Number sense is an important part of mathematics learning, and is essential to our daily lives. Jo Boaler states, “People with number sense are those who can use numbers flexibly. When asked to solve 7 x 8 someone with number sense may have memorized 56 but they would also be able to work out that 7 x 7 is 49 and then add 7 to make 56, or they may work out ten 7’s and subtract two 7’s (70-14). They would not have to rely on a distant memory” (Fluency With Fear).
We know that we want learners to know their math facts - they should be automatic - but the question is, what is the best way to do this? Here are some great strategies to help your child develop their number sense:
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Use mathematical models (e.g., 5 rack, 10 rack, math rack, number line, array, relational rods, two-sided counters) to build, develop and support the understanding of numbers.
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Work with your child to identify the various ways in which math facts can be understood, such as “+ 1”, ”- 1”, “+ 2”, “- 2”, “doubles”, “making 10”.
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Learn about number properties as they notice patterns in addition, subtraction, multiplication and division.
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Look for relationships between numbers – for example: 3 × 6 is the same as 6 + 6 + 6.
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Represent operations performed on numbers in different ways.
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Analyze results of operations (e.g., What happens when two odd numbers are added?)
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Practise by playing games (see below - and for more, refer to Fluency Without Fear)
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Practise frequently
For additional information, please see the following articles:
Fluency Without Fear (Jo Boaler)
Understanding Learning Disabilities: How Processing Affects Mathematics Learning (YRDSB)
Focusing on the Fundamentals of Math (Government of Ontario)
Primary Task: How Many Are Hiding?
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In this activity you and your child each have the same number of cubes and a cup.
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Take turns hiding some of your cubes in the cup and showing the leftovers.
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Work out the answer to the question “How many are hiding,” and say the full number combination.
Example: I have 10 cubes and I decide to hide 4 in my cup. My group can see that I only have 6 cubes. Students should be able to say that I’m hiding 4 cubes and that 6 and 4 make 10.
Fluency Without Fear (Jo Boaler)
Junior Task: How Close to 100?
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This game is played in partners.
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Two people share a blank 100 grid (10x10).
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The first partner rolls two number dice. The numbers that come up are the numbers the player uses to make an array on the 100 grid. They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible.
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After the player draws the array on the grid, she writes in the number sentence that describes the grid.
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The game ends when both players have rolled the dice and cannot put any more arrays on the grid.
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How close to 100 can you get?
Fluency Without Fear (Jo Boaler)
For digital versions of the game, check out Grid on the App store.
Intermediate Task: Number Talk
Pose an abstract math problem such as 18 x 5 and ask your child to solve the problem mentally. Look for different ways you could have solved the problem (see below for some examples).
Fluency Without Fear (Jo Boaler)
Check out the Monthly Math Problem!