Challenges

A 3x3 grid of numbers. Rows and columns sum to 15. Numbers: top row 8, 1, 6; middle row 3, 5, 7; bottom row 4, 9, 2. Yellow background.

The text ‘12+6+2 = 20 triangles’ is at the top above an image of three stars on a yellow background. The first star, labelled ‘x12’, is a six-pointed star divided into 12 smaller triangles by intersecting lines. One of the small triangles in a star point is shaded red to highlight it Next to the first star is another six-pointed star, labelled ‘x6’. It is also divided into 12 smaller triangles by intersecting lines. A larger triangle, made by combining 4 of these smaller triangles, is shaded red to highlight it. Below both stars is a third six-pointed star, labelled ‘x2’. It is also divided into 12 smaller triangles by intersecting lines. An even larger triangle, made by combining 9 of these smaller triangles, is shaded red to highlight it.

A light blue triangle on a yellow background has the number 5 written inside. On each point of the triangle is a number: 4, 6 and 14.

A table on a yellow background. The table is divided into three rows of four columns. The top row is blue and the first column is the text ‘Sam picks’, the next column has text ‘Pears’, the next has text ‘Oranges’ and the final column has the text ‘Pears & Oranges’. On the next row underneath ‘Sam picks’ is the text “A pear’, in the next column is the text ‘Oranges’, the next column has the text ‘Pears & Oranges’ and the final column has the text ‘Pears’. Along the bottom row, the first column has the text ‘An orange’, the next column has ‘Pears & Oranges’, next is text ‘Pears’ and in final column is the text ‘Oranges’.

Nine black dots arranged equally spaced as a three by three grid on yellow background. A blue line is drawn to represent four lines drawn to connect all the black dots without lifting the pen. An arrow drawn diagonally starts from the dot in the top left hand corner, passing through the middle dot and ending at the dot on the bottom right corner. The next line is drawn from this dot straight up passing through the dot on the right side extending beyond the dot in the top right corner. Then the next line is drawn at a 45 degree angle through the middle top of the top line and the middle dot of the left hand side extending beyond the dot in line with the bottom row of dots. The final line is down from this point along the bottom three dots finishing at the dot in the bottom right corner.

At the top of the image the text ’32 + 16 + 6 + 2 = 56 squares’ appears above 4 grid shapes on yellow background. The following grid shape is displayed four times: ‘A white grid divided into small squares arranged in an array 7x6 layout (7 rows and 6 columns) on a yellow background. Along the top row three squares are missing after the first two squares. Along the left hand side two squares are missing leaving the first two and the bottom two squares. Along the bottom row two squares followed by three missing squares then two squares. Along the right hand side two squares are missing leaving the first two and the bottom two squares. The four grids are labelled and shaded as follows: The first grid, labelled ‘x32’, has one small square shaded red, the second grid, labelled ‘x16’, has four small squares shaded red to represent a 2x2 square, the third grid, labelled ‘x6’, has nine small squares shaded red to represent a 3x3 square, the fourth grid, labelled ‘x2’, has sixteen small squares shaded red to represent a 4x4 square.

A series of seven connected circles are arranged on a yellow background. The top row consists of three circles arranged equidistant in a horizontal line. Each circle has a number inside: 7, 2 and 3. Below this row, a single circle with the number 4 inside is placed in the middle, aligned with the centre of the row above. Below the middle circle is another row of three circles, also arranged equidistant in a horizontal line. Each of these circles has a number inside: 5, 6 and 1.

A line drawing of a pit labelled 30 m in depth, with the height marked by an arrow. A small amount of water is drawn at the bottom of the pit. At the top of the pit on both sides, there are grassy strips drawn to indicate ground level. On the grassy strip on the left hand side sits a frog.

Sixteen are arranged in a pattern on yellow background. The central pattern represents a hexagon with six matchsticks radiating from a central point and a matchstick for each side. On the top side of the hexagon two matchsticks are added to form a triangular shape. On the bottom side of the hexagon two matchsticks are added to form another triangular shape. Two of the matchsticks radiating from the central point are white. Two of the matches that make up the sides of the hexagon shape are also white. The remaining matchsticks are brown with red ‘heads’

A 5x5 grid is on a yellow background. Each grid square contains a number. On the bottom row, the first square on the lefthand side, is shaded green, contains the number five and is labelled ‘Start’ with an arrow. The following numbers on the squares are: 5, 6, 5, 5. On next row above, has squares with numbers: 7, 8, 8, 8, 6. The squares containing 9,4,5,7 are shaded in blue. On next row above, has squares with numbers: 6, 6, 4, 9, 9. The squares containing 6 are shaded in blue. On next row above, has squares with numbers: 8, 9, 4, 5, 7. The square containing 7 is shaded in blue. On the top row the numbers in squares are: 4, 9, 7, 7. With the last square also shaded in blue with the number 4 and labelled ‘Finish’ with an arrow.

The text ‘Total number of triangles’ appears at the top of the page above four squares arranged in a row. Each of the four squares is divided by a horizontal and a vertical line that intersect at the centre, forming four squares. Each square is divided by two diagonal lines that intersect, forming four triangles within each square. The first square has a triangle shaded blue and labelled ‘+16’. In the bottom corner two of the square, two adjacent small triangles are also shaded in blue to form a larger triangle. It is labelled ‘+16’. The second square has four adjacent small triangles shaded in blue, forming a larger triangle with one side equal to the side of the square. It is labelled '+4'. The third square has four adjacent small triangles shaded in blue, forming a larger triangle with one side equal to the vertical line that divides the square. It is labelled '+4'. The fourth square has eight adjacent small triangles shaded in blue, forming a larger triangle with one side equal to the side of the square and another side equal to the other side of the square. It is labelled '+4'. After the row of squares the text ‘=44’ is in a black circle to represent the answer to the total number of triangles. The text ‘Total number of squares’ appears under the row of squares. Below the text are another row of four squares arranged in a row. Each of the four squares is divided by a horizontal and a vertical line that intersect at the centre, forming four squares. Each square is divided by two diagonal lines that intersect, forming four triangles within each square. The first square has four adjacent triangles shaded blue to form a square. It is labelled ‘+14’. The second square has two small triangles shaded in blue, forming a smaller square. It is labelled '+4'. The third square has eight adjacent small triangles shaded in blue, forming a large square. It is labelled '+1'. The fourth square is fully shaded in blue. It is labelled '+1'. After the row of squares the text ‘=10’ is in a black circle to represent the answer to the total number of squares.