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Term pack

Grade 5 Math

Name: ________________________

Skills in this pack

  • Decimal place value
  • Adding and subtracting decimals
  • Multiplying and dividing larger numbers
  • Decimals
  • Adding and subtracting fractions
  • Unlike fractions and mixed numbers
  • Multiplying and dividing fractions and decimals
  • Number patterns
  • Averages
  • Volume with unit cubes
  • Coordinate geometry
  • Understanding quadrilaterals

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Grade 5 Math · 1 of 12

Decimal place value

Say what each digit is worth in a decimal number.

Before you start

This line runs from 0 to 1 in tenths. Look at where each tenth falls, and how much of the way along 0.7 really is.

0.00.10.20.30.40.50.60.70.80.91.0

Every decimal between 0 and 1 lives somewhere on this line. There is nothing beyond the ends of it, however many digits are written.

  1. 1.In 5.062, what is the 6 worth?

    • a) 6 thousandths
    • b) 6 ones
    • c) 6 hundredths
    • d) 6 tenths

  2. 2.In 12.905, which digit is in the hundredths place?

    • a) 0
    • b) 2
    • c) 5
    • d) 9

  3. 3.Which of these is the same as 0.6?

    • a) 0.60
    • b) 0.06
    • c) 0.006
    • d) 6.0

  4. 4.Which number is the largest?

    • a) 0.409
    • b) 0.4999
    • c) 0.5
    • d) 0.45

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

    • 2.03
    • 2.3
    • 2.4
    • 2.31

  6. 6.One point on this line is 4 tenths and 7 hundredths. Which point is it?

    Mark the line with an X.

    0.400.450.50

  7. 7.Put these in order, smallest first.

    • 0.11
    • 0.1
    • 0.21
    • 0.2

  8. 8.What is 7.8 rounded to the nearest whole number?

    • a) 80
    • b) 8
    • c) 7.5
    • d) 7

Decimal place value · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 2 of 12

Adding and subtracting decimals

Add and subtract numbers with tenths and hundredths by keeping the columns lined up.

Before you start

This line runs from 0 to 1. The numbered ticks are tenths, and the plain ticks between them fall halfway again. Look at how far apart 0.05 and 0.5 really are.

0.000.100.200.300.400.500.600.700.800.901.00

Ten hundredths make one tenth. That is why 0.5 is far bigger than 0.05, even though both are written with a 5.

  1. 1.Work each one out, then put them in order, smallest answer first.

    • 3.6 - 0.7
    • 1.9 + 0.5
    • 1.2 + 0.3
    • 2.5 - 0.4

  2. 2.5.8 - 2.3 = ?

  3. 3.Which of these is 1.05 + 0.9?

    • a) 1.95
    • b) 1.85
    • c) 2.05
    • d) 1.14

  4. 4.2.5 + 1.3 = ?

  5. 5.0.75 + 0.25 = ?

  6. 6.4.6 + 2.35 = ?

  7. 7.Tap where 2.6 + 0.7 lands.

    Mark the line with an X.

    2.02.53.03.54.0

  8. 8.A notebook costs $12.50 and a pencil costs $4.25. What do they cost together? Give just the number.

Adding and subtracting decimals · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 3 of 12

Multiplying and dividing larger numbers

Multiply by a two-digit number, divide with a remainder, and multiply or divide by 10, 100 and 1000.

  1. 1.144 crayons are shared equally between 12 children. How many crayons does each child get?

  2. 2.23 × 14 = ?

  3. 3.34 × 100 = ?

  4. 4.56 × 1000 = ?

  5. 5.What is the remainder when 47 is divided by 6?

  6. 6.Which of these is 48 × 25?

    • a) 1200
    • b) 960
    • c) 1000
    • d) 1250

  7. 7.Match each calculation to its answer.

    • 7 × 10
    • 7 × 100
    • 7 × 1000
    • 9000 ÷ 10
    • 9000 ÷ 1000
    • 9
    • 7000
    • 70
    • 900
    • 700

  8. 8.Work each one out, then put them in order, smallest answer first.

    • 15 × 11
    • 12 × 12
    • 23 × 9
    • 18 × 10

Multiplying and dividing larger numbers · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 4 of 12

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.

3.03.13.23.33.43.53.63.73.83.94.0

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. 1.8.6 - 3.75 = ?

  2. 2.Match each fraction to the decimal that is worth the same.

    • 1/2
    • 1/4
    • 3/4
    • 1/5
    • 3/10
    • 0.3
    • 0.25
    • 0.5
    • 0.2
    • 0.75

  3. 3.What is 0.6 + 0.45?

  4. 4.A pencil is 12.5 inches long and a pen is 14.2 inches long. How much longer is the pen, in inches? Give just the number.

  5. 5.Write 7/10 as a decimal.

  6. 6.Tap where 2.75 sits.

    Mark the line with an X.

    2.002.252.502.753.00

  7. 7.3.4 + 2.75 = ?

  8. 8.Which of these decimals is the largest?

    • a) 0.609
    • b) 0.5
    • c) 0.7
    • d) 0.68

Decimals · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 5 of 12

Adding and subtracting fractions

Add and subtract fractions, including ones with different denominators.

  1. 1.7/10 - 3/10 = ? Write your answer as a fraction.

  2. 2.2/3 + 1/6 = ? Write your answer as a fraction.

  3. 3.5/6 - 1/3 = ? Write your answer as a fraction.

  4. 4.Which fraction is worth the same as 1/2?

    • a) 4/6
    • b) 2/5
    • c) 3/6
    • d) 5/12

  5. 5.1/3 + 1/4 = ? Write your answer as a fraction.

  6. 6.1/5 + 2/5 = ? Write your answer as a fraction.

  7. 7.5/8 - 2/8 = ? Write your answer as a fraction.

  8. 8.3/4 - 1/2 = ? Write your answer as a fraction.

Adding and subtracting fractions · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 6 of 12

Unlike fractions and mixed numbers

Add and subtract fractions with different denominators, and swap between mixed numbers and improper fractions.

  1. 1.2/3 + 1/6 = ? Write your answer as a fraction.

  2. 2.Sort each fraction by how it compares with a half.

    Groups: Less than a half · More than a half

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

  3. 3.3/4 - 1/8 = ? Write your answer as a fraction.

  4. 4.1/2 + 1/5 = ? Write your answer as a fraction.

  5. 5.A film lasts 3 1/2 hours, and 1 1/4 hours of it have been watched. How much is left? Write your answer as a mixed number.

  6. 6.Write 2 1/3 as an improper fraction.

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

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

  8. 8.Three eighths of a cake are eaten in the morning and two eighths in the afternoon. What fraction of the cake has been eaten? Write your answer as a fraction.

Unlike fractions and mixed numbers · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 7 of 12

Multiplying and dividing fractions and decimals

Multiply and divide fractions and decimals, and know when the answer will be smaller than what you started with.

  1. 1.Work out each one, then sort it by whether the answer is less than 1 or more than 1.

    Groups: Less than 1 · More than 1

    • 0.5 × 0.8
    • 2/3 ÷ 1/3
    • 3/4 × 2
    • 0.9 ÷ 0.3
    • 1/4 ÷ 2
    • 1/3 × 1/2

  2. 2.Multiply a whole number by a fraction smaller than 1. The answer is always...

    • a) bigger than the whole number you started with
    • b) a whole number too
    • c) smaller than the whole number you started with
    • d) exactly the same as the whole number

  3. 3.1/2 ÷ 1/4 = ?

  4. 4.2/5 ÷ 1/10 = ?

  5. 5.3/4 ÷ 2 = ? Write your answer as a fraction.

  6. 6.3/5 × 10 = ?

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

    • 0.4
    • 1/3
    • 0.75
    • 1/2
    • 0.25

  8. 8.0.4 × 0.3 = ?

Multiplying and dividing fractions and decimals · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 8 of 12

Number patterns

Work out the rule behind a pattern of numbers and carry the pattern on.

Before you start

This line starts at 1 and every mark along it is 4 further on. Move from mark to mark and see which numbers the pattern lands on.

1917253341

Once you know what happens between two neighboring marks you know every number on the line, however far along it you go. Finding the rule is the work; the next number then costs nothing.

  1. 1.What is the missing number? 45, 40, ?, 30, 25

  2. 2.A pattern of squares grows: 1 square, then 4, then 9. How many squares are in the next step?

    • a) 14
    • b) 20
    • c) 16
    • d) 12

  3. 3.A pattern goes 12, 16, 20 and carries on. Tap the number that comes next.

    Mark the line with an X.

    1012141618202224262830

  4. 4.What comes next? 3, 7, 11, 15, ?

  5. 5.What comes next? 1, 4, 9, 16, ?

  6. 6.Sort each pattern by what its rule does.

    Groups: Adds the same amount each time · Doubles each time

    • 4, 8, 16, 32
    • 2, 4, 6, 8
    • 5, 10, 15, 20
    • 7, 12, 17, 22
    • 3, 6, 12, 24
    • 1, 2, 4, 8

  7. 7.What comes next? 1, 1, 2, 3, 5, 8, ?

  8. 8.What is the rule for 2, 5, 8, 11, 14?

    • a) Add 3
    • b) Add 2
    • c) Multiply by 2
    • d) Add 4

Number patterns · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 9 of 12

Averages

Find the average of a small set of numbers by sharing the total out equally.

  1. 1.Three parcels weigh 2 lb, 5 lb and 8 lb. What is their average mass, in pounds? Give just the number.

  2. 2.Five numbers have an average of 6. A sixth number, 12, is added to the set. What happens to the average?

    • a) It goes down
    • b) It goes up
    • c) It becomes 12
    • d) It stays the same

  3. 3.Match each pair of numbers to its average.

    • 2, 4
    • 4, 6
    • 6, 10
    • 10, 14
    • 14, 20
    • 12
    • 3
    • 8
    • 17
    • 5

  4. 4.Which of these sets of numbers has an average of 5?

    • a) 2, 4, 6
    • b) 1, 5, 9
    • c) 3, 5, 8
    • d) 4, 6, 8

  5. 5.Work out each average, then sort it by size.

    Groups: Average is less than 10 · Average is 10 or more

    • 1, 2, 3
    • 14, 16, 18
    • 5, 6, 7
    • 2, 4, 6
    • 8, 10, 12
    • 9, 11, 13

  6. 6.Three children have 5, 8 and 11 stickers. They share them all out equally. How many does each child end up with?

  7. 7.Two numbers have an average of 9. One of them is 6. What is the other?

  8. 8.A player scores 20, 30 and 40 points in three games. What is the average score?

Averages · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 10 of 12

Volume with unit cubes

Find the volume of a box by counting the unit cubes that fill it.

  1. 1.A box is 5 cubes long, 2 cubes wide and 3 cubes tall. How many unit cubes fill it?

  2. 2.A box holds 20 unit cubes in a single layer. Filled 4 layers deep, how many unit cubes does it hold?

  3. 3.Work out each box, then sort it by how many unit cubes it holds.

    Groups: Fewer than 24 cubes · 24 cubes or more

    • 2 by 2 by 5
    • 4 by 4 by 2
    • 5 by 5 by 1
    • 1 by 3 by 6
    • 2 by 2 by 4
    • 3 by 4 by 2

  4. 4.A cuboid is built from 36 unit cubes in 3 equal layers. How many cubes are in each layer?

  5. 5.A cuboid is 6 inches long, 3 inches wide and 2 inches tall. What is its volume, in cubic inches? Give just the number.

  6. 6.Put these boxes in order, starting with the one that holds the fewest unit cubes.

    • 3 by 3 by 3
    • 2 by 3 by 3
    • 3 by 4 by 3
    • 2 by 2 by 3

  7. 7.Which of these boxes holds the most unit cubes?

    • a) 2 by 3 by 4
    • b) 2 by 2 by 6
    • c) 3 by 3 by 3
    • d) 1 by 5 by 5

  8. 8.A tower is built from 3 layers, and each layer holds 4 cubes. How many cubes is that altogether?

Volume with unit cubes · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 11 of 12

Coordinate geometry

Read and plot points on the coordinate plane and name the quadrant they lie in.

Before you start

The two axes cut the page into four quarters. Find out what each one is called — all four, in any order, nothing to get right.

1234
  1. 1. First quadrant
  2. 2. Second quadrant
  3. 3. Third quadrant
  4. 4. Fourth quadrant

They are numbered counterclockwise from the top right. Both coordinates are positive in the first and both are negative in the third.

  1. 1.In which quadrant does the point (-4, 2) lie?

    • a) Fourth
    • b) First
    • c) Third
    • d) Second

  2. 2.In which quadrant does the point (3, 5) lie?

    • a) Fourth
    • b) First
    • c) Second
    • d) Third

  3. 3.Sort each point by which axis it sits on.

    Groups: On the x-axis · On the y-axis

    • (5, 0)
    • (9, 0)
    • (0, -7)
    • (0, 5)
    • (-3, 0)
    • (0, 2)

  4. 4.Match each point to where it lies.

    • (2, 3)
    • (-2, 3)
    • (-2, -3)
    • (2, -3)
    • (0, 0)
    • Second quadrant
    • First quadrant
    • The origin
    • Fourth quadrant
    • Third quadrant

  5. 5.What are the coordinates of the origin?

    • a) (1, 1)
    • b) (1, 0)
    • c) (0, 0)
    • d) (0, 1)

  6. 6.How far is the point (6, 8) from the y-axis? Give just the number.

  7. 7.In which quadrant does the point (-2, -6) lie?

    • a) Second
    • b) Third
    • c) Fourth
    • d) First

  8. 8.What is the x-coordinate of the point (7, -3)?

Coordinate geometry · Grade 5 Math · www.arenapublications.com/learn

Grade 5 Math · 12 of 12

Understanding quadrilaterals

Work out the angles in a polygon and use the properties of parallelograms, rhombuses, rectangles and squares.

Before you start

The four corners of this parallelogram hold four angles. Find out how big each one is — nothing here is right or wrong.

1234
  1. 1. Angle A — 45°
  2. 2. Angle B — 135°
  3. 3. Angle C — 45°
  4. 4. Angle D — 135°

Opposite corners match. Any two corners next to each other add up to 180°, which is why one known angle gives you all four.

  1. 1.Match each regular polygon to the size of one of its exterior angles, in degrees.

    • Equilateral triangle
    • Square
    • Regular pentagon
    • Regular hexagon
    • Regular decagon
    • 90
    • 60
    • 120
    • 36
    • 72

  2. 2.Sort each property by whether it is true of every parallelogram.

    Groups: True of every parallelogram · Not true of every parallelogram

    • Opposite angles are equal
    • All four sides are equal
    • The diagonals are equal in length
    • Every angle is a right angle
    • The diagonals cut each other in half
    • Opposite sides are equal

  3. 3.What do the interior angles of a pentagon add up to, in degrees? Give just the number.

  4. 4.One angle of a parallelogram is 65 degrees. What is the angle next to it, in degrees? Give just the number.

  5. 5.What do the four angles of any quadrilateral add up to, in degrees? Give just the number.

  6. 6.The diagonals of a parallelogram cross at the middle. One diagonal is cut into two pieces of 5 inches each. How long is that whole diagonal, in inches? Give just the number.

  7. 7.What do the interior angles of a hexagon add up to, in degrees? Give just the number.

  8. 8.Three angles of a quadrilateral are 80, 100 and 65 degrees. What is the fourth, in degrees? Give just the number.

Understanding quadrilaterals · Grade 5 Math · www.arenapublications.com/learn

Answer keys — Grade 5 Math

In the same order as the worksheets.

Decimal place value

  1. 1. c) 6 hundredths
  2. 2. a) 0
  3. 3. a) 0.60
  4. 4. c) 0.5
  5. 5. 1. 2.03 2. 2.3 3. 2.31 4. 2.4
  6. 6. 0.47
  7. 7. 1. 0.1 2. 0.11 3. 0.2 4. 0.21
  8. 8. b) 8

Adding and subtracting decimals

  1. 1. 1. 1.2 + 0.3 2. 2.5 - 0.4 3. 1.9 + 0.5 4. 3.6 - 0.7
  2. 2. 3.5
  3. 3. a) 1.95
  4. 4. 3.8
  5. 5. 1
  6. 6. 6.95
  7. 7. 3.3
  8. 8. 16.75

Multiplying and dividing larger numbers

  1. 1. 12
  2. 2. 322
  3. 3. 3400
  4. 4. 56000
  5. 5. 5
  6. 6. a) 1200
  7. 7. 7 × 10 → 70; 7 × 100 → 700; 7 × 1000 → 7000; 9000 ÷ 10 → 900; 9000 ÷ 1000 → 9
  8. 8. 1. 12 × 12 2. 15 × 11 3. 18 × 10 4. 23 × 9

Decimals

  1. 1. 4.85
  2. 2. 1/2 → 0.5; 1/4 → 0.25; 3/4 → 0.75; 1/5 → 0.2; 3/10 → 0.3
  3. 3. 1.05
  4. 4. 1.7
  5. 5.
    • 0.7
    • .7
    • 0.70
  6. 6. 2.75
  7. 7. 6.15
  8. 8. c) 0.7

Adding and subtracting fractions

  1. 1. 2/5
  2. 2. 5/6
  3. 3. 1/2
  4. 4. c) 3/6
  5. 5. 7/12
  6. 6. 3/5
  7. 7. 3/8
  8. 8. 1/4

Unlike fractions and mixed numbers

  1. 1. 5/6
  2. 2. 1/3 → Less than a half; 5/8 → More than a half; 2/5 → Less than a half; 3/4 → More than a half; 1/6 → Less than a half; 7/10 → More than a half
  3. 3. 5/8
  4. 4. 7/10
  5. 5. 2 1/4
  6. 6. 7/3
  7. 7. 1. 1/6 2. 1/3 3. 1/2 4. 2/3
  8. 8. 5/8

Multiplying and dividing fractions and decimals

  1. 1. 1/3 × 1/2 → Less than 1; 3/4 × 2 → More than 1; 2/3 ÷ 1/3 → More than 1; 0.5 × 0.8 → Less than 1; 0.9 ÷ 0.3 → More than 1; 1/4 ÷ 2 → Less than 1
  2. 2. c) smaller than the whole number you started with
  3. 3. 2
  4. 4. 4
  5. 5. 3/8
  6. 6. 6
  7. 7. 1. 0.25 2. 1/3 3. 0.4 4. 1/2 5. 0.75
  8. 8. 0.12

Number patterns

  1. 1. 35
  2. 2. c) 16
  3. 3. 24
  4. 4. 19
  5. 5. 25
  6. 6. 2, 4, 6, 8 → Adds the same amount each time; 3, 6, 12, 24 → Doubles each time; 5, 10, 15, 20 → Adds the same amount each time; 1, 2, 4, 8 → Doubles each time; 7, 12, 17, 22 → Adds the same amount each time; 4, 8, 16, 32 → Doubles each time
  7. 7. 13
  8. 8. a) Add 3

Averages

  1. 1. 5
  2. 2. b) It goes up
  3. 3. 2, 4 → 3; 4, 6 → 5; 6, 10 → 8; 10, 14 → 12; 14, 20 → 17
  4. 4. b) 1, 5, 9
  5. 5. 2, 4, 6 → Average is less than 10; 8, 10, 12 → Average is 10 or more; 1, 2, 3 → Average is less than 10; 9, 11, 13 → Average is 10 or more; 5, 6, 7 → Average is less than 10; 14, 16, 18 → Average is 10 or more
  6. 6. 8
  7. 7. 12
  8. 8. 30

Volume with unit cubes

  1. 1. 30
  2. 2. 80
  3. 3. 2 by 2 by 5 → Fewer than 24 cubes; 3 by 4 by 2 → 24 cubes or more; 1 by 3 by 6 → Fewer than 24 cubes; 4 by 4 by 2 → 24 cubes or more; 2 by 2 by 4 → Fewer than 24 cubes; 5 by 5 by 1 → 24 cubes or more
  4. 4. 12
  5. 5. 36
  6. 6. 1. 2 by 2 by 3 2. 2 by 3 by 3 3. 3 by 3 by 3 4. 3 by 4 by 3
  7. 7. c) 3 by 3 by 3
  8. 8. 12

Coordinate geometry

  1. 1. d) Second
  2. 2. b) First
  3. 3. (5, 0) → On the x-axis; (0, 5) → On the y-axis; (-3, 0) → On the x-axis; (0, -7) → On the y-axis; (9, 0) → On the x-axis; (0, 2) → On the y-axis
  4. 4. (2, 3) → First quadrant; (-2, 3) → Second quadrant; (-2, -3) → Third quadrant; (2, -3) → Fourth quadrant; (0, 0) → The origin
  5. 5. c) (0, 0)
  6. 6. 6
  7. 7. b) Third
  8. 8. 7

Understanding quadrilaterals

  1. 1. Equilateral triangle → 120; Square → 90; Regular pentagon → 72; Regular hexagon → 60; Regular decagon → 36
  2. 2. Opposite sides are equal → True of every parallelogram; Opposite angles are equal → True of every parallelogram; The diagonals cut each other in half → True of every parallelogram; All four sides are equal → Not true of every parallelogram; The diagonals are equal in length → Not true of every parallelogram; Every angle is a right angle → Not true of every parallelogram
  3. 3. 540
  4. 4. 115
  5. 5. 360
  6. 6. 10
  7. 7. 720
  8. 8. 115

Grade 5 Math · www.arenapublications.com/learn