All the Ways to Make 6 and 7

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Watch the idea first — 57 seconds. Then read on, and try it yourself in the next step.

Go in order

Start with 0 in the first tray. Then 1. Then 2. You will not miss any.

Go in order and you cannot miss one

Start with 0 in the first tray. The other holds 6. Now 1. The other holds 5. Now 2. The other holds 4. Now 3, and 3. Keep going: 4 and 2, 5 and 1, 6 and 0. Seven ways. Going in order is how you know you have them all.

Step 2: Try It Yourself

Find every way. The gallery fills as you go.

Move the blocks to find every way to make 6.

6

0

6

First tray

Empty

Tap one to move it across

Second tray

Tap one to move it back

0 and 6 make 6.

Ways to make 6

0 of 7 found

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Blocks in all

First tray

The same whole, in a frame. One part is colored; the rest is the other part.

How many6

6 and 4 make 10. There are 4 empty spaces.

3 and 3 make 6.

Counters

First part

Step 3: In Real Life

Cupcakes on two plates

Six cupcakes for two plates. 5 and 1. 4 and 2. 3 and 3. Every way works. Only one is fair.

Step 4: Watch an Example

Watch how to find them in order.

Watch Ana Find Them in Order

Ana finds every way to make 6 without missing one.

Step 1
She starts with 0 blocks in the first tray. That leaves 6.
6
0
6
First tray
Empty
Tap one to move it across
Second tray
Tap one to move it back
0 and 6 make 6.
Blocks in all6
First tray0

Watch Leo Find the Ways to Make 7

Leo finds the ways to make 7. He starts. You finish.

Step 1
Leo starts with 0 in the first tray. The other holds 7.
7
0
7
First tray
Empty
Tap one to move it across
Second tray
Tap one to move it back
0 and 7 make 7.
Blocks in all7
First tray0

Step 5: Your Turn

Practice makes it stick.

Two Pockets

Problem 1 of 14

Sam has 7 marbles in two pockets. One pocket has 5. How many are in the other?

Two Plates

Problem 2 of 14

Mom has 6 cupcakes and two plates. Each plate gets the same. How many on each plate?

Parts of 6 and 7

Find the other part.

Problem 3 of 14

1 and what make 6?

Problem 4 of 14

2 and what make 7?

Problem 5 of 14

6 and what make 7?

Problem 6 of 14

0 and what make 6?

Find the Mistake

A friend made a slip. Find it, then fix it.

Problem 7 of 14

Leo lists the ways to make 6. What went wrong?

Leo’s ways to make 6

10 and 6
21 and 5
33 and 3
44 and 2
55 and 1
66 and 0

Problem 8 of 14

Fix Leo’s list. 2 and what make 6?

Problem 9 of 14

Ana wants to make 7. She fills two trays. What went wrong?

Problem 10 of 14

Ana keeps 4 in the first tray. 4 and what make 7?

Which Way?

Pick the way that works best.

Problem 11 of 14

You want every way to make 7. Which way is best?

Problem 12 of 14

You know 2 and 5 make 7. Which way finds 5 and what make 7?

Now Try 7

Change the whole to 7. How many ways will there be? Find them all.

Problem 13 of 14

7

0

7

First tray

Empty

Tap one to move it across

Second tray

Tap one to move it back

0 and 7 make 7.

Ways to make 7

0 of 8 found

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Blocks in all

First tray

Show the Missing Part

Build it, then check.

Problem 14 of 14

6 is 3 and how many? Show that part.

Tap the boxes.

How many0

Counters

Step 6: Quick Check

Show what you know.

Question 1 of 2

4 and what make 6?

Question 2 of 2

3 and what make 7?

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

Stretch 1 of 1

6 has seven ways. How many ways make 5?

What You Learned

A number can be split many ways.
Going in order helps you find them all.
2 and 4 makes 6, and so does 4 and 2.

For the grown-up

Counting and knowing how many are different skills. A child can recite to twenty and still recount a row of six every time they are asked, because the last number said has not yet become the answer to "how many".

Watch for recounting. If they count a group, are asked how many, and start again from one, the link has not formed yet. It is extremely common at this age and is not a memory problem.

When it happens, count together slowly and then close your hand over the group and ask again. Hiding the objects is what forces the number to stand in for them.

There is more than one way to make 6. There are seven ways in all.

Work in order so you find them all — Start with 0 and 6, then 1 and 5, then 2 and 4. Going in order is how you know when you have finished, instead of hoping you have.

One side grows, the other shrinks — Every time the first part goes up by one, the second goes down by one. It has to, or the whole would change.