Number Patterns

NZ Level 3

Write multi-step number sentences from descriptions

Lesson

Learning mathematics is like learning a language. Even better, we can use maths to describe patterns or relationships between two things. Number sentences, called equations, are like stories telling us how a value has been changed to produce another value.

Just like some clever people can translate between two languages, we are now going to look at how to translate between English and Maths. Good news- you've already started learning how to do this (even if you didn't realise it)! Let's look at an example:

- In English: "I had $5$5 stickers. I earned another $3$3 stickers. Now I have $8$8 stickers."
- In Maths: $5+3=8$5+3=8

When we translate from Maths to English, we don't know as much of the "story" but we can still describe how the numbers change. Let's look at how a number (let's call it $N$`N`) has been changed.

- In Maths: $N+5=12$
`N`+5=12 - In English: "When we add
**a number**and $5$5 together, then answer is $12$12."

Did you see?

Notice how instead of $N$`N`, I wrote, "a number."

Don't forget!

Just like there's a proper way to write sentences in English, make sure you consider the order of operations when writing equations.

Which number sentence means:

"The quotient of $6\times9$6×9 and $6$6 is subtracted from $200$200."

$6\div\left(6\times9\right)-200$6÷(6×9)−200

A$6\times\left(6\times9\right)-200$6×(6×9)−200

B$200-6\times\left(6\times9\right)$200−6×(6×9)

C$200-\left(6\times9\right)\div6$200−(6×9)÷6

D$6\div\left(6\times9\right)-200$6÷(6×9)−200

A$6\times\left(6\times9\right)-200$6×(6×9)−200

B$200-6\times\left(6\times9\right)$200−6×(6×9)

C$200-\left(6\times9\right)\div6$200−(6×9)÷6

D

Use the rule to complete the table of values:

"The starting number is doubled, then $4$4 is subtracted."

Starting Number ($N$ `N`)$12$12 $13$13 $14$14 $15$15 Answer ($A$ `A`)$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ Which of these equations describes the rule above?

$A=2\times\left(N-4\right)$

`A`=2×(`N`−4)A$A=N\times2-4$

`A`=`N`×2−4B$A=N^2-4$

`A`=`N`2−4C$A=2+N-4$

`A`=2+`N`−4D$A=2\times\left(N-4\right)$

`A`=2×(`N`−4)A$A=N\times2-4$

`A`=`N`×2−4B$A=N^2-4$

`A`=`N`2−4C$A=2+N-4$

`A`=2+`N`−4D

Use the rule to complete the table of values:

"The starting number has $9$9 added to it. The sum is then multiplied by $5$5."

Starting Number ($N$ `N`)$4$4 $5$5 $6$6 $7$7 Answer ($A$ `A`)$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ Which of these equations describes the rule above?

$A=N+9\times5$

`A`=`N`+9×5A$A=\left(N+9\right)\div5$

`A`=(`N`+9)÷5B$A=N+5$

`A`=`N`+5C$A=\left(N+9\right)\times5$

`A`=(`N`+9)×5D$A=N+9\times5$

`A`=`N`+9×5A$A=\left(N+9\right)\div5$

`A`=(`N`+9)÷5B$A=N+5$

`A`=`N`+5C$A=\left(N+9\right)\times5$

`A`=(`N`+9)×5D

Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.