Addition by counting on
🎯 In this topic you will
- Add numbers by counting on using a number line.
- Break numbers into smaller parts to support addition.
- Use complements to 10 to solve addition problems efficiently.
🧠 Key Words
- calculation
- complement
- method
- regroup
- solve
Show Definitions
- calculation: The process of using numbers and operations to work out a mathematical answer.
- complement: A number that combines with another number to make a target value, such as making 10 in addition.
- method: A systematic way or strategy used to solve a mathematical problem.
- regroup: To rearrange numbers in place value columns, often by carrying or borrowing, to make calculations easier.
- solve: To find the correct answer to a mathematical problem by applying appropriate steps.
Counting On to Add
We often add some more to what we have. If you have 9 marbles and win 4 in a game, it is better to count on 4 from 9 to see that you have 13 rather than having to count them all. Using a number line to help, you will be able to count on from a number instead of having to count everything.
❓ EXERCISES
1. Count on in ones. Draw your jumps.
👀 Show answer
a. $13 + 4 = 17$
b. $9 + 7 = 16$
2. Here is Erin’s number line.
What calculation is she solving?
👀 Show answer
❓ EXERCISES
3. Count on in ones. Draw and label one jump to find each total.
👀 Show answer
a. $6 + 9 = 15$
b. $11 + 8 = 19$
4. Here is Tomas’ number line.
What calculation is he solving?
👀 Show answer
🧠 Think like a Mathematician
Question: What happens when you add $0$ to a number?
How could you show adding to $0$ on a number line? For example, $0 + 4$.
Method:
- Start at $0$ on the number line.
- Count forward $4$ steps in ones.
- Mark where you land on the number line.
- Write the addition sentence that matches your jump.
Follow-up Questions:
Show Answers
- 1: You land on $4$, because $0 + 4 = 4$.
- 2: Adding $0$ does not change the number; the total stays the same.
- 3: General rule: $a + 0 = a$ for any number $a$.
❓ EXERCISES
5. Regroup $9$ in two different ways.
Regroup $15$ in two different ways.
👀 Show answer
$9 = 5 + 4$, $9 = 6 + 3$
$15 = 10 + 5$, $15 = 7 + 8$
❓ EXERCISES
6. Use complements to $10$ to help you add.
👀 Show answer
a.$8 + 7 = 15$
b.$9 + 5 = 14$
🧠 Think like a Mathematician
Question: Make a poster to show the three methods you have used to add using a number line.
How will you make each method easy to understand?
Method:
- Draw a clear number line from $0$ to $20$.
- Show the first method using counting on in ones.
- Show the second method using one large jump.
- Show the third method using complements to $10$.
- Add labels and short explanations to make each method easy to follow.
- Check that someone else could understand your poster.
Follow-up Questions:
Show Answers
- 1: The large jump or complements method is usually quickest for bigger numbers.
- 2: Counting on in ones is useful for small additions or when first learning how addition works.
- 3: Complements to $10$ help because reaching $10$ first makes the remaining addition easier to calculate.
❓ EXERCISES
7. Aliya drew a jump of $3$ and a jump of $2$. She started from number $7$. What was her calculation?
👀 Show answer
8. Choose a number from each circle to add together on a number line. Do this twice. Choose which method to use each time. Write your number sentence.
👀 Show answer
$8 + 5 = 13$
$12 + 7 = 19$
❓ EXERCISES
9. Work in a group of $4$. Use the calculations from question $8$ to help you find equivalent facts.
👀 Show answer
$6 + 9 = 7 + 8$
$8 + 5 = 9 + 4$
🧠 Think like a Mathematician
Question: Sumi says you can always use any of the three methods to add on a number line. It does not matter what the numbers are. Do you agree? Explain your thinking.
Think:
- Recall the three methods you have learned for adding on a number line.
- Try a few different addition examples using each method.
- Compare which methods work efficiently for small and large numbers.
- Decide whether Sumi’s statement is always true and explain why.
Follow-up Questions:
Show Answers
- 1: Yes, all three methods give the correct total when used properly.
- 2: The complements to $10$ or single large jump method is usually most efficient for bigger numbers.
- 3: Counting in ones is good for small numbers or beginners, large jumps are quicker for simple additions, and complements to $10$ are best when a number is close to $10$.