3.10 Find unknown quantities

Find the right hand side of the equation first then use a number line to complete the number sentence.

Add the numbers in the right hand side of the equation in a vertical algorithm. \begin{array}{c} & &1 &9 \\ &+ &1 &6 \\ \hline \\ \hline \end{array}

Add the ones column first: 9 + 6 = 15. Bring down the 5 and carry the 1 to the tens column. \begin{array}{c} & &\text{}^1 1 &9 \\ &+ &1 &6 \\ \hline & & &5 \\ \hline \end{array}

Add the tens column: 1 + 1 + 1 = 3. \begin{array}{c} & &\text{}^1 1 &9 \\ &+ &1 &6 \\ \hline & &3 &5 \\ \hline \end{array}

The simplified number sentence would be: 48 - ⬚ = 35

Locate 48 in the number line.

Jump back from 48 and count the number of units until we reach 35.

We have jumped back 13 units from 48. So the complete number sentence would be: 48 - 13 = 19 + 16

Use the number line below to count how many jumps of 9 there are between 0 and 135.

Locate where 0 and 135 is.

We can see that there are 15 jumps of 9 from 0 to 135. So, the complete statement is 9 \times 15 = 135

Simplify the number sentence and solve it to help with the more complicated number sentence.

We can simplify the number sentence to be: 40 = 8 + ⬚

To find the unknown, we locate where 8 is then jump to the right to get 40.

We have jumped 32 spaces to the right of 8.40 = 8 + 32

To complete the original number sentence, we need to find the unknown for the following number sentence: 8 \times ⬚ = 32

We can count up by multiples of 8 to get: 8,\,16,\,24,\,32, so we get 32 after 4 counts. This means that: 8\times 4 = 32

The complete number sentence is: 40 = 8 + 8 \times 4