Explain Why Addition Strategies Work Using Place Value

Students will articulate and justify why their addition strategies work by referencing place value and properties of operations. They will use words, drawings, and/or equations to communicate their mathematical reasoning.

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

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12 rungs. A star at the top.

Why split 28 + 35 by place value?

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Easier to add tens, then ones

How it is taught

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You add tens and ones because of place value.

Explaining means saying why the steps keep the total.

Read it: Explain the extra ten

You have nineteen cubes. Thirty-nine more sit beside them. Look at the ring of ten — that is the ones that would not fit.

Add the ones and say it: nine and nine make eighteen.
Trade ten of those eighteen for a ten; eight stay.
Add the extra ten with the tens: 19 + 39 = 58.

Counting every cube from one works, but it is slow when nineteen and thirty-nine sit together.

Eighteen ones is the same pile as one ten and eight ones, so the ring does not change how many cubes you have.

If you cannot say where the extra ten came from, you add one and three and lose it.

When ones make ten or more, trade ten for a ten and say they are the same amount.

Adding the tens as one plus three, and never saying where the extra ten went.

Say it: nine and nine make eighteen, so ten of them join the tens and eight stay.

45 + 16 = ___ — 61. Add the ones: 5 + 6 = 11. Trade 10 of them for a ten, then add the tens.

38 + 25

Let's add thirty-eight plus twenty-five. We can break the numbers apart by place value to see why our strategy works.

Thirty-eight is three tens and eight ones — that's thirty plus eight.

Twenty-five is two tens and five ones — that's twenty plus five.

Now we group the tens with the tens, and the ones with the ones.

Add the tens first. Thirty plus twenty is fifty.

Add the ones. Eight plus five is thirteen.

Put them back together: fifty plus thirteen.

Fifty plus thirteen is sixty-three.

This works because we can add in any order — and tens always add to tens, ones to ones.

Grade 2 · Why breaking apart by tens and ones works

So thirty-eight plus twenty-five equals sixty-three. That's place value at work!

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.9

Explain why addition and subtraction strategies work, using place value and the properties of operations

Grade 2

Quoted from the Common Core State Standards.

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Explain Why Subtraction Strategies Work Using Place Value

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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