Use Properties of Operations to Add and Subtract within 100

Students will apply the commutative and associative properties of addition to rearrange and group numbers for easier computation within 100. They will also use the relationship between addition and subtraction to solve problems flexibly.

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Grade 2 · Fluent Addition and Subtraction within 100 · question 1 of 3

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12 rungs. A star at the top.

15 + (11 + 19) =

How it is taught

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You can break a subtract into tens then ones.

Addends can swap; subtract cannot.

Read it: Add the pair that makes a ten first

17 + 23 + 23: the ones of 17 and 23 make 10, so add that pair first: 40. Then 40 + 23 = 63.

Look at the ones: 7, 3 and 3.
Find the pair whose ones make 10: 17 + 23 = 40.
Add the last number: 40 + 23 = 63.

You can add in any order or grouping, and the total stays the same.

A pair whose ones make 10 leaves a number with 0 ones, and that is easy to add to.

All the ones together make 13: 1 ten and 3 ones, so the total is 63.

Group the numbers whose ones make 10. The order does not change the total.

Adding the ones, getting 13, and writing 13 in the ones place.

13 ones is 1 ten and 3 ones: the ten joins the tens. The total is 63.

23 + 27 + 34 = ___ — 84. 23 and 27 have ones that make 10, so add that pair first. All the ones make 14, so 1 ten is traded out.

27 + 13 + 23

Three numbers to add? Let's use the properties of operations to make it easy.

Our problem is twenty-seven plus thirteen plus twenty-three.

Look at the ones digits. Seven and three make ten — a friendly pair!

We can swap the order. The commutative property says that's okay.

Grade 2 · Add smarter using commutative & associative properties

Now group twenty-seven and twenty-three together. That's the associative property.

Twenty-seven plus twenty-three is fifty.

Fifty plus thirteen is sixty-three.

Properties helped us pick easy pairs. The answer is sixty-three!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Standard

CCSS.2.NBT.B.5

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

Grade 2

Quoted from the Common Core State Standards.

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What a star here means

A star here is the top of a twelve-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 2

This is one rung of 85 in Grade 2 mathematics, in the order they build on each other.

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