Term pack
Year 7 Maths
Name: ________________________
Skills in this pack
- Knowing our numbers
- Whole numbers
- Factors and multiples
- HCF and LCM
- Understanding fractions
- Decimals
- Basic geometrical ideas
- Understanding elementary shapes
- Lines and angles
- Congruent triangles
- Line symmetry
- Perimeter and area
- Pictographs and bar graphs
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Year 7 Maths · 1 of 13
Knowing our numbers
Compare, order, round and estimate with numbers of four digits and more.
Before you start
Move between four thousand and five thousand, a hundred at a time. Watch which end of the line you are nearer.
Halfway is 4500. Everything to the left of it is nearer 4000 and everything to the right is nearer 5000 — which is the whole of rounding to the nearest thousand, and why 4783 goes up rather than down.
1.Make the largest number you can from the digits 4, 7, 1 and 9, using each digit once.
2.Round 4678 to the nearest hundred, then tap it on the line.
Mark the line with an X.
3.Which of these is the largest number?
- a) 46857
- b) 46587
- c) 46875
- d) 46785
4.Put these numbers in order, smallest first.
- 9899
- 98909
- 9989
- 98990
- 98099
5.Make the smallest number you can from the digits 5, 2, 8 and 6, using each digit once.
6.Which of these is the smallest number?
- a) 30909
- b) 30099
- c) 39009
- d) 30990
7.What is the predecessor of 40000?
8.Sort each number by whether it is closer to 5000 or to 6000.
Groups: Closer to 5000 · Closer to 6000
- 5120
- 5499
- 5750
- 5045
- 5501
- 5890
Knowing our numbers · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 2 of 13
Whole numbers
Use the order, identity, grouping and splitting properties of whole numbers to make arithmetic easier.
Before you start
Move along the whole numbers. Notice that each one has a next one, and that only zero has nothing before it.
The line stops at 0 on the left because that is where the whole numbers start — but it never has to stop on the right.
1.Which of these is NOT a whole number? (The whole numbers are 0, 1, 2, 3, …)
- a) 0
- b) 17
- c) -4
- d) 206
2.What is the successor of 6099?
3.25 × 17 × 4 = ?
4.Work out each one, then sort it by whether the answer is a whole number. (The whole numbers are 0, 1, 2, 3, …)
Groups: Is a whole number · Is not a whole number
- 3 - 8
- 6 × 0
- 12 ÷ 4
- 12 ÷ 5
- 7 - 7
- 9 ÷ 2
5.Put these whole numbers in order, smallest first.
- 190
- 109
- 1
- 91
- 0
- 19
6.What is the predecessor of 3000?
7.7 × 98 = ?
8.Match each calculation to its answer.
- 25 × 4
- 25 + 4
- 25 - 4
- 100 ÷ 4
- 4 × 4
- 29
- 100
- 21
- 16
- 25
Whole numbers · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 3 of 13
Factors and multiples
Find factors and multiples, use divisibility tests, and tell a prime number from a composite one.
Before you start
Every mark on this line is a multiple of 3. Move along them and see how many you already know from the 3 times table.
The line could carry on for ever, because a number has no last multiple. Factors go the other way: 36 has exactly nine of them and then they run out.
1.Which of these numbers is divisible by 9?
- a) 4651
- b) 4650
- c) 4652
- d) 4653
2.Put these numbers in order by how many factors they have, fewest first.
- 12
- 13
- 9
- 8
- 16
3.Which number between 20 and 30 is a multiple of 9?
4.Match each number to how many factors it has.
- 7
- 8
- 16
- 12
- 36
- 2
- 6
- 9
- 5
- 4
5.Which of these numbers is composite?
- a) 53
- b) 59
- c) 51
- d) 61
6.How many prime numbers are there between 10 and 20?
7.How many factors does 12 have?
8.Which of these numbers is prime?
- a) 39
- b) 49
- c) 29
- d) 91
Factors and multiples · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 4 of 13
HCF and LCM
Find the highest common factor and the lowest common multiple of two numbers, and use them to answer sharing and repeating problems.
Before you start
Every mark here is a multiple of 4 and a multiple of 6 at the same time. Move from one to the next.
Zero is a multiple of everything, so it never counts. The first mark after it is 12, and that is what the LCM of 4 and 6 means — the earliest place their two lists of multiples meet.
1.Work out the LCM of each pair, then sort by whether it is below 30 or above 30.
Groups: LCM below 30 · LCM above 30
- 9 and 12
- 3 and 8
- 4 and 6
- 5 and 8
- 7 and 10
- 6 and 9
2.One bell rings every 6 minutes and another rings every 8 minutes. They have just rung together. In how many minutes will they next ring together?
3.What is the LCM of 5 and 8?
4.What is the HCF of 7 and 13?
5.Two ropes are 12 cm and 18 cm long. Both are cut into equal pieces, as long as possible, with nothing left over. How long is each piece, in centimetres? Give just the number.
6.Match each pair of numbers to their HCF.
- 6 and 9
- 8 and 12
- 10 and 15
- 14 and 21
- 16 and 24
- 8
- 3
- 5
- 4
- 7
7.What is the HCF of 24 and 36?
8.Which pair of numbers has an HCF of 1?
- a) 10 and 15
- b) 8 and 12
- c) 9 and 15
- d) 8 and 15
HCF and LCM · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 5 of 13
Understanding fractions
Place fractions on a number line, find equivalent fractions, compare them, and switch between mixed numbers and improper fractions.
Before you start
Move along the line and watch the quarters go past. See which fractions land on a whole number and which land between two of them.
Every fourth step lands on a whole number, because four quarters make one whole. That is the same fact as 4/4 = 1.
1.What fraction of an hour is 45 minutes? Write it in its simplest form.
2.Match each fraction to an equivalent one with a larger bottom number.
- 1/2
- 1/3
- 2/5
- 3/4
- 2/3
- 4/12
- 10/15
- 9/12
- 8/20
- 5/10
3.Which of these fractions is NOT equivalent to 2/3?
- a) 8/12
- b) 6/8
- c) 4/6
- d) 10/15
4.Put these fractions in order, smallest first.
- 1/4
- 1/2
- 1/6
- 1/3
- 3/4
- 2/3
5.Write 2 3/5 as an improper fraction.
6.Fill in the missing number: 2/5 = ?/20
7.Fill in the missing number: 3/4 = 15/?
8.Which fraction is larger, 3/5 or 5/8?
- a) 5/8
- b) You cannot compare them
- c) They are equal
- d) 3/5
Understanding fractions · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 6 of 13
Decimals
Compare and order decimals, add and subtract them, and switch between decimals and fractions.
Before you start
Move between 3 and 4 in tenths. A whole line of numbers is hiding between two whole ones.
Nothing says the line has to stop at tenths. Chop each of these gaps into ten again and hundredths appear — 3.14, 3.15 — and you could keep chopping for ever.
1.Put these decimals in order, smallest first.
- 0.09
- 0.5
- 0.4
- 1.05
- 0.41
2.A pencil is 12.5 cm long and a pen is 14.2 cm long. How much longer is the pen, in centimetres? Give just the number.
3.Tap where 2.75 sits.
Mark the line with an X.
4.8.6 - 3.75 = ?
5.Write 7/10 as a decimal.
6.Which of these decimals is the largest?
- a) 0.68
- b) 0.7
- c) 0.609
- d) 0.5
7.Sort each decimal by whether it is closer to 0 or closer to 1.
Groups: Closer to 0 · Closer to 1
- 0.91
- 0.7
- 0.2
- 0.09
- 0.55
- 0.45
8.What is 0.6 + 0.45?
Decimals · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 7 of 13
Basic geometrical ideas
Tell points, lines, rays and line segments apart, name the parts of an angle and a circle, and count the sides and diagonals of a polygon.
Before you start
Three lines are drawn on this circle. Take them in turn and find out what each one is called, looking at where each one starts and where it ends.
- 1. Radius — centre to edge
- 2. Diameter — right across, through the centre
- 3. Chord — edge to edge, missing the centre
Every diameter is also a chord — it is simply the longest one, and the only kind that passes through the centre.
1.How many diagonals can be drawn inside a quadrilateral?
2.An angle is made where two rays meet at a point. How many arms does one angle have?
3.Two straight lines in the same flat surface never meet, however far they are extended. What are they called?
- a) Perpendicular lines
- b) Intersecting lines
- c) Concurrent lines
- d) Parallel lines
4.A circle has a radius of 7 cm. How long is its diameter, in centimetres?
- a) 7
- b) 21
- c) 3.5
- d) 14
5.How many line segments make up the sides of a hexagon?
6.Three straight lines have been drawn on this circle. Tap the diameter.
Write the number of the part.
7.Put these shapes in order by how many sides they have, fewest first.
- Quadrilateral
- Triangle
- Hexagon
- Pentagon
- Octagon
8.A line has no ends, a ray has one end, and a line segment has two. Which of the three has a length you could measure with a ruler?
- a) A line
- b) All three of them
- c) A line segment
- d) A ray
Basic geometrical ideas · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 8 of 13
Understanding elementary shapes
Classify angles by size, triangles by their sides and their angles, and tell flat shapes from solid ones.
Before you start
Four angles, drawn side by side and getting wider as you go. Find out what each one is called.
- 1. Acute
- 2. Right angle
- 3. Obtuse
- 4. Straight
Acute is under 90°, obtuse is over it, and the straight one is a half turn — 180°, which is why it stopped looking like a corner at all.
1.A triangle has sides of 5 cm, 5 cm and 8 cm. How many of its sides are equal in length?
2.An angle of 200° is which kind of angle?
- a) Acute
- b) Reflex
- c) Straight
- d) Obtuse
3.Put these kinds of angle in order by size, smallest first.
- Obtuse
- Acute
- Right
- Straight
- Reflex
4.This triangle has one right angle. Tap the corner where it is.
Write the number of the part.
5.Sort each shape by whether it is flat or solid.
Groups: Flat shape · Solid shape
- Sphere
- Triangle
- Cube
- Cylinder
- Square
- Circle
6.Match each angle to the name for its size.
- 45°
- 90°
- 120°
- 180°
- 300°
- Acute
- Straight
- Right
- Obtuse
- Reflex
7.An angle of 145° is which kind of angle?
- a) Acute
- b) Right
- c) Reflex
- d) Obtuse
8.All three angles of an equilateral triangle are equal, and they add up to 180°. How big is each one, in degrees?
Understanding elementary shapes · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 9 of 13
Lines and angles
Use complementary, supplementary, vertically opposite and parallel-line angle facts.
Before you start
Two straight lines cross, and only one of the four angles they make has been given to you. Find out how big each of the others is.
- 1. 70° — given
- 2. 110° — supplementary
- 3. 70° — opposite
- 4. 110° — also opposite
Going round the crossing the angles read 70, 110, 70, 110. Each neighbouring pair sits on a straight line and adds to 180°, and each opposite pair is equal — which is the same fact told twice.
1.Parallel lines are cut by a transversal. One co-interior angle is 115°. What is the other, in degrees?
2.Match each angle to its complement — the angle that makes it up to 90°.
- 20°
- 35°
- 10°
- 25°
- 40°
- 55°
- 70°
- 65°
- 50°
- 80°
3.Sort each angle as acute or obtuse.
Groups: Acute · Obtuse
- 92°
- 170°
- 12°
- 78°
- 145°
- 35°
4.Two angles sit on a straight line, and one is three times the other. How big is the smaller one, in degrees?
5.Two straight lines cross. One of the four angles is 130°. What is the angle next to it, in degrees?
6.Two angles are complementary. One of them is 65°. What is the other, in degrees?
7.Angles round a point add up to how many degrees?
8.A pair of parallel lines is cut by a transversal. Alternate angles are always...
- a) right angles
- b) complementary
- c) supplementary
- d) equal
Lines and angles · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 10 of 13
Congruent triangles
Decide when two triangles are congruent using SSS, SAS, ASA and RHS.
1.Two right-angled triangles have equal hypotenuses and one pair of equal shorter sides. Which rule proves they are congruent?
- a) ASA
- b) SAS
- c) SSS
- d) RHS
2.Triangle ABC is congruent to triangle PQR. AB is 7 cm long. How long is PQ, in centimetres?
3.Two triangles have two pairs of angles equal, and the side between those angles is equal too. Which rule proves they are congruent?
- a) SAS
- b) SSS
- c) ASA
- d) RHS
4.Triangle ABC is congruent to triangle PQR. The area of ABC is 24 square centimetres. What is the area of PQR, in square centimetres?
5.Two triangles have two pairs of sides equal, and the angle between those sides is equal too. Which rule proves they are congruent?
- a) ASA
- b) RHS
- c) SAS
- d) SSS
6.Triangle ABC is congruent to triangle PQR. Angle A is 55°. How big is angle P, in degrees?
7.Sort each set of matching parts by whether it is enough to prove congruence.
Groups: Proves congruence · Does not prove congruence
- AAA
- ASA
- SSA
- SAS
- SSS
- RHS
8.Is knowing that all three pairs of angles are equal enough to prove two triangles congruent?
- a) Yes, always
- b) Only for right-angled triangles
- c) Only for isosceles triangles
- d) No — that only makes them the same shape, not the same size
Congruent triangles · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 11 of 13
Line symmetry
Find the lines of symmetry of shapes and letters, and tell a mirror line from a line that only looks like one.
1.Match each of these to the number of lines of symmetry it has.
- The letter F
- The letter T
- The letter H
- Equilateral triangle
- Regular pentagon
- 3
- 5
- 0
- 2
- 1
2.This kite has one line of symmetry. Three lines have been drawn on it. Tap the one that is a line of symmetry.
Write the number of the part.
3.How many lines of symmetry does the capital letter H have?
4.How many lines of symmetry does the capital letter F have?
5.Which of these capital letters has no line of symmetry?
- a) R
- b) X
- c) E
- d) M
6.A regular shape has 8 lines of symmetry. How many sides does it have?
7.How many lines of symmetry does the capital letter T have?
8.Put these in order by how many lines of symmetry they have, fewest first.
- Regular hexagon
- Square
- Scalene triangle
- Equilateral triangle
- The letter T
- Rectangle that is not a square
Line symmetry · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 12 of 13
Perimeter and area
Find the perimeter and the area of rectangles, squares and shapes built from them, and measure area by counting squares.
1.A rectangle has a perimeter of 30 cm and a length of 9 cm. How wide is it, in centimetres? Give just the number.
2.A shape drawn on squared paper covers 12 full squares and 6 half squares. What is its area, in squares?
3.A rectangle has an area of 48 square centimetres and a length of 8 cm. How wide is it, in centimetres? Give just the number.
4.Match each square to its area.
- side 2
- side 3
- side 5
- side 6
- side 9
- 36
- 4
- 9
- 81
- 25
5.Which of these rectangles has the largest area?
- a) 7 by 4
- b) 6 by 5
- c) 8 by 3
- d) 9 by 2
6.A square has sides of 7 cm. What is its area, in square centimetres? Give just the number.
7.A rectangle is 9 cm long and 4 cm wide. What is its area, in square centimetres? Give just the number.
8.A square has sides of 7 cm. What is its perimeter, in centimetres? Give just the number.
Perimeter and area · Year 7 Maths · www.arenapublications.com/learn
Year 7 Maths · 13 of 13
Pictographs and bar graphs
Record data with tallies, read pictographs and bar graphs where one unit stands for many, and answer questions from them.
Before you start
Every line across this graph is worth 5 books. Look at how far up each bar reaches and work out what it is worth.
- 1. Monday — 30 books
- 2. Tuesday — 15 books
- 3. Wednesday — 40 books
- 4. Thursday — 25 books
Count the lines, not the bars. Monday reaches six lines up and each line is worth 5 books, which is why it is 30 and not 6 — that is the whole job a scale does.
Move the bars up and down, and watch the number each one stands for.
One line up is not one book. Every line you cross is worth 5, so a bar that grows by one line grows by five — that is the scale doing its job.
1.A bar graph shows 6, 11, 9 and 4 goals across four matches. In how many of the matches were fewer than 8 goals scored?
2.A shop sold 14 pens on Monday, 9 on Tuesday, 21 on Wednesday and 17 on Thursday. Put the days in order, fewest pens first.
- Thursday
- Tuesday
- Monday
- Wednesday
3.A bar graph shows 12 red, 8 blue, 15 green and 5 yellow counters. How many counters are there altogether?
4.This bar chart shows how many apples a stall sold on four days. Tap the bar for the day it sold the most.
Write the number of the part.
5.A shop sold 14 pens on Monday, 9 on Tuesday, 21 on Wednesday and 17 on Thursday. Sort each day by whether it sold fewer or more than 15 pens.
Groups: Fewer than 15 pens · More than 15 pens
- Tuesday
- Thursday
- Wednesday
- Monday
6.On a pictograph one whole symbol stands for 8 cars, and half a symbol is drawn at the end of a row. How many cars does that half symbol stand for?
7.A tally chart shows 3 full groups of five and 2 extra lines. What number does it show?
8.In a pictograph, one symbol stands for 5 books. How many books do 7 symbols stand for?
Pictographs and bar graphs · Year 7 Maths · www.arenapublications.com/learn
Answer keys — Year 7 Maths
In the same order as the worksheets.
Knowing our numbers
- 1. 9741
- 2. 4700
- 3. c) 46875
- 4. 1. 9899 2. 9989 3. 98099 4. 98909 5. 98990
- 5. 2568
- 6. b) 30099
- 7. 39999
- 8. 5120 → Closer to 5000; 5890 → Closer to 6000; 5499 → Closer to 5000; 5501 → Closer to 6000; 5045 → Closer to 5000; 5750 → Closer to 6000
Whole numbers
- 1. c) -4
- 2. 6100
- 3. 1700
- 4. 12 ÷ 4 → Is a whole number; 12 ÷ 5 → Is not a whole number; 7 - 7 → Is a whole number; 3 - 8 → Is not a whole number; 6 × 0 → Is a whole number; 9 ÷ 2 → Is not a whole number
- 5. 1. 0 2. 1 3. 19 4. 91 5. 109 6. 190
- 6. 2999
- 7. 686
- 8. 25 × 4 → 100; 25 + 4 → 29; 25 - 4 → 21; 100 ÷ 4 → 25; 4 × 4 → 16
Factors and multiples
- 1. d) 4653
- 2. 1. 13 2. 9 3. 8 4. 16 5. 12
- 3. 27
- 4. 7 → 2; 8 → 4; 16 → 5; 12 → 6; 36 → 9
- 5. c) 51
- 6. 4
- 7. 6
- 8. c) 29
HCF and LCM
- 1. 4 and 6 → LCM below 30; 3 and 8 → LCM below 30; 6 and 9 → LCM below 30; 5 and 8 → LCM above 30; 9 and 12 → LCM above 30; 7 and 10 → LCM above 30
- 2. 24
- 3. 40
- 4. 1
- 5. 6
- 6. 6 and 9 → 3; 8 and 12 → 4; 10 and 15 → 5; 14 and 21 → 7; 16 and 24 → 8
- 7. 12
- 8. d) 8 and 15
Understanding fractions
- 1.
- 3/4
- 3 / 4
- three quarters
- three-quarters
- 2. 1/2 → 5/10; 1/3 → 4/12; 2/5 → 8/20; 3/4 → 9/12; 2/3 → 10/15
- 3. b) 6/8
- 4. 1. 1/6 2. 1/4 3. 1/3 4. 1/2 5. 2/3 6. 3/4
- 5.
- 13/5
- 13 / 5
- 6. 8
- 7. 20
- 8. a) 5/8
Decimals
- 1. 1. 0.09 2. 0.4 3. 0.41 4. 0.5 5. 1.05
- 2. 1.7
- 3. 2.75
- 4. 4.85
- 5.
- 0.7
- .7
- 0.70
- 6. b) 0.7
- 7. 0.2 → Closer to 0; 0.7 → Closer to 1; 0.45 → Closer to 0; 0.55 → Closer to 1; 0.09 → Closer to 0; 0.91 → Closer to 1
- 8. 1.05
Basic geometrical ideas
- 1. 2
- 2. 2
- 3. d) Parallel lines
- 4. d) 14
- 5. 6
- 6. 2 — the line right across through the centre
- 7. 1. Triangle 2. Quadrilateral 3. Pentagon 4. Hexagon 5. Octagon
- 8. c) A line segment
Understanding elementary shapes
- 1. 2
- 2. b) Reflex
- 3. 1. Acute 2. Right 3. Obtuse 4. Straight 5. Reflex
- 4. 2 — the bottom left corner
- 5. Square → Flat shape; Cube → Solid shape; Circle → Flat shape; Sphere → Solid shape; Triangle → Flat shape; Cylinder → Solid shape
- 6. 45° → Acute; 90° → Right; 120° → Obtuse; 180° → Straight; 300° → Reflex
- 7. d) Obtuse
- 8. 60
Lines and angles
- 1. 65
- 2. 20° → 70°; 35° → 55°; 10° → 80°; 25° → 65°; 40° → 50°
- 3. 35° → Acute; 92° → Obtuse; 78° → Acute; 145° → Obtuse; 12° → Acute; 170° → Obtuse
- 4. 45
- 5. 50
- 6. 25
- 7. 360
- 8. d) equal
Congruent triangles
- 1. d) RHS
- 2. 7
- 3. c) ASA
- 4. 24
- 5. c) SAS
- 6. 55
- 7. SSS → Proves congruence; SAS → Proves congruence; ASA → Proves congruence; RHS → Proves congruence; AAA → Does not prove congruence; SSA → Does not prove congruence
- 8. d) No — that only makes them the same shape, not the same size
Line symmetry
- 1. The letter F → 0; The letter T → 1; The letter H → 2; Equilateral triangle → 3; Regular pentagon → 5
- 2. 3 — the upright line
- 3. 2
- 4. 0
- 5. a) R
- 6. 8
- 7. 1
- 8. 1. Scalene triangle 2. The letter T 3. Rectangle that is not a square 4. Equilateral triangle 5. Square 6. Regular hexagon
Perimeter and area
- 1. 6
- 2. 15
- 3. 6
- 4. side 2 → 4; side 3 → 9; side 5 → 25; side 6 → 36; side 9 → 81
- 5. b) 6 by 5
- 6. 49
- 7. 36
- 8. 28
Pictographs and bar graphs
- 1. 2
- 2. 1. Tuesday 2. Monday 3. Thursday 4. Wednesday
- 3. 40
- 4. 4 — Thursday
- 5. Monday → Fewer than 15 pens; Tuesday → Fewer than 15 pens; Wednesday → More than 15 pens; Thursday → More than 15 pens
- 6. 4
- 7. 17
- 8. 35
Year 7 Maths · www.arenapublications.com/learn