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Number and Algebra, NAP-C1-32 SA

Percy buys a cricket ball and a set of stumps.

The total cost is $23.

The stumps cost $3 more than the ball.

What is the cost of the ball?

$  
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`$10`

Show Worked Solution

`text(Test some numbers:)`

 `text(Stumps $12 – Ball $11)`

`= $1\ text(difference)`

`text(Stumps $13 – Ball $10)`

`= $3\ text(difference)`

 

`=>\ text(The ball must cost $10.)`

Number and Algebra, NAP-B1-21

What is the difference between the most sick days and the least sick days?

`11` `12` `13` `14`
 
 
 
 
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`13`

Show Worked Solution

`text{Most sick days (Bella) = 15}`

`text{Least sick days (Kim) = 2}`

`:.\ text(Difference)` `= 15 – 2`
  `= 13`

Number and Algebra, NAP-G1-33 SA

Marcel has the six cards pictured below.
 


  

Marcel can arrange the six cards into a number sentence that make a total, as shown below.
 


 

What is the largest total Marcel can make using all the cards in a number sentence?
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`971`

Show Worked Solution

`text(The largest total is made when the highest 3 digit)`

`text(number has the smallest 1 digit number deducted.)`

`=> 973 – 2 = 971`

Number and Algebra, NAP-D1-04

Chantelle showed this number on her calculator

She changed it so that it became this number.

What did Chantelle do to change 376 to 306?

 
 `text(added 7)`
 
 `text(subtracted 7)`
 
 `text(added 70)`
 
 `text(subtracted 70)`
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`text(subtracted 70)`

Show Worked Solution

`376 – 70 = 306`

`=>\ text(subtracted 70)`

Number and Algebra, NAP-E1-23

In Year 3 there are 17 more girls than boys.

Ari knows there are 35 girls.

How can Ari work out the number of boys in Year 3.

 
 `text(add 35 to 17)`
 
 `text(subtract 17 from 35)`
 
 `text(multiply 17 by 35)`
 
 `text(divide 35 by 17)`
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`text(subtract 17 from 35)`

Show Worked Solution

`text(subtract 17 from 35)`

Number and Algebra, NAP-G1-18

The table shows the heights of 5 children.

Who is 5 centimetres shorter than the tallest child?

`text(Greg)` `text(Marcia)` `text(Peter)` `text(Jan)` `text(Cindy)`
 
 
 
 
 
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`text(Jan)`

Show Worked Solution

`text{The tallest is Greg (157 cm).}`

`=>\ text(5cm shorter is 152 cm.)`

`:.\ text(Jan is 5 cm shorter than the tallest child.)`

Number and Algebra, NAP-I1-35 SA

Alvin and Curtly picked 47 apples from an apple tree.

Curtly picked 11 more apples than Alvin.

How many apples did Curtly pick?
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`29`

Show Worked Solution

`text(Strategy one:)`

`text(Try possible numbers,)`

`text(24 Curtly − 23 Alvin ⇒ 1 difference)`

`text(25 Curtly − 22 Alvin ⇒ 3 difference)`

`vdots`

`text(29 Curtly − 18 Alvin ⇒ 11 difference)`

`:.\ text(Curtly picked 29 apples.)`

 

`text{Strategy two (use of algebra):}`

`text(Let Alvin pick)\ \ x\ \ text(apples)`

`text(Curtly picks)\ \ x + 11\ \ text(apples)`

`x +x + 11` `=47`
`2x` `=36`
`x` `=18`

 

`:.\ text(Curtly picks  18 + 11 = 29 apples)`

Number and Algebra, NAP-I1-26

Harriet and Eva have 44 toys altogether.

Harriet has 29 toys.

Which number sentence can be used to find the number of toys Eva has?

`44 - 29 = 15` `44 + 29 = 73` `29 - 44 = 15` `29 - 15 = 14`
 
 
 
 
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`44 – 29 = 15`

Show Worked Solution
`text(Eva’s toys)` `=44-29`
  `=15`

Number and Algebra, NAP-I1-13 SA

The scales below are evenly balanced.

What is the weight of the small cube?

  grams
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`text(13 grams)`

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`text(S)text(ince the scales are evenly balanced,)`

`36` `= 23 + text(weight of small cube)`

 

`:.\ text(Weight of small cube)` `= 36 – 23`
  `= 13\ text(grams)`