientists, boosting students' engagement and learning outcomes.

Juice Images / Alamy Stock Photo

Educators are increasingly encouraged to update the learning experiences in their classrooms. This includes more attention to STEM learning, such as promoting the integration of technology and science instruction into everyday classroom experiences, and implementing pedagogical frameworks like open-ended inquiry learning and problem-based learning that mirror the work real professionals engage in-frameworks that guide students to " play the whole game at the junior level."

These considerations are important for guiding students to be ready to take on a highly scientific and technological world. Merely implementing more open-ended science instruction or using applications on laptops or iPads doesn't necessarily improve student learning, though. It's how we design and use technology in schools that can truly improve students' learning outcomes.

Fortunately, the scaffolds and supports within technologies can act in the service of science learning.

Role-Playing as Scientists

Allowing students to get into the shoes of scientists and to mirror the work they do is a powerful technique to get students interested in a science field by offering them opportunities to practice the skills that scientists use on a daily basis. This can increase students' sense of identity in science, self-efficacy in science work, and general affect toward science.

Digital structures that enable students to step into the shoes of scientists include first-person narratives and role-playing scenarios like the digital learning environment EcoMUVE, which was developed by the Harvard Graduate School of Education. It is a curriculum for middle school students in which they enter a virtual world and must figure out why their local ecosystem is declining. In programs like this, students can play as an avatar and explore an engaging virtual world, talk to scientist non-player characters, use scientific tools, and conduct authentic experiments.

By working through these digital scenarios, students practice science-related skills and processes, ultimately contributing to the transfer of scientific understandings.

Problematizing Learning Tasks

Problematization is a pedagogical technique that makes parts of a learning task problematic in some way, with a goal of increasing students' problem-solving skills. Problematization is often used to invite students to puzzle over specific processes and ideas. In EcoXPT -a soon-to-be-released program from Harvard-new scientific information is dispensed as the program progresses, meaning that students must rethink their initial hypothesis.

Digital structures that provide this kind of just-in-time information include help buttons and tutorials. During digitally enabled open-ended and problem-based learning scenarios, reminding students about available automated help and tutorial buttons during a confusing part of the work allows them the opportunity to further their understanding at their own learning edge. Tutorials can help explain difficult concepts or tools that students use in these digital learning contexts, ultimately deepening their scientific understandings.

Illustrating Complex Processes

There are many complex processes that students have to reason through in science learning. Oftentimes, these processes are at the heart of the scientific understandings we hope students will gain. For example, consider genetic processes, which can be difficult for students to grasp. Teaching Genetics With Dragons from the Concord Consortium has three programs that offer middle and high school students an engaging way to learn about some of the complex intricacies of genetics in a playful digital learning platform.

This kind of experience aids students as they reason through highly complex and scientific processes.

The Value of Interactivity

A key beneficial aspect of digital learning is interactivity. Technology can also provide many opportunities for students and teachers to collaborate, such as when students are working in larger groups in online peer learning interactions. Numedeon's Whyville is a great example of an online community where preteen students can create a character, interact with friends online, and participate in science, math, and history activities. Teachers can aid students in thinking about their role in the online community, and how their learning is progressing throughout such online activities.

Teachers play an integral role in these interactions as mentors supporting students in their developing understandings by providing additional support and pushing students to deeper learning.

Aiding Teachers in Assessment

Assessing student understanding in science learning is important for teachers, who must determine where their students are and figure out how to design learning experiences to deepen their knowledge even more. Digital learning contexts allow teachers to build in different types of assessments to periodically assess student understanding. These assessments can be formative and diagnostic, or summative.

These assessments can include typical quizzes or multiple-choice questions that appear in order to assess students' understanding of scientific content. Digital quizzes allow for quick feedback to students, aiding them in assessing their own learning, which can be particularly helpful in learning complex scientific concepts and processes. Digital quiz results can also be visible to teachers, highlighting student progress and allowing them to see where each student is in their learning without the hassle of paper and pencil grading. Digital assessment may also take the form of a concept map, a medium that allows students to express their understanding visually.

# data[].attributes.attachment_link.title
The Value of Digital Tools in Science Classes

# data[].attributes.attachment_link.description
Digital learning experiences can be used to mirror the work of real scientists, boosting students' engagement and learning outcomes.

# data[].attributes.attachment_link.description
The more we study the creation through that which is truly science, the more clearly we see that it must be the handiwork of God.

# data[].attributes.attachment_link.readable_text
Over the past few decades evangelicals have expressed a renewed interest in the concept of vocation. No longer is it uncommon to hear call to "think Christianly" about our work or, for academics, their fields of study. Some people (like me) go a step further and claim that we're merely fooling ourselves if we believe that we can approach our vocations at the deepest levels of engagement with a sense of religious neutrality. "Thinking Christianly" about our work is not something we add on as an afterthought; it radically changes the nature of our work.

Not surprisingly, this view is often met with skepticism. Even those who agree with my general point do not see, for example, how there could be a particularly Christian view to subjects like mathematics.

While I certainly understand their hesitation, I do in fact believe there is a Christian view of mathematics. Indeed, I believe that there is a distinctly Christian view of everything.

The reason this idea seems so foreign (if not downright absurd) is that most of our theories about the world have only a minimal pragmatic affect on how we actually live our lives. Both my neighbor and I, for example, may get sunburned even if we hold radically different beliefs about the sun. The fact that I think the sun is a ball of nuclear plasma while he believes that it is pulled across the sky in a chariot driven by the Greek god Helios doesn't change the fact that we both have to use sunscreen. It is only when we move beneath the surface concepts ("The sun is hot.") to deeper levels of explanation ("What is the essential nature of entities like the sun?") that our religious beliefs come into play.

Even the concept that 1 + 1 = 2-a formula which almost all people agree with on a surface level-has different meanings based on what theories are proposed as answers. These theories, claims philosopher Roy Clouser, show that going more deeply into the concept of 1 + 1 = 2 reveals important differences in the ways it is understood, and that these differences are due to the divinity beliefs they presuppose.

But before we can see why this is true, let's review the claims made in my previous article about what constitutes a religious belief.

A belief is a religious belief, says Clouser, provided that (1) It is a belief in something(s) or other as divine, or (2) It is a belief concerning how humans come to stand in relation to the divine. The divine, in this definition, is whatever is "just there." He contends that self-existence is the defining characteristic of divinity, so that the control of theories by a belief about what is self-existent is the same as control by a divinity belief and thus amounts to religious control of all theories.

Whether we refer to it as being self-existent, uncaused, radically independent, etc., it is the point beyond which nothing else can be reduced. Unless we posit an infinite regress of dependent existences, we must ultimately arrive at an entity that fits the criteria for the divine.

Different traditions, religions, and belief systems may disagree about what or who has divine status, or whether such an ontological concept should be considered a "religious belief." But what they all agree upon is that something has such a status. A theist, for instance, will say that the divine is God while a materialist will claim that matter is what fills the category of divine. Therefore, if we examine our concepts in enough detail, we discover that at a deeper level we're not agreeing on what the object is that we're talking about. Our explanations and theories about things will vary depending on what is presupposed as the ultimate explainer. And the ultimate explainer can only be the reality that has divine status.

Returning to our example, we find that the meaning of 1 + 1 = 2 is dependent on how we answer certain questions, such as: What do "1" or "2" or "+" or "=" stand for? What are those things? Are they abstract or must they have a physical existence? And how do we know that 1 + 1 = 2 is true? How do we attain that knowledge?

Let's look at the answers proposed by four philosophers throughout history:

Leibnitz's view -When Gottfried Wilhelm Leibniz, an inventor of the calculus, was asked by one of his students, "Why is one and one always two, and how do we know this?" Leibnitz replied, "One and one equals two is an eternal, immutable truth that would be so whether or not there were things to count or people to count them." Numbers, numerical relationships, and mathematical laws (such as the law of addition) exist in this abstract realm and are independent of any physical existence. In Leibnitz's view, numbers are real things that exist in a dimension outside of the physical realm and would exist even if no human existed to recognize them.

Russell's view -Bertrand Russell took a position diametrically opposed to Leibnitz. Russell believed it was absurd to think that there is another dimension with all the numbers in it and claimed that math was essentially nothing more than a short cut way of writing logic. In Russell's view, logical classes and logical laws-rather than numbers and numerical relationships-are the real things that exist in a dimension outside of the physical realm.

Mill's view -John Stuart Mill took a third position that denied the extra-dimensional existence of numbers and logic. Mill believed that all that we can know to exist are our own sensations-what we can see, taste, hear, and smell. And while we may take for granted that the objects we see, taste, hear, and smell exist independently of us, we cannot know even this. Mill claims that 1 and 2 and + stand for sensations, not abstract numbers or logical classes. Because they are merely sensations, 1 + 1 has the potential to equal 5, 345, or even 1,596. Such outcomes may be unlikely but, according to Mill, they are not impossible.

Dewey's view -The American philosopher John Dewey took another radical position, implying that the signs 1 + 1 = 2 do not really stand for anything but are merely useful tools that we invent to do certain types of work. Asking whether 1 + 1 = 2 is true would be as nonsensical as asking if a hammer is true. Tools are neither true nor false; they simply do some jobs and not others. What exists is the physical world and humans (biological entities) that are capable of inventing and using such mathematical tools.

For each of these four philosophers what was considered to be divine ("just there") had a significant impact on how they answered the questions about the nature of the simple equation. For Leibnitz it was mathematical abstractions; for Russell it was logic; for Mill is was sensations; and for Dewey it was the physical/biological world. On the surface we might be able to claim that all four men understood the equation in the same way. But as we moved deeper we found their religious beliefs radically altered the conceptual understanding of 1 + 1 = 2.

What all of the explanations have in common, what all non-theistic views share, is a tendency to produce theories that are reductionist-the theory claims to have found the part of the world that everything else is either identical with or depends on. This is why the Christian view on math, science, and everything else must ultimately differ from theories predicated on other religious beliefs. We may appear to agree on the surface, but dig a little deeper and we find that what we believe about God changes everything.

20 Things You Can Do Right Now to Prevent Dechurching

We're currently experiencing the largest and fastest religious shift in the history of the United States. But there are practical things we can do inside our local churches.

Jim Davis and Michael Graham have commissioned the largest and most comprehensive study of dechurching in America. Informed by their findings, they've written a book and developed this corresponding toolkit with resources to help you address the dechurching phenomenon.

We're delighted to offer you the 'Rechurching Toolkit' for FREE today. Click on the link below to get instant access to this resource-worth $100-and be equipped to understand and address the issues behind dechurching.
Download your FREE "Rechurching Toolkit" today "

# data[].attributes.attachment_link.title
What Does 1 + 1 = 2 Mean?-Why Christianity Matters for Math (and Everything Else)

# data[].attributes.attachment_link.description
TGC editor Joe Carter discusses that there is a distinctly Christian view of everything, particularly math. We ought to "think Christianly" about all things

# data[].attributes.attachment_link.title
March Madness Basketball STEM Activity Engineering, Sports, Elementary

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
5E Instructional Model Explained: A Framework for Inquiry-Based Learning

# data[].attributes.attachment_link.description
Learn how to use the 5E instructional model to engage students in inquiry-based learning.

# data[].attributes.headline
Integrating ELD Standards Into Math & Science

# data[].attributes.subject
Integrating ELD Standards Into Math & Science

# data[].attributes.attachment_link.title
Integrating the CA ELD standards into K-12 Mathematics and Science Teaching and Learning

# data[].attributes.headline
Scientific Method vs. Engineering Design Process

# data[].attributes.subject
Scientific Method vs. Engineering Design Process

# data[].attributes.attachment_link.title
6th Grade Science diagnostic exam by Vachhani Learning | TPT

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Science Exit Tickets Bundle | 4th + 5th Grade Matter Space Energy | Exit Slips

# data[].attributes.attachment_link.description
This page failed to load. Our development team has been informed of the issue.

# data[].attributes.attachment_link.title
Quizizz - The world's most engaging learning platform

# data[].attributes.attachment_link.description
Find and create gamified quizzes, lessons, presentations, and flashcards for students, employees, and everyone else. Get started for free!

# data[].attributes.attachment_link.title
Next Generation Science Standards First Grade Student Checklist

# data[].attributes.attachment_link.description
Keep a record of the science standards addressed during the school year using this checklist containing each Next Generation Science Standard (NGSS) for first grade. This checklist provides boxes for teachers to track students who have mastered the standards and those who need additional practice.