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Math · Grade 2 Math

Chapter 1: Fluency Within 20

Choosing a Strategy

Look at the numbers before you start.

Lesson
7
Time
About 15 minutes
Practice sheets
0 of 17 done
Part 1 of 7Let's Learn

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Watch the idea first — 51 seconds. Then read on, and try it yourself in the next step.

You now have four tools: doubles, near doubles, make ten, and take from ten.

Read the numbers first

Two numbers the same means a double. One apart means a near double. An 8 or 9 means make ten.

Step 2: Try It Yourself

Tap and try it out.

Try each pair two ways, then decide which felt faster.
First ten
The rest

8 needs 2 more to make ten. Take 2 from the 7.

The beads change color after five, so five is visible without counting.
15 beads moved across in total.
15 beads moved across in total.

How many15

That is 3 full fives, which is 15.

Step 3: In Real Life

Mental math at the store

5 + 6 is a near double. 9 + 4 is a make-ten. 8 + 2 is just counting on. A good shopper looks at the numbers before starting.

Step 4: Watch an Example

One step at a time.

Watch Ana Choose

Ana has three facts to add. They are 6 + 6, 9 + 4, and 7 + 8.

  1. Step 1

    In 6 + 6, both numbers are the same. It is a double.

    Six
    Six
    Six6
    Six6

Watch Leo Choose

Leo works out 7 + 6. He starts. You finish.

  1. Step 1

    He looks at the numbers first. They are 7 and 6.

    Seven
    Six
    Seven7
    Six6

Step 5: Your Turn

Practice makes it stick.

The Shop

Problem 1 of 13

A pen costs 9 cents. An eraser costs 7 cents. How much do they cost together?

Pen cents
Eraser cents
cents

The Garden

Problem 2 of 13

Ana planted 6 seeds. Leo planted 7 seeds. How many seeds did they plant?

Ana
Leo
seeds

Which Strategy?

Look at the numbers first. Then pick or solve.

Problem 3 of 13

Which strategy fits 9 + 5 best?

Nine
Five

Problem 4 of 13

Which strategy fits 7 + 7 best?

Seven
Seven

Problem 5 of 13

8 + 6 = ?

First ten
The rest
First number8
Second number6

Problem 6 of 13

13 − 8 = ?

Find the Mistake

A friend picked a tool. Find the slip, then fix it.

Problem 7 of 13

Zoe works out 6 + 7. She gets 12. What was her slip?

Zoe's work for 6 + 7

  1. 16 + 7
  2. 26 + 6 = 12
  3. 312

Problem 8 of 13

What should Zoe get for 6 + 7?

Six
Seven

Problem 9 of 13

Leo works out 8 + 5. He gets 15. What was his slip?

Leo's work for 8 + 5

  1. 18 + 5
  2. 210 + 5
  3. 315

Problem 10 of 13

What should Leo get for 8 + 5?

First ten
The rest
First number8
Second number5

Which Way?

Look at the numbers. Pick the way that fits.

Problem 11 of 13

8 + 7. Which ways work?

Eight
Seven

Problem 12 of 13

7 + 2. Which way is quicker?

Seven
Two

Slide the Beads

Build it, then check.

Problem 13 of 13

Slide 15 beads across.

Slide the beads.
0 beads moved across in total.
0 beads moved across in total.

How many0

Step 6: Quick Check

Show what you know.

Question 1 of 2

9 + 7 = ?

Question 2 of 2

Which strategy fits 6 + 7 best?

Ready for more?Optional. Past the lesson, for anyone who wants it.

Stretch 1 of 1

16 − 8 = ? Look for a double.

What You Learned

  • Look at the numbers before you start working.
  • Equal numbers mean a double. An 8 or 9 means make ten.
  • More than one strategy can be right. Counting one by one is the slow one.
For the grown-up

Fluency within twenty is not speed for its own sake. Facts that come without thinking free up the working memory that the next four years of mathematics need, and a child recomputing 8 + 6 every time has nothing left over for the problem it sits inside.

Watch for finger counting that has gone underground — a pause, a glance away, lips moving. The strategy has not gone; it has just got quieter.

Short and often beats long and rare. Two minutes of the facts they nearly know is worth more than twenty minutes of the ones they already do.

More than one road works — For 8 + 7 you could make ten or use the double 7 + 7. Both are good. Counting one by one is not.

Look before you calculate — By now you have several strategies: doubles, near doubles, making ten, taking from ten, and counting on. A skilled adder does not use the same one every time. They glance at the numbers first and choose. That glance takes a moment and saves far more.

What each pair of numbers is telling you — Same number twice? Use a double. One or two apart? Near double. One number is 8 or 9? Make ten. Adding 1, 2 or 3? Just count on — no strategy needed. Subtracting from a teen number with a big subtrahend? Take from ten. The numbers themselves signal which tool fits.

There is no single right method — Two children can solve 7 + 8 differently and both be correct — one through 7 + 7 = 14 then add one, the other through making ten. Math allows more than one good path. What matters is that your path is reliable and that you can explain it.

Let the numbers choose the tool — 6 + 7: near double. 6 + 6 = 12, one more, 13. 9 + 4: make ten. Move one across. 10 + 3 = 13. 13 − 9: count up from 9. Ten, eleven, twelve, thirteen. Four hops. Three problems, three tools. Look at the numbers before you start working.