Scales, lines and patterns: KS2 and 11 Plus maths practice
Reading scales and number lines, matchstick patterns, borders of tiles, shaded parts of a grid, and rectangles with the same perimeter.
OftenIn many papers, especially GL AssessmentAbout 60 seconds a question in the test
The big idea
Many entrance questions are drawings to read carefully. On a scale or a number line, first find what one small space is worth: the gap between two numbers, shared by the spaces between them.
Matchstick patterns grow by the same number of sticks each time, because each new shape shares a stick with the one before. Find how many each pattern adds, then the rule.
A border of tiles round a pond needs one tile for each square along every side, and one more tile in each corner.
Tips that save marks
Never assume the small marks go up in ones.
For a pattern, write the counts in a row and look at the gaps.
For the biggest area with a fixed perimeter, make the sides as close as you can.
A worked example
On a scale the numbers go up in hundreds and there are five spaces between them. What is each space worth?
One hundred shared between five spaces.
One hundred divided by five is twenty.
Answer: twenty.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 60 seconds
A sandpit 3 m long and 3 m wide has a path 1 m wide all round it, as in the picture. What is the area of the path?
Show the worked answer
Answer: C, 16 m²
How to work it out
The sandpit and path together make a rectangle 5 m by 5 m = 25 m².
Take away the sandpit, 9 m²: 25 − 9 = 16 m².
Why the other options are wrong
A (12 m²): This leaves out the four corner squares of the path.
B (25 m²): This is the sandpit and path together; take away the sandpit.
D (7 m²): This adds only 1 m to each length; the path is on both sides, so add 2 m.
E (16 m): The number is right, but an area is in square metres.
Question 2Aim for about 60 seconds
What percentage of the grid is shaded?
Show the worked answer
Answer: C, 52%
How to work it out
13 of the 25 squares are shaded: 13/25 = 52/100 = 52%.
Why the other options are wrong
A (56%): This counts one square too many.
B (5.2%): This makes the bottom 10, not 100.
D (48%): This is the part that is NOT shaded.
E (13%): This counts each square as 1%; there are 25 squares, so each is 4%.
Question 3Aim for about 60 seconds
What number is arrow D pointing to on this number line?
Show the worked answer
Answer: B, 0.44
How to work it out
The numbered marks go up in 0.05s with 5 spaces between them, so each space is 0.01.
Arrow D is at 0.44.
Why the other options are wrong
A (0.8): This counts each space as 0.1; there are 5 spaces between the numbered marks, so each is 0.01.
C (0.31): This is where arrow A points; the question asks about arrow D.
D (0.43): This is one small space short.
E (0.45): This is one small space too far.
Question 4Aim for about 60 seconds
What number is arrow B pointing to on this number line?
Show the worked answer
Answer: C, 0.33
How to work it out
The numbered marks go up in 0.05s with 5 spaces between them, so each space is 0.01.
Arrow B is at 0.33.
Why the other options are wrong
A (0.34): This is one small space too far.
B (0.32): This is one small space short.
D (0.6): This counts each space as 0.1; there are 5 spaces between the numbered marks, so each is 0.01.
E (0.31): This is where arrow A points; the question asks about arrow B.
Question 5Aim for about 60 seconds
A pond 7 m long and 4 m wide has a path 1 m wide all round it, as in the picture. What is the area of the path?
Show the worked answer
Answer: A, 26 m²
How to work it out
The pond and path together make a rectangle 9 m by 6 m = 54 m².
Take away the pond, 28 m²: 54 − 28 = 26 m².
Why the other options are wrong
B (26 m): The number is right, but an area is in square metres.
C (54 m²): This is the pond and path together; take away the pond.
D (12 m²): This adds only 1 m to each length; the path is on both sides, so add 2 m.
E (22 m²): This leaves out the four corner squares of the path.
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