Early Math · Grade K

Making Ten and Breaking Numbers Apart

Quick answer

A number can be broken into two parts in more than one way: 5 is 4 and 1, and it is also 3 and 2. The most useful break is into ten. A ten-frame shows it: the filled boxes and the empty boxes together make a full frame of 10, so the empty boxes show how many more are needed to make ten.

What you'll learn

  • Break numbers up to 10 into two parts in more than one way
  • Find the number that makes 10 with a given number
  • Record the parts with drawings and number sentences

A number has parts

Here are 55 dots. Some are blue and some are orange.

Five as four and one A ten-frame with four blue dots and one orange dot, five in all.
Five as four and one

44 blue and 11 orange make 55. So 55 is 44 and 11.

The same 55 dots can be split in a new way:

Five as three and two A ten-frame with three blue dots and two orange dots, five in all.
Five as three and two

Now 55 is 33 and 22. A number can be split in more than one way.

5=4+15=3+25 = 4 + 1 \qquad 5 = 3 + 2

Make ten

Ten is a very big deal in math. So it helps to know the ways to make 1010.

Put 77 dots in a ten-frame. How many more do you need to fill it?

Seven in a ten-frame A ten-frame with seven dots: five on top and two on the bottom. Three boxes are empty.
Seven in a ten-frame

Look at the empty boxes. There are 33. So 77 and 33 make 1010.

7+3=107 + 3 = 10

Why the empty boxes show the answer

A ten-frame has 1010 boxes. Each box is either full or empty.

So the full ones and the empty ones always add up to 1010. If 77 are full, the rest are empty, and the rest is how many more you need.

Full boxes plus empty boxes make 1010, every time.

All the ways to make ten

PartPartWhole
11991010
22881010
33771010
44661010
55551010

Turn a pair around and it still makes 1010. 99 and 11 is the same total as 11 and 99.

Worked examples

Common mistakes

Practice problems

  1. What goes with 99 to make 1010?

    Answer

    11

    Full solution

    A frame with 99 has 11 empty box.

  2. What goes with 55 to make 1010?

    Answer

    55

    Full solution

    The top row is full and the bottom row is empty. The bottom row has 55 boxes.

  3. How many more make 1010?

    How many more make ten? A ten-frame with six dots: five on top and one on the bottom. Four boxes are empty.
    How many more make ten?
    Answer

    44

    Full solution

    Count the empty boxes: there are 44. So 6+4=106 + 4 = 10.

  4. Split 44 into two parts. Give two ways.

    Answer

    33 and 11; 22 and 22

    Full solution

    4=3+14 = 3 + 1 and 4=2+24 = 2 + 2. You could also say 4=4+04 = 4 + 0.

  5. What goes with 22 to make 1010?

    Answer

    88

    Full solution

    A frame with 22 has 88 empty boxes.

  6. Split 77 into two parts. Give two ways.

    Answer

    Two of: 66 and 11, 55 and 22, 44 and 33

    Full solution

    Any two parts that make 77 work. 7=5+27 = 5 + 2 and 7=4+37 = 4 + 3 are two ways.

  7. What goes with 33 to make 1010?

    Answer

    77

    Full solution

    3+7=103 + 7 = 10. It is the same pair as 77 and 33, turned around.

  8. Split 1010 into two equal parts.

    Answer

    55 and 55

    Full solution

    The top row of a ten-frame is 55, and so is the bottom row.

  9. Split 88 into two parts where one part is 66. What is the other part?

    Answer

    22

    Full solution

    Start at 66 and count on to 88: 77, 88. That is 22 more.

  10. To make 1010 from 66, Rosa puts 66 in a ten-frame and says the answer is 66. What went wrong?

    Hint

    Which boxes show how many more you need?

    Answer

    She counted the full boxes. She needs the empty ones: 44.

    Full solution

    The 66 full boxes are what she has. The empty boxes are what she needs.

    There are 44 empty boxes, so 6+4=106 + 4 = 10.

Frequently asked questions

What does it mean to break a number apart?

To split it into two parts that add back to it. 6 can be 5 and 1, 4 and 2, or 3 and 3.

What are the ways to make 10?

1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, and the same pairs turned around, plus 0 and 10.

How does a ten-frame help make ten?

Fill the frame with the number you have. The empty boxes show how many more make 10.

Why is making ten useful?

Ten is the building block of our numbers. Knowing the pairs that make 10 makes adding bigger numbers much faster later on.

Is 3 and 7 different from 7 and 3?

The order is different, but both make 10. Turning the parts around never changes the total.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.K.OA.A.3Operations and Algebraic ThinkingDecompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
  • CCSS.MATH.CONTENT.K.OA.A.4Operations and Algebraic ThinkingFor any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.