smc-692-20-Patterns and images

Number and Algebra, NAP-J2-28

Caroline has 56 match sticks.

She uses 6 match sticks to make two small triangles.

What is the largest number of small triangles like this that Caroline can make with her 56 match sticks?

`17`	`18`	`19`	`20`

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`18`

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`text(3 match sticks are used for 1 triangle.)`

`text(Number of triangles)`	`= 56 ÷ 3`
	`= 18\ text(remainder 2)`

`:.\ text(18 triangles.)`

Number and Algebra, NAP-K2-08

Oliver is using matchsticks to make a pattern of squares.

How many matchsticks will Oliver need to make square 5?

5	16	20	24

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`20`

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`text(Pattern 1 = 4)`

`text(Pattern 2 = 8)`

`text(Pattern 3 = 12)`

`=> 4\ text(matchsticks are added each square)`

`:.\ text(Square 5)\ =5 xx 4 = 20\ text(matchsticks)`

Number and Algebra, NAP-J2-09

Pablo makes a sculpture using identical cubes.

There were four cubes in the bottom two rows.

How many cubes did Pablo put in the top two rows altogether?

5	7	9	12

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`12`

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`text(S)text(econd top row = 5 cubes)`

`text(Top row = 7 cubes)`

`:.\ text(There are 12 cubes in the top two rows.)`

Number and Algebra, NAP-B2-23

Jake makes a pattern with black and white balls.

Altogether, how many balls are needed for the 5th pattern?

`13`	`14`	`15`	`18`

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`14`

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`text(White ball pattern: 2, 3, 4, 5, 6 …)`

`text(Black ball pattern: 4, 5, 6, 7, 8, …)`

`:.\ text(Total balls in pattern 5)`

`=6\ text(white balls) + 8\ text(black balls)`

`=14\ text(balls)`

Number and Algebra, NAP-C2-24

Camilla designs the following pattern with matchsticks.

How many sticks will Pattern 4 have?

`21`	`27`	`29`	`35`

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`29`

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`text(Each branch end in Pattern 3 will connect to)`

`text(2 more sticks.)`

`:.\ text(Pattern 4 sticks)`	`=13 + (8 xx 2)`
	`=29`

Number and Algebra, NAP-F2-14

Goliath places dice on the table so that they make the pattern below.

Which of these, when repeated, will make the pattern?

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Number and Algebra, NAP-E2-29

Adam is making a pattern with black and white triangular tiles as shown below.

At each stage, tiles are added to edges that don't already have a tiles on them.

What is the total number of tiles needed for Pattern 5?

`28`	`34`	`38`	`42`

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`38\ text(tiles)`

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`38\ text(tiles)`

Number and Algebra, NAP-G2-20

Rob uses sticks to make a pattern.

He starts with 3 sticks for Design 1.

How many sticks does Rob need for Design 5?

`39`	`42`	`45`	`48`

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`45`

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`text(One possible strategy:)`

`text(Each new row contains an extra triangle than the row above.)`

`=>\ text(Design 5 will have 5 triangles on the bottom row.)`

`:.\ text(Total sticks)`	`= 30 + (5 xx 3)`
	`= 30 + 15`
	`= 45`