Explain Why Subtraction Strategies Work Using Place Value

Students will explain and justify their subtraction strategies by referencing place value understanding and the relationship between addition and subtraction. They will show that ungrouping preserves the value of the minuend.

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Grade 2 · Explaining Addition and Subtraction Strategies · question 1 of 3

0 of 12

12 rungs. A star at the top.

33 = 2 tens and ones

How it is taught

0:00 of 3:42

Subtraction can take tens from tens.

The total stays fair when you ungroup a ten.

Read it: Break a hundred, then a ten

302 − 175: there are 2 ones and 0 tens. Break a hundred into 10 tens, then a ten into 10 ones. Now take away by place: 127.

5 ones must go, and there are only 2, with 0 tens to break.
Break 1 hundred into 10 tens, then 1 ten into 10 ones: 2 hundreds, 9 tens and 12 ones.
Take away by place: 12 − 5 = 7, 9 − 7 = 2, 2 − 1 = 1. 127.

A hundred is 10 tens and a ten is 10 ones, so nothing is lost when you break them.

With 0 tens, the hundred breaks first.

Explain each break, and check by adding back: 127 + 175 = 302.

Break from the next place up, 1 place at a time, until there is enough.

Taking 2 from 5 in the ones, 0 from 7 in the tens, and writing 273.

5 ones must go from 2. Break a hundred, then a ten: 302 − 175 = 127.

57 − 18 = ___ — 39. 8 ones must go, and there are only 7 ones loose. Break 1 rod into 10 ones. The same number, grouped differently: 4 rods and 17 ones. Take 18 away: 57 − 18 = 39.

53 − 27

We have 53 stickers and want to give 27 away. Let's find how many will be left.

We stack the numbers by place value — tens on the left, ones on the right.

Subtraction starts with the ones. Can we take 7 away from just 3?

Three is too small. We don't have enough ones, so we'll ungroup a ten.

Take one ten from the five tens. That leaves four tens up here.

That one ten becomes 10 ones. Joined with the 3, we now have 13 ones.

Look — forty plus thirteen still equals fifty-three. The value didn't change!

Grade 2 · Ungrouping a ten keeps the value the same

Now we can subtract the ones. Thirteen minus seven is six.

Then the tens. Four tens minus two tens leaves two tens.

So 53 minus 27 is 26. Twenty-six stickers are left!

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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