Addition
In this topic you will
- Add ones or tens to a $2$-digit number.
- Add $3$ or more small numbers together.
- Use complements of $10$ to find complements of $20$ and tens numbers to $100$.
Key Words
- column addition
- complement (of $10$, $20$ and tens numbers to $100$)
- digit
- place holder
- place value grid
Show Definitions
- column addition: A method of adding numbers by writing them under each other in place-value columns (ones, tens, hundreds) and adding each column.
- complement (of $10$, $20$ and tens numbers to $100$): The number you add to reach a target total such as $10$, $20$, or a multiple of $10$ up to $100$ (for example, the complement of $10$ to $10$ is $3$).
- digit: Any single number symbol from $0$ to $9$ used to write larger numbers.
- place holder: A symbol (often $0$) used to show an empty place in a number so the place value of the other digits stays correct.
- place value grid: A chart with columns such as tens and ones that helps you sort digits into the correct place value when reading, writing, or calculating with numbers.
Adding amounts together
You will often need to add two amounts together to find out how many altogether.
Using place value to calculate
As the numbers get larger, counting takes too long and it is easy to make a mistake. A place value grid will help you to calculate.
❓ EXERCISES
Exercise $5.1$
1. Draw two different arrangements for $7$ on the ten frames.
👀 Show answer
Example answers (two different arrangements for $7$):
- Arrangement $1$: Fill the first row with $5$ dots, then place $2$ dots at the start of the second row. (That makes $5 + 2 = 7$.)
- Arrangement $2$: Place $4$ dots on the first row and $3$ dots on the second row. (That makes $4 + 3 = 7$.)
2. Find the totals.
a. $41 + 6$$=$
b. $35 + 4$$=$
c. $73 + 4$$=$
d. $62 + 7$$=$
e. $37 + 2$$=$
f. $53 + 3$$=$
👀 Show answer
a.$41 + 6 = 47$
b.$35 + 4 = 39$
c.$73 + 4 = 77$
d.$62 + 7 = 69$
e.$37 + 2 = 39$
f.$53 + 3 = 56$
3. Find the totals.
a. $64 + 5$
b. $71 + 6$
c. $46 + 2$
👀 Show answer
a.$64 + 5 = 69$
b.$71 + 6 = 77$
c.$46 + 2 = 48$
❓ EXERCISES
$4.$ Find the totals.
a. $57 + 10 =$
b. $34 + 10 =$
c. $79 + 10 =$
d. $48 + 20 =$
e. $65 + 20 =$
f. $26 + 30 =$
👀 Show answer
a.$57 + 10 = 67$
b.$34 + 10 = 44$
c.$79 + 10 = 89$
d.$48 + 20 = 68$
e.$65 + 20 = 85$
f.$26 + 30 = 56$
$5.$ Find the totals.
a. $37 + 10$
b. $61 + 20$
c. $56 + 30$
👀 Show answer
a.$37 + 10 = 47$
b.$61 + 20 = 81$
c.$56 + 30 = 86$
$6.$ $6 + 4 = 10.$ Use this to help you write two number sentences to show complements of $20$ and one number sentence to show complements of $100$ using tens numbers.
👀 Show answer
Two complements of $20$:
$16 + 4 = 20$
$6 + 14 = 20$
One complement of $100$ using tens numbers:
$60 + 40 = 100$
$7.$ Use the number bonds for $5$ to help you write number sentences to show the complements of $50$ using tens numbers.
👀 Show answer
$10 + 40 = 50$
$20 + 30 = 50$
$50 + 0 = 50$
❓ EXERCISES
$8$. Find the totals.
a. $9 + 6 + 1 =$
b. $5 + 7 + 5 =$
c. $7 + 4 + 3 =$
Write some calculations that add $4$ single-digit numbers for your partner to solve. Swap calculations.
What made the calculations hard or easy? Discuss with your partner.
👀 Show answer
a.$9 + 6 + 1 = 16$
b.$5 + 7 + 5 = 17$
c.$7 + 4 + 3 = 14$
Examples of $4$ single-digit additions:
$3 + 7 + 2 + 8 = 20$
$9 + 1 + 4 + 6 = 20$
$5 + 5 + 5 + 5 = 20$
$8 + 2 + 7 + 3 = 20$
What made them hard or easy: They are easier when you can spot pairs that make $10$ (like $7+3$ or $9+1$) or doubles (like $5+5$). They are harder when the numbers do not make easy pairs and you have to keep track of lots of small steps.
🧠 Think like a Mathematician
Task: Keep adding three single-digit numbers in the same pattern.
$1 + 2 + 3 = 6$
$2 + 3 + 4 = \_\_\_$
$3 + 4 + 5 = \_\_\_$$\dots$
What do you notice?
Can you say why? Think about it and write your reasons.
Show Answers
- Totals:$2 + 3 + 4 = 9$ and $3 + 4 + 5 = 12$.
- What you might notice: The totals go up by $3$ each time: $6, 9, 12, \dots$.
- Why this happens: Each time, every number in the sum increases by $1$, so the total increases by $1 + 1 + 1 = 3$.