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\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
International Baccalaureate · PYP 1

Number Bonds to 10 and Doubles

⌚ ~82 min ▢ 8 blocks ✓ 54 exercises ➣ Prerequisites : Numbers to 100, Adding Within 10
I Complements to 10

We look for the pairs of numbers that make 10 together.
A ten-frame is a box that holds exactly 10 counters. There are 7 counters in the box.
Figure
How many empty spaces are there? How many more counters do we need to make a full ten?

By counting the empty spaces, we can see that we need 3 more counters to make 10.
Figure
The number 3 is the complement of 7: together, they make 10.


Definition — Complements to 10
The complement to 10 of a number from 0 to 10 is the number we add to it to make 10: the two numbers form a number bond to 10.
Number Complement Sum Cubes Ten-Frame Fingers
\(\textcolor{colordef}{0}\) \(\textcolor{colorprop}{10}\) \(\textcolor{colordef}{0}+\textcolor{colorprop}{10}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{1}\) \(\textcolor{colorprop}{9}\) \(\textcolor{colordef}{1}+\textcolor{colorprop}{9}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{2}\) \(\textcolor{colorprop}{8}\) \(\textcolor{colordef}{2}+\textcolor{colorprop}{8}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{3}\) \(\textcolor{colorprop}{7}\) \(\textcolor{colordef}{3}+\textcolor{colorprop}{7}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{4}\) \(\textcolor{colorprop}{6}\) \(\textcolor{colordef}{4}+\textcolor{colorprop}{6}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{5}\) \(\textcolor{colorprop}{5}\) \(\textcolor{colordef}{5}+\textcolor{colorprop}{5}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{6}\) \(\textcolor{colorprop}{4}\) \(\textcolor{colordef}{6}+\textcolor{colorprop}{4}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{7}\) \(\textcolor{colorprop}{3}\) \(\textcolor{colordef}{7}+\textcolor{colorprop}{3}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{8}\) \(\textcolor{colorprop}{2}\) \(\textcolor{colordef}{8}+\textcolor{colorprop}{2}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
\(\textcolor{colordef}{9}\) \(\textcolor{colorprop}{1}\) \(\textcolor{colordef}{9}+\textcolor{colorprop}{1}=10\) Figure Figure Figure\(+\)Figure\(=\)Figure
The complement to 10 of \(10\) is \(0\): \(\textcolor{colordef}{10}+\textcolor{colorprop}{0}=10\).
Method — Counting Up to 10
To find the complement of a number, count up from this number to 10. For \(\textcolor{colordef}{7}\): \(8\), \(9\), \(10\) — we count 3 numbers, so \(\textcolor{colordef}{7}+\textcolor{colorprop}{3}=10\). We can raise one finger for each number counted.
Example
Find the complement of \(\textcolor{colordef}{8}\).

Counting up from \(8\): \(9\), \(10\) — that is \(\textcolor{colorprop}{2}\) numbers, so \(\textcolor{colordef}{8}+\textcolor{colorprop}{2}=10\).
Figure

Skills to practice
  • Finding Complements to 10 Using Ten-Frames
  • Finding Complements to 10 Using Cubes
  • Finding Complements to 10 Using Fingers
  • Finding Complements to 10
II The Doubles

Dad buys marbles for Hugo and Louis. To be fair, he buys 3 marbles for Hugo, and the same number for Louis.
Figure
How many marbles does Dad buy in all?

Dad buys \(3 + 3 = \textbf{6}\) marbles: twice the same number. When we add a number to itself, we get its double: the double of 3 is 6.


Definition — Double
The double of a number is the number plus itself. $$\text{double of } 4 = 4 + 4 = 8$$ The doubles to know by heart:
Number 1 2 3 4 5 6 7 8 9 10
Double 2 4 6 8 10 12 14 16 18 20
It works for whole tens too: the double of \(30\) is \(60\), because \(3\) tens plus \(3\) tens make \(6\) tens.
Example
Find the double of \(7\).

The double of \(7\) is \(\textcolor{colordef}{7} + \textcolor{colorprop}{7}\). The first \(\textcolor{colordef}{7}\) and \(\textcolor{colorprop}{3}\) of the second \(\textcolor{colorprop}{7}\) fill one ten-frame, and the other \(\textcolor{colorprop}{4}\) go into a second ten-frame.
Figure
$$\begin{aligned}[t]\textcolor{colordef}{7}+\textcolor{colorprop}{7} &= \textcolor{colordef}{7}+\textcolor{colorprop}{3}+\textcolor{colorprop}{4} && \text{(split the second \(7\))}\\ &=10+\textcolor{colorprop}{4} && \text{(\(\textcolor{colordef}{7}+\textcolor{colorprop}{3}=10\))}\\ &=\textbf{14}\end{aligned}$$

Example
Find the double of \(40\).

The double of \(40\): \(4\) tens plus \(4\) tens make \(8\) tens, so \(40 + 40 = \textbf{80}\).

Skills to practice
  • Finding Doubles
  • Finding the Number from its Double
  • Solving Problems with Doubles
III Going further
Skills to practice
  • Completing 10 with Pictures
  • Quiz