Differentiation in Primary Mathematics

Play based learning is appropriate at every age as far as I am concerned, but it is essential for differentiation in math instruction at the primary level. Math is a personal favourite subject to teach, but this was entirely unexpected.  I failed grade 12 math.  😏

Twice. 🥴

 I know that I was bored to tears, and I just zoned out entirely.  Had there been group work at least there would have been an element of accountability.  I also know that I love to learn by doing, and diverse instructional strategies  would have undoubtedly engaged me more. 

I was surprised to discover my love of math when I was asked to teach grade 8 and 9 math. Believe me when I say that I had to teach myself every single thing that I taught the students. 

My differentiation in math instruction was not done well at that time.  I was barely surviving, but I have learned along the way.

According to Carol Tomlinson, a leader in differentiation in instruction, the strategies for differentiation fit under these 4 umbrellas:

Content – what the student is expected to learn and / or how the student will access to the information they need to learn it
Process – how the student interacts with or engages with the learning in order to learn
Products – how does the students demonstrate they understand the material
Learning environment – the way the classroom operates and feels to the students.

Many of the strategies do fit under more than one umbrella, which only makes life simpler!

Let me share some of my favourite ways of differentiating math.

To Group or Not to Group

Other than my brief foray into middle school math, my teaching focus was grades 1 and 2 math.  Most years I taught combined grades. About half the time I taught the whole class, and the other half the time the students were always in their small group.  

To be clear, there were still times when I was teaching whole group that we broke up into small groups.  And there were definitely times during the small group instruction years that I taught the whole class. 

However, essentially for whole group instruction I was planning one lesson, and for the small group years I was planning 3 groups. 

In my experience the whole class instruction is fun, and I certainly found it more dynamic. However, I do find that even with all of the ways I differentiated there was someone being pushed too hard, or being held back too long.  

Small group instruction is better for teaching students more precisely at their level.  However, there were still kiddos who were struggling to keep up.  And often times it took me an hour to prep just that one subject. 
However, there was something I learned that helped a lot; differentiating numbers.

Differentiation of Numbers

This type of differentiation is super simple for tailoring instruction to students’ needs. If you change the size of the number, you are changing the challenge for the students.  Thia option is really about applying the areas of offering choice, and varying content.  

As adults that add 2-digit numbers, we understand that adding 53 and 46 is not really that much more difficult than adding 23 and 16, but to timid students, the latter numbers are far less intimidating.

Additionally, for stronger students you may want to add numbers such as 44 and 37, and suddenly they are thrust into the world of independent problem solving as they figure out for themselves how to regroup. The next step is 55 and 48, and now they have crossed over into numbers bigger than one hundred.

Lastly, if you are using dice, remember that 6-sided dice limit the difficulty far more than 10 or an 18-sided dice. 

More advanced students can roll the 6-sided dice twice for each number in their equation? Once to determine the tens column, and then again to determine the ones column.

Differentiation in Math Problems

Let’s talk about a few different ideas for differentiating word problems in math.

As a former Learning Support teacher the first step I take to differentiate word problems in math is to make them accessible to everyone.  What have I done to ensure the struggling reader who loves math is able to read the problem? 

A. We want to keep engage students engaged, and not let them become disenchanted by a problem with reading.

1. I read the problem aloud to the whole class. But this doesn’t really allow everyone to work at their own pace.
2. Small group work so the reading is done by a peer.
3. Partner work where students’ different strengths offer support to each other.
4. My least favourite option because it can be cumbersome in the primary classroom is if you have a text-to-speech option.

B. Can you offer students choices as to ways to demonstrate their understanding?

1. Maybe using an equation and showing their work.
2. Could they create drawings that reflect the topic of the word problem (ie if the word problem is about baking cookies their drawings would be about cookies), and demonstrate their understanding of the math skill.  
3. What about building their answer with their favourite tool, and then providing a word or number sentence to connect what they have built with the problem? 
4. Personally I love John van deWalle’s big 5 assessment. It is very open-ended and provides choice for the students.

C. Write equations on the board or show pictures, and have students create word problems, verbal or written, for each other to solve. Have the students whose turn it is  to solve the problem sit with their backs to the board, so they can’t see the clues.

Differentiation Math Questions

There are so very many ways that you can differentiate the same math equation. Posing the same question in different ways, and allowing the student to choose their question provides differentiation through choice and complexity. 

Let’s take a look at at a doubles equation: 4 + 4 = 8.  Primary students are often quite confused with both equations and word problems if the unknown number is not in the sum or difference spot as in this video. Khan Academy also has an excellent video on the unknown number.   

Move the Unknown Number to Different Spots to Change Complexity.

Check these differentiated math resources I created for Doubles Addition and Subtraction to support teachers with planning differentiation in math instruction.

As mentioned above, providing students with options for presenting their understanding is an effective part of differentiation in math instruction.  Often that is by allowing them choices between presentations, or images, in written format etc.

Using Student Recording Sheets to Differentiate

However, there are also ways to differentiate by using different student recording sheet. A favourite math resource of mine, “Sums and Differences for grades 1 & 2” (this is NOT an affiliate link, but I loved it), by Carole Fullerton.

At the end of each unit she provided different worksheets for grade 1 and grade 2. However, they were only identified as for separate grades in the teachers guide.

She based the differences within the worksheets on the BC curriculum requirements for grades 1 & 2.

In a similar fashion, the Write the Room activities I shared with you above also come with differentiated worksheets.

All of these options come with or without a number line, and come with each resource for multiple ways of planning differentiation in math instruction, and multiple choices for each student. 

Phew!!  That is a lot of differentiated options.

An Opportunity to Easily Provide Work at a Student’s Individual Level

And that’s just for Doubles. 😉 Consider your options for differentiation if you had students working on the task cards developing automaticity on the strategy at their personal level.  😅

Finally, do I dare say it, I also have board games that offer a similar but different type of differentiation for more options. Eek!

Differentiation in Primary Mathematics Writing

Differentiated worksheets are just one way to provide your students with differentiated options for demonstrating their understanding through writing in math class. I loved having my students work in their journals.  

You can:

1. Differentiate the prompt complexity or challenge.
2. Have a series of prompts available and during journal time students the next prompt in order. This differentiates by allowing everyone to work at their own pace. 
3. Offer a selection of ways to demonstrate understanding (ie: write an equation, write a word problem, draw a picture, explain their thinking, provide a fact family etc.), and have students choose 2-3 depending upon the skills you are working on at the time.
4. Make journals one of the options on a choice board, so they can choose to write in their journal or do something else. 
5. Offer open-ended prompts for students and see how students demonstrate their understanding.

Differentiated Instruction in Math Using Different Tools

Note: The following links are not affiliate links. I provide them as a service to you.

Various tools for computation during differentiation in math instruction are helpful when planning your differentiation in math instruction, and these are what I consider the essentials.  There are so many more.

Tools for Whole Class Use

There are some tools that are not only engaging, but they allow me to do some formative assessment on the spot. They are for the whole class.

Note: I am not earning commission from these links. They are solely here for your convenience and understanding.

• Plastic pockets for games, worksheets, and everything that you want to reuse.
• Whiteboard markers for using either on whiteboards or plastic sleeves
• Whiteboard erasers I have used these, but, truthfully, I just cut up washcloths for the students so that I could wash them. 🤢
• Handheld whiteboards these particular boards come with markers that aren’t great, but the boards are worth it!
• Magnetic 10 Frames are one of my favourite tools for using visuals to support student understanding of so many of the math concepts and strategies.
• Cuisenaire rods are a tool that are great for visual, kinesthetic and tactile learners as they can be used for multiple operations, fractions – if you are looking for resources with activities for how to use them please check out Carole Fullerton’s store. I taught the whole class using these, but at time when we weren’t using them the students could choose them.
•  Versatiles students can practise and self-assess all the skills. These are also amazing at having students practice multi-step solutions and stretching short term memory. The down side is buying enough books for all of the skills for your students. These were always used for a center.

Tools That Students Had the Option to Use

• make your own rekenreks  or there are  rekenreks you can purchase.
• Abacus although this is not the one I used.  Different coloured beads for each group of 10, and strong wood construction are essential.
• 6 sided dice, 10 sided dice ,  20 sided dice , the larger the number the tougher the equation. Students mostly had a choice, but occasionally their choice was encouraged.
• dice inside dice are the same as using 2 six sided dice, but the kiddos loved them!
• Subitizing ten-sided dice are important for all students to use to practice subitizing., and they also add a little bit of extra challenge for students who need challenge but aren’t ready for 20 sided dice.
• Math links for counting, building, adding, subtracting, patterning etc. 
• Magnatiles for making 2d to 3D shapes
• Tangrams  great for spatial relations.
• Wooden Attribute blocks
• Number Line tape , but I did not tape this to the desks.  I laminated each number line, punched a hole in one end, and hung them on the whiteboard with hooks.

These are all open ended tools; not flash cards or other prepackaged activities. Although some prepackaged activities existed in my classroom, they were few and far between.

Your budget is limited. Invest in tools wisely.

Get Started with Differentiation in Math Elementary Classrooms

There are many, many ways to provide differentiation in math classrooms, and we are all working with different curriculums.  You may be tied heavily to a curriculum provided by a school or district, or you may wish you had more direction from your school or district.

What I have provided here is, obviously, not a curriculum, but hopefully there are ideas here that you can take one day and one step at a time.  No two groups of children are going to be the same, so every time you explore a new thing, and take a new step of faith you are expanding your tool belt for the next group.  

If you can’t afford the tools or resources I have linked to here, find something similar that will do the same thing. Or visit local garage sales, talk to friends and neighbours, and ask parents for donations. 

Meanwhile, have fun in Math!!

If you do, I know they will. Engagement makes all other ways you provide differentiation in math that much better for students.

And remember, affirm yourself for the steps you are taking. Every step is a big deal.

Share one of your favourite math tools in the comment below.

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