B. Number · Number Sense: Numbers to 50 and FractionsTens and Ones: Building and Breaking Apart Numbers
B1.2 B1.1About 35 minutes
Learning goals- I can build a number to 50 using tens and ones.
- I can tell how many tens and ones are in a number.
- I can break a number apart in more than one way.
Words to know
ten
A group of 10 ones. A full ten frame shows one ten.
ones
Single things that are not in a group of ten.
compose
To build or put a number together from parts. 3 tens and 4 ones compose 34.
decompose
To break a number apart into parts. 34 can be decomposed into 30 and 4.
parts and whole
The whole is the total. The parts are the smaller numbers that make it.
Building numbers like a builder
Imagine you have a giant pile of 34 building blocks. Counting them one by one takes a long time, and it's easy to lose your place. What if we put them in groups of ten?
Groups of ten make big numbers easy to count and easy to understand. Today you will compose (build) and decompose (break apart) numbers using tens and ones.
What is a ten?
When we have 10 ones, we can bundle them into one ten. Think of 10 popsicle sticks with an elastic around them, a full ten frame, or a ten rod in base-ten blocks.
10 ones = 1 ten
Tens and ones in a number
In a two-digit number:
- The first digit tells how many tens.
- The second digit tells how many ones.
Look at 34. The 3 means 3 tens (that's 30). The 4 means 4 ones.
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| Number | Tens | Ones | Count it |
|---|
| 34 | 3 | 4 | 10, 20, 30, 31, 32, 33, 34 |
| 21 | 2 | 1 | 10, 20, 21 |
| 47 | 4 | 7 | 10, 20, 30, 40, 41, 42, 43, 44, 45, 46, 47 |
| 50 | 5 | 0 | 10, 20, 30, 40, 50 |
| 9 | 0 | 9 | 1, 2, 3, 4, 5, 6, 7, 8, 9 |
Worked exampleComposing a number
Grandpa has 4 bags of hockey pucks with 10 pucks in each bag. He also has 6 loose pucks. How many pucks does he have?
- 4 bags of 10 is 4 tens. Count by 10s: 10, 20, 30, 40.
- 6 loose pucks is 6 ones. Keep counting: 41, 42, 43, 44, 45, 46.
- 4 tens and 6 ones compose the number 46.
Worked exampleDecomposing a number
How many tens and how many ones are in 28?
- Look at the first digit: 2. That means 2 tens (20).
- Look at the second digit: 8. That means 8 ones.
- Check with ten frames: 2 full ten frames and 8 more is 10, 20, 21, 22, 23, 24, 25, 26, 27, 28. Yes!
28 = 2 tens and 8 ones, or 20 + 8.
Breaking numbers apart in different ways
A number can be broken apart in many ways, not just tens and ones! The whole stays the same, but the parts change.
Let's decompose 12:
| Part | Part | Whole |
|---|
| 10 | 2 | 12 |
| 6 | 6 | 12 |
| 5 | 7 | 12 |
| 8 | 4 | 12 |
| 11 | 1 | 12 |
| 9 | 3 | 12 |
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12 cookies on two plates: 5 and 7 make 12.Bigger numbers can be broken apart in many ways too. Here are some ways to make 34:
- 30 and 4 (3 tens and 4 ones)
- 20 and 14 (2 tens and 14 ones)
- 10 and 24 (1 ten and 24 ones)
- 17 and 17 (two equal parts, or doubles!)
- 25 and 9
All of these are still 34. If we open one ten and spill out its ones, we still have the same amount!
Big idea
When we trade 10 ones for 1 ten (or 1 ten for 10 ones), the number does not change. 1 ten and 10 ones are the same amount.
Worked exampleMany ways to make a number
Show 25 in three different ways.
- Way 1: tens and ones. 25 is 2 tens and 5 ones, or 20 and 5.
- Way 2: open a ten. 1 ten and 15 ones, or 10 and 15.
- Way 3: think of money or fives. 25 is five groups of 5: 5, 10, 15, 20, 25. Or 20 and 5, or 15 and 10.
25 = 20 + 5 = 10 + 15 = 5 + 5 + 5 + 5 + 5. All show 25.
Making ten
Knowing the pairs of numbers that make 10 is a super power! It helps you fill a ten frame quickly.
0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5
Just for funWhy is a ten rod never lonely?
Because it is 10 ones all stuck together!
Hands-on activityBundle it up!
You need: about 50 small things (straws, popsicle sticks, pasta, buttons or LEGO bricks), elastics or small bags or cups, and paper.
- Grab a big handful. Don't count yet!
- Make groups of 10. Put an elastic around each 10 sticks, or put 10 things in each cup.
- Count the groups by 10s, then count the leftovers by 1s.
- Write the number. Say: "I have \_\_ tens and \_\_ ones. That makes \_\_."
- Now open up one group of ten. How many tens and ones now? Is it still the same number?
- Grab a new handful and do it again!
Hands-on activityPart-part-whole mat
Fold a paper in half and draw a line. Put 15 buttons on the table. Split them between the two halves in as many different ways as you can. Write each way: 10 and 5, 8 and 7, 12 and 3 ... How many ways did you find?
Your turn!
1How many tens and ones are in 43?
2What number is 2 tens and 9 ones?
3What number is 5 tens and 0 ones?
4Fill in the blank: 37 = 30 + \_\_
5Fill in the blank: 20 + 6 = \_\_
63 full ten frames and 2 more dots. What number is it?
71 ten and 16 ones. What number is it?
10 + 16 = 26. (It's the same as 2 tens and 6 ones.)
8Find two numbers that make 15. Can you find another way?
Some answers: 10 and 5, 7 and 8, 9 and 6, 12 and 3, 14 and 1.
More practice: warm-up
1How many tens and ones are in 19?
2What number is 4 tens and 2 ones?
3Fill in the blank: 40 + 5 = \_\_
4How many more strawberries do you need to make 10?
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There are 6. 6 and 4 make 10.
5True or false: 10 ones is the same amount as 1 ten.
True. We can bundle 10 ones into 1 ten.
More practice: on your own
1Hana has 3 bundles of 10 popsicle sticks and 5 loose sticks. What number does she have?
3 bundles is 3 tens: 10, 20, 30. Then 5 ones: 31, 32, 33, 34, 35. She has 35 sticks (3 tens and 5 ones).
2Fill in the blanks: 48 = \_\_ tens and \_\_ ones
4 tens and 8 ones. The first digit tells the tens and the second digit tells the ones.
3What number is 2 tens and 12 ones?
2 tens is 20. 20 and 12 more is 32. (12 ones is 1 ten and 2 ones, so it is the same as 3 tens and 2 ones.)
4Break apart 16 in two different ways.
Some answers: 10 and 6, 8 and 8, 9 and 7, 11 and 5, 12 and 4. Each pair makes 16.
5Nadia has 27 stickers. Each page of her sticker book holds 10. How many pages can she fill? How many stickers are left over?
27 is 2 tens and 7 ones. She can fill 2 pages, and 7 stickers are left over.
Challenge
1Find the mistake! Owen says 3 tens and 6 ones is 63. Is he right? Explain.
No. 3 tens is 30, and 6 ones more makes 36. The tens digit comes first. 63 would be 6 tens and 3 ones.
2Ana has 4 ten rods. Ben has 2 ten rods and 20 ones cubes. Who has more? How do you know?
They have the same amount. Ana has 40. Ben's 20 ones cubes can be bundled into 2 tens, so he has 2 tens and 2 tens, which is 4 tens, or 40.
3Show 23 with ten rods and ones cubes in three different ways.
2 tens and 3 ones (20 and 3). 1 ten and 13 ones (10 and 13). 0 tens and 23 ones (all cubes). Each way is still 23.
Quiz
1. What number has 3 tens and 8 ones?
3. Which is another way to make 24?
4. Kai has 1 ten and 13 ones. What number does he have?
6. Which number is the same as 4 tens and 5 ones?
7. Leah has 3 tens and 11 ones. What number does she have?
What your child is learning: that numbers to 50 can be built from tens and ones (place value), and that a number can be broken apart in many ways while the total stays the same. This is a key idea for adding and subtracting later.
Common mistakes and how to help:
- Thinking the 3 in 34 means three. Ask "3 what?" and point to 3 bundles of ten. Physical bundles (straws, popsicle sticks) are better than pictures at first.
- Writing "1 ten and 13 ones" as 113. Build it with objects, then count. Show that 13 ones can be traded for 1 ten and 3 ones.
- Believing there is only one right way to split a number. Praise different answers: "8 and 7 and 10 and 5 both make 15. Can you find another?"
Everyday practice: bundle crayons or utensils into tens. Ask how many tens and ones there are in your house number or in your child's age in months.
Math talk questions: "How do you know?" "Is there another way to make that number?" "What changed and what stayed the same when we opened the ten?"