Complete Guide to Making Tens Strategy in Grade 1

Master the making tens strategy: number bonds, addition facts, and mental math through comprehensive explanations and visual learning aids.

Detailed Solutions: Exercises 1 to 3
1 Making tens with 9 + 5
Exercise 1
Solve: 9 + 5 using the making tens strategy
Definition:

Making Tens Strategy: A mental math technique that uses the benchmark number 10 to simplify addition problems by breaking apart numbers strategically

Making tens method:
  1. Look at the first number and determine how many more are needed to make 10
  2. Break apart the second number into two parts: the amount needed to make 10 and the remainder
  3. Add to make 10, then add the remainder
Original Problem
9 + 5
Make Tens
9 + 1 = 10
Remainder
4 left
Final Answer
10 + 4 = 14
Step 1: Identify what's needed to make 10

Starting with 9, we need 1 more to make 10

Step 2: Break apart the second number

Split 5 into 1 and 4 (because 1 + 4 = 5)

Step 3: Make 10 and add the remainder

9 + 1 = 10, then 10 + 4 = 14

Making Tens Visualization
9️⃣
Start with 9
9
➕
Plus 1 more
to make 10
🎯
Make 10
9 + 1 = 10
➕
Add remainder
10 + 4 = 14
0 2 4 6 8 10 12 14 16
9
10
14
9 + 5 = (9 + 1) + 4 = 10 + 4 = 14
9
1
4
9 + 5 = 14
Final answer:

9 + 5 = 14

Applied rules:

• Number Bonds: Understanding that 9 + 1 = 10

• Decomposition: Breaking apart numbers into manageable parts

• Associative Property: Grouping numbers in a way that makes addition easier

2 Making tens with 8 + 6
Exercise 2
Solve: 8 + 6 using the making tens strategy
Definition:

Number Bonds: Pairs of numbers that add up to a specific total (especially 10)

Original Problem
8 + 6
Make Tens
8 + 2 = 10
Remainder
4 left
Final Answer
10 + 4 = 14
Step 1: Identify what's needed to make 10

Starting with 8, we need 2 more to make 10

Step 2: Break apart the second number

Split 6 into 2 and 4 (because 2 + 4 = 6)

Step 3: Make 10 and add the remainder

8 + 2 = 10, then 10 + 4 = 14

Number Bonds for Making Tens
8️⃣
First Number
8
❓
To Make 10
8 + 2 = 10
6️⃣
Second Number
6 = 2 + 4
✅
Final Answer
10 + 4 = 14
0 2 4 6 8 10 12 14 16
8
10
14
8 + 6 = (8 + 2) + 4 = 10 + 4 = 14
8
2
4
8 + 6 = 14
Final answer:

8 + 6 = 14

Applied rules:

• Number Bonds to 10: 8 + 2 = 10

• Decomposition: Breaking 6 into 2 + 4

• Strategy: Making 10 first simplifies the addition

3 Making tens with 7 + 5
Exercise 3
Solve: 7 + 5 using the making tens strategy
Definition:

Mental Math Strategy: Using known facts to solve more complex problems efficiently

Original Problem
7 + 5
Make Tens
7 + 3 = 10
Remainder
2 left
Final Answer
10 + 2 = 12
Step 1: Identify what's needed to make 10

In 7 + 5, we need 3 more to make 10 from 7

Step 2: Break apart the second number

Split 5 into 3 and 2 (because 3 + 2 = 5)

Step 3: Make 10 and add the remainder

7 + 3 = 10, then 10 + 2 = 12

Mental Math Visualization
7️⃣
Start with 7
7
➕
Plus 3
7 + 3 = 10
5️⃣
Break 5
5 = 3 + 2
✅
Answer
10 + 2 = 12
0 2 4 6 8 10 12 14 16
7
10
12
7 + 5 = (7 + 3) + 2 = 10 + 2 = 12
7
3
2
7 + 5 = 12
Final answer:

7 + 5 = 12

Applied rules:

• Number Bonds: 7 + 3 = 10

• Decomposition: Breaking 5 into 3 + 2

• Mental Math: Using 10 as a benchmark makes calculations easier

Making Tens Strategy: Complete Summary
Comprehensive Guide to Making Tens Strategy
Key Definitions

Making Tens Strategy: A mental math technique that uses the benchmark number 10 to simplify addition problems by breaking apart numbers strategically.

Number Bonds: Pairs of numbers that add up to a specific total, especially 10 (like 7 + 3, 6 + 4).

Decomposition: Breaking apart numbers into smaller, more manageable parts to make calculations easier.

Core Rules & Principles

• Benchmark Rule: Use 10 as a reference point since it's easy to add to any number

• Decomposition Rule: Break apart the second number to provide what's needed to make 10

• Associative Property: Group numbers in a way that makes addition easier

Step-by-Step Method

1. Look at the first number and determine what's needed to make 10

2. Break apart the second number into the needed amount and the remainder

3. Add to make 10, then add the remainder

4. Verify your answer by counting or using another strategy

Examples & Applications

Simple: 8 + 4 = (8 + 2) + 2 = 10 + 2 = 12

Intermediate: 9 + 6 = (9 + 1) + 5 = 10 + 5 = 15

Advanced: 7 + 8 = (7 + 3) + 5 = 10 + 5 = 15

Common Pitfalls

• Forgetting to adjust the second number after making 10

• Miscounting the needed amount to make 10

• Not recognizing when the strategy applies

Key Takeaways

• Practice number bonds to 10 until they become automatic

• Use visual aids like ten frames and number lines

• Choose the most efficient approach based on the numbers

\(a + b = (a + c) + d\)
Where a + c = 10 and c + d = b
Number Bonds to 10
1 + 9 = 10
One and nine make ten
Number Bonds to 10
2 + 8 = 10
Two and eight make ten
Number Bonds to 10
3 + 7 = 10
Three and seven make ten
Number Bonds to 10
4 + 6 = 10
Four and six make ten
Number Bonds to 10
5 + 5 = 10
Five and five make ten
Tip 1: Practice number bonds to 10 daily until they become automatic.
Tip 2: Use fingers, counters, or drawings to visualize the process.
Tip 3: Start with the larger number to minimize counting.
Tip 4: Always check your work by counting or using another strategy.
Tip 5: Apply the same principle to subtraction by thinking about related addition facts.
Detailed Solutions: Exercises 4 to 5
4 Making tens for subtraction
Exercise 4
Solve: 15 - 7 using the making tens strategy
Definition:

Making Tens for Subtraction: Using knowledge of tens and related addition facts to solve subtraction problems

Original Problem
15 - 7
Think Addition
7 + ? = 15
Make Tens
7 + 3 = 10
Then 5 More
10 + 5 = 15
Final Answer
3 + 5 = 8
Step 1: Think of the related addition fact

What plus 7 equals 15? (7 + ? = 15)

Step 2: Use making tens strategy

From 7, how many to make 10? That's 3. Then from 10 to 15 is 5 more.

Step 3: Add the amounts together

3 + 5 = 8, so 15 - 7 = 8

Subtraction Using Making Tens
1️⃣5️⃣
Total
15
➖
Take Away
7
❓
Left Over
8
💡
Strategy
Think: 7 + 8 = 15
0 2 4 6 8 10 12 14 16
7
10
15
15 - 7 = 8 because 7 + 8 = 15
7
3
5
15 - 7 = 8
Final answer:

15 - 7 = 8

Applied rules:

• Related Facts: Understanding that addition and subtraction are inverse operations

• Making Tens: Using 10 as a benchmark for calculation

• Decomposition: Breaking the problem into manageable parts

5 Complex making tens
Exercise 5
Solve: 6 + 9 using the making tens strategy
Definition:

Flexible Making Tens: Choosing which number to make tens from based on efficiency

Original Problem
6 + 9
Make Tens from 9
9 + 1 = 10
Break Apart 6
6 = 1 + 5
Final Answer
10 + 5 = 15
Step 1: Look at both numbers

6 + 9: It's easier to make 10 from 9 (need 1) than from 6 (need 4)

Step 2: Break apart the other number

Break 6 into 1 + 5, so we can make 9 + 1 = 10

Step 3: Add the remaining part

10 + 5 = 15

Flexible Making Tens Strategy
6️⃣
First Number
6
9️⃣
Second Number
9
🎯
Make Tens from 9
9 + 1 = 10
✅
Final Answer
10 + 5 = 15
0 2 4 6 8 10 12 14 16
9
10
15
6 + 9 = 9 + 6 = (9 + 1) + 5 = 10 + 5 = 15
9
1
5
6 + 9 = 15
Final answer:

6 + 9 = 15

Applied rules:

• Commutative Property: 6 + 9 = 9 + 6

• Efficiency: Choose the easier number to make 10 from

• Flexibility: Adapt the strategy to fit the numbers given

Questions & Answers

Question: My child is struggling with the making tens strategy. They understand that 8 needs 2 more to make 10, but they get confused when breaking apart the second number. How can I help them?

Answer: This is a very common challenge! Here's a systematic approach to help your child:

  • Use concrete manipulatives: Have your child use 10 small objects (counters, blocks, etc.) to physically show the numbers. Place 8 objects on one side and 5 on the other.
  • Visualize the "bridge": Show them that they need to take 2 from the group of 5 to add to the 8 to make 10. This leaves 3 in the second group.
  • Practice the decomposition separately: Before attempting addition, practice just breaking apart numbers. For example, "Show me all the ways to make 5" (0+5, 1+4, 2+3).
  • Use ten frames: Draw or use physical ten frames to show how numbers fill up to make 10.

The key is to slow down and focus on the decomposition step. Many children need extra practice with breaking apart numbers before they can apply it in the context of addition.

Question: Should I teach students to always make 10 from the first number, or should they have flexibility in choosing which number to build from?

Answer: Flexibility is crucial! While many textbooks introduce making tens by building from the first number, students should learn to choose the most efficient approach. Consider 3 + 9 versus 9 + 3:

  • For 3 + 9: It's more efficient to take 1 from 3 to make 9 into 10, leaving 2, so 10 + 2 = 12
  • For 9 + 3: It's more efficient to take 1 from 3 to make 9 into 10, leaving 2, so 10 + 2 = 12

Teach students to look at both numbers and choose the path that requires fewer steps. In 8 + 6, taking 2 from 6 to make 8 into 10 is more direct than taking 4 from 8 to make 6 into 10. This develops number sense and mathematical reasoning skills.

Start with the systematic approach (building from the first number) to establish the concept, then gradually introduce flexibility as students become more comfortable.

Question: Why do we have to make 10? Can't I just count on my fingers?

Answer: Great question! Counting on fingers works for small numbers, but making 10 helps you become faster and better at math. Think of it like this:

  • Counting takes time: If you have to add 8 + 7 by counting, you might count 8, 9, 10, 11, 12, 13, 14, 15 - that's 7 counts!
  • Making 10 is faster: You know 8 needs 2 more to make 10, and 7 has 2 + 5, so 10 + 5 = 15. Just 2 steps!
  • It builds your brain: Making 10 helps you understand how numbers work together, which makes harder math easier later.

Once you practice making 10, it becomes automatic - like knowing that 5 + 5 = 10. It's a tool that makes math easier and more fun!

Plus, when you get to bigger numbers like 18 + 7, making 10 from 18 (which becomes 20 + 5 = 25) is much easier than counting 19, 20, 21, 22, 23, 24, 25!