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Term pack

Grade 3 Math

Name: ________________________

Skills in this pack

  • 6 times table
  • 7 times table
  • 2, 3, 4 and 5 times tables
  • 8, 9 and 10 times tables
  • Sharing equally
  • Number patterns
  • Halves and quarters
  • Equivalent fractions
  • Comparing and ordering fractions
  • Understanding fractions
  • Measuring with standard units
  • Reading a picture graph
  • How heavy, and how much it holds
  • Perimeter: once round the outside
  • Area by counting squares
  • Reading bar charts
  • Bar graphs with scales
  • Perimeter and area
  • Pictographs and bar graphs
  • Shapes and symmetry

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Grade 3 Math · 1 of 20

6 times table

Recall the six times table up to 6 × 12.

  1. 1.6 × 11 = ?

  2. 2.6 × 3 = ?

  3. 3.Which times fact gives 54?

    • a) 8 × 7
    • b) 6 × 8
    • c) 9 × 5
    • d) 6 × 9

  4. 4.6 × 9 = ?

  5. 5.Which one is 6 × 8?

    • a) 54
    • b) 46
    • c) 42
    • d) 48

  6. 6.6 × 4 = ?

    • a) 28
    • b) 32
    • c) 20
    • d) 24

  7. 7.Match each times fact to its answer.

    • 6 × 2
    • 6 × 5
    • 6 × 8
    • 6 × 10
    • 12
    • 30
    • 48
    • 60

  8. 8.6 × 12 = ?

6 times table · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 2 of 20

7 times table

Recall the seven times table up to 7 × 12.

  1. 1.Which times fact gives 63?

    • a) 7 × 9
    • b) 6 × 9
    • c) 8 × 9
    • d) 7 × 8

  2. 2.7 × 12 = ?

  3. 3.7 × 3 = ?

  4. 4.Which one is 7 × 7?

    • a) 56
    • b) 49
    • c) 42
    • d) 47

  5. 5.7 × 9 = ?

  6. 6.The line counts in sevens. Tap where 7 × 6 lands.

    Mark the line with an X.

    0142842567084

  7. 7.7 × 8 = ?

    • a) 63
    • b) 54
    • c) 56
    • d) 49

  8. 8.7 × 6 = ?

7 times table · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 3 of 20

2, 3, 4 and 5 times tables

Recall the two, three, four and five times tables up to 12.

Before you start

This line counts in fives all the way to 60. Move along it and say each number out loud.

051015202530354045505560

Every number you land on ends in a 5 or a 0 — that is the whole five times table.

  1. 1.Put these answers in order, smallest first.

    • 4 × 6
    • 3 × 6
    • 2 × 8
    • 5 × 6

  2. 2.Sort each number by whether it is in the 5 times table.

    Groups: In the 5 times table · Not in it

    • 18
    • 25
    • 32
    • 45

  3. 3.5 × 11 = ?

  4. 4.5 × 9 = ?

    • a) 50
    • b) 45
    • c) 54
    • d) 40

  5. 5.Tap where 5 × 4 lands.

    Mark the line with an X.

    05101520253035404550

  6. 6.Tap where 3 × 5 lands.

    Mark the line with an X.

    036912151821242730

  7. 7.Match each times fact to its answer.

    • 2 × 7
    • 3 × 7
    • 4 × 7
    • 5 × 7
    • 35
    • 28
    • 14
    • 21

  8. 8.3 × 8 = ?

2, 3, 4 and 5 times tables · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 4 of 20

8, 9 and 10 times tables

Recall the eight, nine and ten times tables up to 12.

  1. 1.10 × 12 = ?

  2. 2.Put these answers in order, smallest first.

    • 8 × 6
    • 10 × 3
    • 8 × 3
    • 9 × 3

  3. 3.Match each times fact to its answer.

    • 9 × 3
    • 9 × 5
    • 9 × 7
    • 9 × 8
    • 27
    • 72
    • 45
    • 63

  4. 4.Which one is 9 × 9?

    • a) 81
    • b) 99
    • c) 72
    • d) 89

  5. 5.Tap where 9 × 4 lands.

    Mark the line with an X.

    09182736455463728190

  6. 6.9 × 6 = ?

  7. 7.10 × 7 = ?

    • a) 700
    • b) 17
    • c) 70
    • d) 107

  8. 8.8 × 4 = ?

8, 9 and 10 times tables · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 5 of 20

Sharing equally

Share a number into equal groups, and work out how many equal groups a number makes.

  1. 1.Put these answers in order, smallest first.

    • 12 ÷ 2
    • 12 ÷ 1
    • 12 ÷ 3
    • 12 ÷ 4

  2. 2.Match each division to its answer.

    • 10 ÷ 2
    • 16 ÷ 4
    • 21 ÷ 3
    • 40 ÷ 5
    • 8
    • 5
    • 4
    • 7

  3. 3.24 ÷ 4 = ?

  4. 4.Share 13 counters between 4 cups. How many are left over?

    • a) 1
    • b) 2
    • c) 0
    • d) 3

  5. 5.Share 12 apples between 3 baskets. How many in each?

  6. 6.20 counters are put in rows of 5. How many rows?

  7. 7.Tap where 15 ÷ 3 lands.

    Mark the line with an X.

    012345678910

  8. 8.Share 20 beads between 4 boxes. How many in each?

Sharing equally · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 6 of 20

Number patterns

Find the rule in a number pattern and carry the pattern on.

  1. 1.The pattern goes 2, 4, 6, 8. What comes next?

    • a) 10
    • b) 16
    • c) 12
    • d) 9

  2. 2.The pattern goes 6, 12, 18, 24. What comes next?

  3. 3.The pattern goes 50, 45, 40, 35. What comes next?

    • a) 30
    • b) 34
    • c) 32
    • d) 25

  4. 4.The pattern goes 5, 10, 15, 20. What comes next?

  5. 5.The pattern goes 2, 4, 8, 16. What comes next?

  6. 6.Match each pattern to the number that comes next.

    • 6, 12, 18
    • 10, 20, 30
    • 7, 14, 21
    • 9, 18, 27
    • 28
    • 24
    • 40
    • 36

  7. 7.Sort each number by whether it is odd or even.

    Groups: Odd · Even

    • 41
    • 27
    • 34
    • 56

  8. 8.The pattern goes 20, 30, 40. Tap where the next number sits.

    Mark the line with an X.

    0102030405060708090100

Number patterns · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 7 of 20

Halves and quarters

Find a half or a quarter of a small amount.

  1. 1.Match each number to half of it.

    • 8
    • 14
    • 26
    • 60
    • 13
    • 7
    • 4
    • 30

  2. 2.What is a quarter of 12?

  3. 3.Which one is the same as one quarter?

    • a) 1/3
    • b) 1/2
    • c) 2/8
    • d) 3/4

  4. 4.Which one is the same as one half?

    • a) 1/4
    • b) 2/4
    • c) 3/4
    • d) 1/3

  5. 5.What is half of 12?

  6. 6.Put these amounts in order, smallest first.

    • Half of 10
    • Half of 6
    • A quarter of 60
    • Half of 40

  7. 7.What is half of 7?

  8. 8.What is a quarter of 8?

Halves and quarters · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 8 of 20

Equivalent fractions

Recognize fractions that are worth the same amount.

Before you start

Shade some of the bar, then cut it into more pieces. What happens to the shaded part?

123456789101112

Cutting the bar into more pieces never changes how much is shaded — only what you call it.

  1. 1.Each mark on this line is one twelfth. Which mark is 2/3 of the whole?

    Mark the line with an X.

    024681012

  2. 2.Sort each fraction by whether it is worth the same as 2/3 or not.

    Groups: The same as 2/3 · Not the same as 2/3

    • 8/12
    • 4/6
    • 3/5
    • 5/8
    • 2/5
    • 10/15

  3. 3.One bar shows 2/3 and the other shows 4/6. Which bar will show more when they are filled in?

    Which bar shows more when they are filled in? Circle one.

    2/34/6

    Top / The same / Bottom

  4. 4.Match each fraction to another fraction worth exactly the same amount.

    • 1/4
    • 2/5
    • 3/8
    • 5/6
    • 6/16
    • 3/12
    • 4/10
    • 10/12

  5. 5.The top bar shows 1/2. Shade the bottom bar so that it shows the same amount.

    Shade the second bar to show the same amount as the first.

    1/2

  6. 6.Fill in the missing number: 3/4 = 15/?

  7. 7.Each of these has its top number missing. Work them out and put them in order, smallest missing number first.

    • 1/2 = ?/10
    • 1/2 = ?/6
    • 2/3 = ?/12
    • 3/4 = ?/16

  8. 8.Which fraction is the same as 5/10?

    • a) 2/5
    • b) 1/2
    • c) 5/5
    • d) 1/5

Equivalent fractions · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 9 of 20

Comparing and ordering fractions

Compare fractions with the same bottom number and with the same top number, and put a set of fractions in order.

  1. 1.Sort each fraction by whether it is smaller or larger than one half.

    Groups: Smaller than a half · Larger than a half

    • 5/8
    • 7/10
    • 2/5
    • 3/4
    • 1/6
    • 1/3

  2. 2.Put these fractions in order, smallest first.

    • 1/8
    • 2/8
    • 5/8
    • 7/8

  3. 3.Put these fractions in order, smallest first.

    • 1/2
    • 1/4
    • 1/10
    • 1/3
    • 1/6

  4. 4.Match each fraction to the fraction worth exactly the same amount.

    • 1/2
    • 1/4
    • 1/3
    • 2/3
    • 8/12
    • 4/12
    • 2/8
    • 3/6

  5. 5.Fill in the missing number: 1/4 = ?/12

  6. 6.Fill in the missing number: 2/5 = ?/10

  7. 7.Each of these is one piece of a whole. Which piece is the largest?

    • a) 1/6
    • b) 1/3
    • c) 1/9
    • d) 1/5

  8. 8.The pieces are all sevenths. Which fraction is the smallest?

    • a) 5/7
    • b) 4/7
    • c) 2/7
    • d) 6/7

Comparing and ordering fractions · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 10 of 20

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.

0.001.002.00

Every fourth step lands on a whole number, because four quarters make one whole. That is the same fact as 4/4 = 1.

  1. 1.Fill in the missing number: 3/4 = 15/?

  2. 2.What fraction of an hour is 45 minutes? Write it in its simplest form.

  3. 3.Tap where 3/4 sits.

    Mark the line with an X.

    0.001.00

  4. 4.Tap where 7/4 sits.

    Mark the line with an X.

    0.001.002.003.00

  5. 5.Sort each fraction by whether it is less than 1 or more than 1.

    Groups: Less than 1 · More than 1

    • 5/9
    • 7/8
    • 5/4
    • 8/3
    • 9/7
    • 3/4

  6. 6.Put these fractions in order, smallest first.

    • 1/6
    • 1/3
    • 3/4
    • 1/2
    • 1/4
    • 2/3

  7. 7.Write 17/5 as a mixed number.

  8. 8.Write 2 3/5 as an improper fraction.

Understanding fractions · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 11 of 20

Measuring with standard units

Choose a sensible unit for a length, a weight or an amount of liquid, and add and take away measurements.

  1. 1.Match each thing to the unit you would measure it in.

    • A pencil
    • A rope across a room
    • A bag of rice
    • Water in a bottle
    • pints
    • inches
    • feet
    • pounds

  2. 2.A ribbon is 90 inches long and 25 inches is cut off. How much is left? Give just the number.

  3. 3.About how tall is a door?

    • a) 70 feet
    • b) 700 feet
    • c) 7 feet

  4. 4.Tap the container that holds the most.

    Write the number of the part.

    123

  5. 5.Sort each question by what it is measuring.

    Groups: Length · Weight

    • How tall is the door?
    • How heavy is the bag?
    • How wide is the table?
    • How much does the melon weigh?

  6. 6.Put these lengths in order, shortest first.

    • 15 inches
    • 90 inches
    • 40 inches
    • 65 inches

  7. 7.Which one is the longest?

    • a) 45 inches
    • b) 40 inches
    • c) 35 inches
    • d) 54 inches

  8. 8.Which one would you measure in miles?

    • a) A pencil
    • b) A book
    • c) A road between two towns
    • d) A spoon

Measuring with standard units · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 12 of 20

Reading a picture graph

Read a picture graph and a simple bar chart, and answer questions about what they show.

  1. 1.A graph shows 8 red counters and 5 blue counters. How many more red counters are there?

  2. 2.This chart shows hats sold on four days. Tap the tallest bar.

    Write the number of the part.

    1234

  3. 3.One picture stands for 2 apples. How many apples do 4 pictures show?

  4. 4.One picture stands for 2 cars. How many pictures show 10 cars?

  5. 5.A class counted 7 cats, 12 dogs, 4 birds and 9 fish. Sort each animal by whether there are fewer or more than 8.

    Groups: Fewer than 8 · More than 8

    • Cats
    • Birds
    • Dogs
    • Fish

  6. 6.A graph shows 6 red and 8 blue counters. Tap how many there are altogether.

    Mark the line with an X.

    02468101214161820

  7. 7.One picture stands for 5 books. How many books do 3 pictures show?

    • a) 20
    • b) 15
    • c) 10
    • d) 8

  8. 8.A shop sold 8 mugs on Monday, 3 on Tuesday, 12 on Wednesday and 5 on Thursday. Put the days in order, fewest hats first.

    • Thursday
    • Tuesday
    • Wednesday
    • Monday

Reading a picture graph · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 13 of 20

How heavy, and how much it holds

Compare how heavy things are, and work out how much a container holds.

Before you start

Two parcels sit on one side of this balance and one on the other, with spare weights below. Try to bring the beam level.

234125

More than one arrangement levels it, and the number of parcels in each pan is never what settles it — only the totals are.

  1. 1.A melon weighs 4 lb and an apple weighs 1. How much heavier is the melon?

  2. 2.One jug holds 2 pt. How much do 5 jugs hold?

  3. 3.Match each parcel to what it weighs after 2 lb more is added.

    • 3 lb
    • 6 lb
    • 10 lb
    • 1 lb
    • 12
    • 8
    • 3
    • 5

  4. 4.A bag weighs 3 lb. What do 4 bags weigh?

  5. 5.Put these in order, lightest first.

    • A car
    • An apple
    • A school bag
    • A pin

  6. 6.Two tins weigh 5 lb each. What do they weigh together?

  7. 7.Which of these is the heaviest?

    • a) A feather
    • b) A leaf
    • c) A pin
    • d) A brick

  8. 8.A jug is marked in pt. Tap the mark for 8.

    Mark the line with an X.

    02468101214161820

How heavy, and how much it holds · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 14 of 20

Perimeter: once round the outside

Find the perimeter of any straight-sided shape by adding the lengths of its sides, and work backwards to a missing side.

Before you start

An L-shaped garden, with every side drawn as its own strip. Find all of them, and count how many there are.

123456
  1. 1. The top side
  2. 2. The short side going down
  3. 3. The step across
  4. 4. The long side going down
  5. 5. The bottom side
  6. 6. The tall side up the left

Six sides, not four — the step in the middle adds two more, and leaving one of those out is the commonest way a perimeter goes wrong.

  1. 1.A square has sides of 9 inches. What is its perimeter, in inches? Give just the number.

  2. 2.Every side of every shape here is 6 inches long. Match each regular shape to its perimeter.

    • Triangle
    • Square
    • Pentagon
    • Hexagon
    • Octagon
    • 36
    • 30
    • 24
    • 48
    • 18

  3. 3.A square has a perimeter of 32 inches. How long is each side, in inches? Give just the number.

  4. 4.A regular octagon has a perimeter of 56 inches. How long is each side, in inches? Give just the number.

  5. 5.A path goes right round a rectangular lawn 15 ft long and 10 ft wide. How far is it once round, in feet? Give just the number.

  6. 6.A rectangle is 12 inches long and 7 inches wide. What is its perimeter, in inches? Give just the number.

  7. 7.Every length here is in inches. Put these shapes in order by perimeter, smallest first.

    • A square of side 8
    • A rectangle 5 by 4
    • A regular hexagon of side 4
    • A square of side 3
    • A square of side 4

  8. 8.Every length here is in inches. Which shape has the largest perimeter?

    • a) A rectangle 8 by 3
    • b) A square of side 6
    • c) A regular pentagon of side 5
    • d) A triangle with sides 7, 7 and 7

Perimeter: once round the outside · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 15 of 20

Area by counting squares

Measure the area of a shape on squared paper by counting the squares it covers, including half squares.

Before you start

Three shapes sit on the same grid of squares. Count the squares under each one and compare what you find with how big each shape looks.

123
  1. 1. Shape A
  2. 2. Shape B
  3. 3. Shape C

Shape B is the tallest and Shape C is the widest, but neither of those is what decides the area — only the count of squares does.

  1. 1.Three shapes are drawn on this grid. Tap the shape that covers the most squares.

    Write the number of the part.

    123

  2. 2.Match each rectangle to the number of squares it covers.

    • 2 across and 3 down
    • 3 across and 3 down
    • 4 across and 5 down
    • 6 across and 6 down
    • 36
    • 9
    • 6
    • 20

  3. 3.A rectangle covers 24 squares and is 6 squares across. How many squares tall is it?

  4. 4.Sort each rectangle by whether it covers fewer or more than 20 squares.

    Groups: Fewer than 20 squares · More than 20 squares

    • 6 across and 4 down
    • 3 across and 5 down
    • 5 across and 5 down
    • 2 across and 9 down
    • 7 across and 3 down
    • 4 across and 4 down

  5. 5.Which rectangle covers the most squares?

    • a) 3 across and 6 down
    • b) 4 across and 4 down
    • c) 2 across and 8 down
    • d) 5 across and 3 down

  6. 6.A rectangle on squared paper is 7 squares across and 4 squares down. How many squares does it cover?

  7. 7.A shape covers 20 full squares and 6 half squares. What is its area, in squares?

  8. 8.A shape drawn on squared paper covers 8 full squares in its upper part and 6 full squares in its lower part. What is its area, in squares?

Area by counting squares · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 16 of 20

Reading bar charts

Read a bar chart, use its scale to turn a bar height into a number, and compare the bars.

  1. 1.Why does a bar chart need a scale up the side?

    • a) So that the bars look neat
    • b) So that every bar is the same width
    • c) So that the height of a bar can be read as a number
    • d) So that the chart has a title

  2. 2.A chart shows 22 visitors on Monday, 15 on Tuesday, 30 on Wednesday and 18 on Thursday. Put the days in order, fewest visitors first.

    • Wednesday
    • Tuesday
    • Thursday
    • Monday

  3. 3.This chart shows how many books were read on each of four days. Tap the bar for the day with the fewest.

    Write the number of the part.

    1234

  4. 4.A bar chart shows 9 visitors on Monday and 14 on Tuesday. How many more visitors were there on Tuesday?

  5. 5.On a bar chart one square of the scale stands for 10 people. A bar is four and a half squares tall. How many people does it stand for?

    • a) 410
    • b) 40
    • c) 45
    • d) 50

  6. 6.A bar chart shows 9, 14, 6 and 11 visitors across four days. How many visitors were there altogether?

  7. 7.This chart shows how many goals four teams scored. Tap the bar for the team that scored the second most.

    Write the number of the part.

    1234

  8. 8.On this chart each square of the scale stands for 4 cars. Match each bar height to the number of cars it shows.

    • 2 squares
    • 3 squares
    • 5 squares
    • 7 squares
    • 8
    • 20
    • 28
    • 12

Reading bar charts · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 17 of 20

Bar graphs with scales

Read values off a bar graph whose scale counts in steps of more than one, and choose a sensible scale of your own.

  1. 1.This bar graph shows how many people visited a library on four days. Tap the bar for the day with the fewest visitors.

    Write the number of the part.

    1234

  2. 2.A bar graph's scale counts in fours. Put these bars in order, shortest first.

    • 2 lines up
    • 3 lines up
    • 5 lines up
    • 7 lines up

  3. 3.A bar graph has four bars, showing 60, 45, 30 and 25. What is the difference between the tallest bar and the shortest?

  4. 4.On a bar graph each square stands for 5 books. A bar is 4 squares tall. How many books does it show?

  5. 5.A bar graph's scale counts in fives. Sort each value by whether its bar lands exactly on a marked line.

    Groups: Lands on a line · Lands between two lines

    • 22
    • 15
    • 35
    • 8
    • 13
    • 40

  6. 6.Why does a bar graph need a scale written up the side?

    • a) To make the graph look neat
    • b) To show which bar is the tallest
    • c) So the height of a bar can be turned into a number
    • d) To give the bars their names

  7. 7.A bar graph has four bars, showing 60, 45, 30 and 25. What do the four bars add up to?

  8. 8.This bar graph shows how many books four classes read. Tap the bar for the class that read the most.

    Write the number of the part.

    1234

Bar graphs with scales · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 18 of 20

Perimeter and area

Find the perimeter and the area of rectangles, squares and shapes built from them, and measure area by counting squares.

  1. 1.A square has sides of 7 inches. What is its perimeter, in inches? Give just the number.

  2. 2.An L-shape is made from a rectangle 10 inches by 4 inches with a square of side 3 inches cut out of one corner. What is its area, in square inches? Give just the number.

  3. 3.A rectangle is 9 inches long and 4 inches wide. What is its area, in square inches? Give just the number.

  4. 4.A rectangle has an area of 48 square inches and a length of 8 inches. How wide is it, in inches? Give just the number.

  5. 5.A square has sides of 7 inches. What is its area, in square inches? Give just the number.

  6. 6.A shape drawn on squared paper covers 12 full squares and 6 half squares. What is its area, in squares?

  7. 7.Which of these rectangles has the largest area?

    • a) 6 by 5
    • b) 9 by 2
    • c) 7 by 4
    • d) 8 by 3

  8. 8.Put these rectangles in order by area, smallest first.

    • 2 by 6
    • 3 by 5
    • 5 by 4
    • 4 by 4
    • 3 by 6

Perimeter and area · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 19 of 20

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.

1234
  1. 1. Monday — 30 books
  2. 2. Tuesday — 15 books
  3. 3. Wednesday — 40 books
  4. 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.

Each line up the side is worth 5.0510152025303540MondayTuesdayWednesday

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. 1.This bar chart shows how many apples a stall sold on four days. Tap the bar for the day it sold the fewest.

    Write the number of the part.

    1234

  2. 2.In a pictograph, one symbol stands for 5 books. How many books do 7 symbols stand for?

  3. 3.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
    • Wednesday
    • Tuesday
    • Monday

  4. 4.On this pictograph one symbol stands for 5 books. Match each row to the number of books it shows.

    • 2 symbols
    • 3 symbols
    • 4 symbols
    • 6 symbols
    • 20
    • 10
    • 15
    • 30

  5. 5.On a bar graph each square of the scale stands for 4 children. A bar is 6 squares tall. How many children does that bar stand for?

  6. 6.A tally chart shows 3 full groups of five and 2 extra lines. What number does it show?

  7. 7.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?

  8. 8.A library counted the books borrowed each day. Draw a bar for every day in the table.

    Draw a bar for every row of the table.

    Monday30
    Tuesday15
    Wednesday40
    Thursday25
    Each line up the side is worth 5.0510152025303540MondayTuesdayWednesdayThursday

Pictographs and bar graphs · Grade 3 Math · www.arenapublications.com/learn

Grade 3 Math · 20 of 20

Shapes and symmetry

Count the sides and corners of a shape, name the parts of a solid, find a line of symmetry, and cover a shape with smaller shapes.

Before you start

Here is a box drawn as a solid. Find a face, an edge and a corner on it.

123
  1. 1. A face
  2. 2. An edge
  3. 3. A corner

A corner is the one place where three edges come together at a point.

Take a tile from the tray and lay it on the hexagon. Cover the whole hexagon with one kind of tile, then clear it and try another kind.

  • Triangle, covers 1 triangle
  • Rhombus, covers 2 triangles
  • Half-hexagon, covers 3 triangles
  • Hexagon, covers 6 triangles

Six triangles, three rhombuses or two half-hexagons — every one of them fills the very same space.

  1. 1.Which shape has no corners?

    • a) Square
    • b) Triangle
    • c) Rectangle
    • d) Circle

  2. 2.Tap the shape where the line folds it exactly in half.

    Write the number of the part.

    123

  3. 3.Half of this hexagon is already covered. Cover the rest of it.

    Draw lines inside the shape to show how the tiles below cover it.

    • Triangle, covers 1 triangle
    • Rhombus, covers 2 triangles
    • Half-hexagon, covers 3 triangles

  4. 4.Which letter has a line of symmetry straight down the middle?

    • a) A
    • b) F
    • c) P
    • d) J

  5. 5.Match each shape to how many sides it has.

    • Triangle
    • Square
    • Pentagon
    • Hexagon
    • 5
    • 3
    • 4
    • 6

  6. 6.Sort each shape by whether it is flat or solid.

    Groups: Flat shape · Solid shape

    • Square
    • Circle
    • Sphere
    • Cube

  7. 7.How many corners does a triangle have?

  8. 8.Put these shapes in order, fewest sides first.

    • Triangle
    • Hexagon
    • Pentagon
    • Square

Shapes and symmetry · Grade 3 Math · www.arenapublications.com/learn

Answer keys — Grade 3 Math

In the same order as the worksheets.

6 times table

  1. 1. 66
  2. 2. 18
  3. 3. d) 6 × 9
  4. 4. 54
  5. 5. d) 48
  6. 6. d) 24
  7. 7. 6 × 2 → 12; 6 × 5 → 30; 6 × 8 → 48; 6 × 10 → 60
  8. 8. 72

7 times table

  1. 1. a) 7 × 9
  2. 2. 84
  3. 3. 21
  4. 4. b) 49
  5. 5. 63
  6. 6. 42
  7. 7. c) 56
  8. 8. 42

2, 3, 4 and 5 times tables

  1. 1. 1. 2 × 8 2. 3 × 6 3. 4 × 6 4. 5 × 6
  2. 2. 25 → In the 5 times table; 32 → Not in it; 45 → In the 5 times table; 18 → Not in it
  3. 3. 55
  4. 4. b) 45
  5. 5. 20
  6. 6. 15
  7. 7. 2 × 7 → 14; 3 × 7 → 21; 4 × 7 → 28; 5 × 7 → 35
  8. 8. 24

8, 9 and 10 times tables

  1. 1. 120
  2. 2. 1. 8 × 3 2. 9 × 3 3. 10 × 3 4. 8 × 6
  3. 3. 9 × 3 → 27; 9 × 5 → 45; 9 × 7 → 63; 9 × 8 → 72
  4. 4. a) 81
  5. 5. 36
  6. 6. 54
  7. 7. c) 70
  8. 8. 32

Sharing equally

  1. 1. 1. 12 ÷ 4 2. 12 ÷ 3 3. 12 ÷ 2 4. 12 ÷ 1
  2. 2. 10 ÷ 2 → 5; 16 ÷ 4 → 4; 21 ÷ 3 → 7; 40 ÷ 5 → 8
  3. 3. 6
  4. 4. a) 1
  5. 5. 4
  6. 6. 4
  7. 7. 5
  8. 8. 5

Number patterns

  1. 1. a) 10
  2. 2. 30
  3. 3. a) 30
  4. 4. 25
  5. 5. 32
  6. 6. 6, 12, 18 → 24; 10, 20, 30 → 40; 7, 14, 21 → 28; 9, 18, 27 → 36
  7. 7. 27 → Odd; 34 → Even; 41 → Odd; 56 → Even
  8. 8. 50

Halves and quarters

  1. 1. 8 → 4; 14 → 7; 26 → 13; 60 → 30
  2. 2. 3
  3. 3. c) 2/8
  4. 4. b) 2/4
  5. 5. 6
  6. 6. 1. Half of 6 2. Half of 10 3. A quarter of 60 4. Half of 40
  7. 7.
    • 3.5
    • 3 1/2
    • 7/2
    • three and a half
  8. 8. 2

Equivalent fractions

  1. 1. 8
  2. 2. 4/6 → The same as 2/3; 3/5 → Not the same as 2/3; 10/15 → The same as 2/3; 5/8 → Not the same as 2/3; 8/12 → The same as 2/3; 2/5 → Not the same as 2/3
  3. 3. they show the same amount
  4. 4. 1/4 → 3/12; 2/5 → 4/10; 3/8 → 6/16; 5/6 → 10/12
  5. 5. 3/6
  6. 6. 20
  7. 7. 1. 1/2 = ?/6 2. 1/2 = ?/10 3. 2/3 = ?/12 4. 3/4 = ?/16
  8. 8. b) 1/2

Comparing and ordering fractions

  1. 1. 1/3 → Smaller than a half; 3/4 → Larger than a half; 2/5 → Smaller than a half; 5/8 → Larger than a half; 1/6 → Smaller than a half; 7/10 → Larger than a half
  2. 2. 1. 1/8 2. 2/8 3. 5/8 4. 7/8
  3. 3. 1. 1/10 2. 1/6 3. 1/4 4. 1/3 5. 1/2
  4. 4. 1/2 → 3/6; 1/4 → 2/8; 1/3 → 4/12; 2/3 → 8/12
  5. 5. 3
  6. 6. 4
  7. 7. b) 1/3
  8. 8. c) 2/7

Understanding fractions

  1. 1. 20
  2. 2.
    • 3/4
    • 3 / 4
    • three quarters
    • three-quarters
  3. 3. 0.75
  4. 4. 1.75
  5. 5. 3/4 → Less than 1; 5/4 → More than 1; 7/8 → Less than 1; 9/7 → More than 1; 5/9 → Less than 1; 8/3 → More than 1
  6. 6. 1. 1/6 2. 1/4 3. 1/3 4. 1/2 5. 2/3 6. 3/4
  7. 7.
    • 3 2/5
    • 3 2 / 5
  8. 8.
    • 13/5
    • 13 / 5

Measuring with standard units

  1. 1. A pencil → inches; A rope across a room → feet; A bag of rice → pounds; Water in a bottle → pints
  2. 2. 65
  3. 3. c) 7 feet
  4. 4. 3 — The bucket
  5. 5. How tall is the door? → Length; How heavy is the bag? → Weight; How wide is the table? → Length; How much does the melon weigh? → Weight
  6. 6. 1. 15 inches 2. 40 inches 3. 65 inches 4. 90 inches
  7. 7. d) 54 inches
  8. 8. c) A road between two towns

Reading a picture graph

  1. 1. 3
  2. 2. 3 — Wednesday
  3. 3. 8
  4. 4. 5
  5. 5. Cats → Fewer than 8; Dogs → More than 8; Birds → Fewer than 8; Fish → More than 8
  6. 6. 14
  7. 7. b) 15
  8. 8. 1. Tuesday 2. Thursday 3. Monday 4. Wednesday

How heavy, and how much it holds

  1. 1. 3
  2. 2. 10
  3. 3. 3 lb → 5; 6 lb → 8; 10 lb → 12; 1 lb → 3
  4. 4. 12
  5. 5. 1. A pin 2. An apple 3. A school bag 4. A car
  6. 6. 10
  7. 7. d) A brick
  8. 8. 8

Perimeter: once round the outside

  1. 1. 36
  2. 2. Triangle → 18; Square → 24; Pentagon → 30; Hexagon → 36; Octagon → 48
  3. 3. 8
  4. 4. 7
  5. 5. 50
  6. 6. 38
  7. 7. 1. A square of side 3 2. A square of side 4 3. A rectangle 5 by 4 4. A regular hexagon of side 4 5. A square of side 8
  8. 8. c) A regular pentagon of side 5

Area by counting squares

  1. 1. 2 — Shape B
  2. 2. 2 across and 3 down → 6; 3 across and 3 down → 9; 4 across and 5 down → 20; 6 across and 6 down → 36
  3. 3. 4
  4. 4. 3 across and 5 down → Fewer than 20 squares; 4 across and 4 down → Fewer than 20 squares; 5 across and 5 down → More than 20 squares; 6 across and 4 down → More than 20 squares; 2 across and 9 down → Fewer than 20 squares; 7 across and 3 down → More than 20 squares
  5. 5. a) 3 across and 6 down
  6. 6. 28
  7. 7. 23
  8. 8. 14

Reading bar charts

  1. 1. c) So that the height of a bar can be read as a number
  2. 2. 1. Tuesday 2. Thursday 3. Monday 4. Wednesday
  3. 3. 3 — Wednesday
  4. 4. 5
  5. 5. c) 45
  6. 6. 40
  7. 7. 4 — Yellow team
  8. 8. 2 squares → 8; 3 squares → 12; 5 squares → 20; 7 squares → 28

Bar graphs with scales

  1. 1. 2 — Tuesday
  2. 2. 1. 2 lines up 2. 3 lines up 3. 5 lines up 4. 7 lines up
  3. 3. 35
  4. 4. 20
  5. 5. 15 → Lands on a line; 22 → Lands between two lines; 35 → Lands on a line; 8 → Lands between two lines; 40 → Lands on a line; 13 → Lands between two lines
  6. 6. c) So the height of a bar can be turned into a number
  7. 7. 160
  8. 8. 4 — Class D

Perimeter and area

  1. 1. 28
  2. 2. 31
  3. 3. 36
  4. 4. 6
  5. 5. 49
  6. 6. 15
  7. 7. a) 6 by 5
  8. 8. 1. 2 by 6 2. 3 by 5 3. 4 by 4 4. 3 by 6 5. 5 by 4

Pictographs and bar graphs

  1. 1. 1 — Monday
  2. 2. 35
  3. 3. 1. Tuesday 2. Monday 3. Thursday 4. Wednesday
  4. 4. 2 symbols → 10; 3 symbols → 15; 4 symbols → 20; 6 symbols → 30
  5. 5. 24
  6. 6. 17
  7. 7. 4
  8. 8. Monday 30, Tuesday 15, Wednesday 40, Thursday 25

Shapes and symmetry

  1. 1. d) Circle
  2. 2. 1 — The square
  3. 3. any covering — e.g. 1 half-hexagon
  4. 4. a) A
  5. 5. Triangle → 3; Square → 4; Pentagon → 5; Hexagon → 6
  6. 6. Square → Flat shape; Cube → Solid shape; Circle → Flat shape; Sphere → Solid shape
  7. 7. 3
  8. 8. 1. Triangle 2. Square 3. Pentagon 4. Hexagon

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