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YEAR 3 · MULTIPLICATION AND DIVISION · 20 MIN

One-/two-digit problems

Represent one- and two-digit multiplication or division stories, then interpret the answer in context.

In this lesson

Before you start
  • Multiplication and linked division
  • Tens and ones
01 / LEARN

Understand the idea.

Choose from the story

Decide what the story is asking before choosing an operation. Multiply when the number of equal groups and their size are known. Divide when the total is known and either the group size or group count is missing.

For a two-digit group size, split each group into easier parts. Three packets of fourteen counters contain three tens and three fours. Add 30+12 to find 42 counters altogether.

Interpret the answer

Division can also use a useful split. Share 48 cards among four players by sharing 40 first, then 8. Each player gets 10 from the first part and 2 from the second, for 12 cards.

A leftover changes how you state the answer. Twenty-three children can make four full teams of five, with three left. If every child needs a team of up to five, those three need a smaller fifth team. Read which question is asked.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find a larger total

A garden has 3 rows with 16 plants in each. How many plants are there?

Worked solution

  1. 1

    Write the equal-group calculation.

    3×16

    There are three rows and sixteen plants in every row.

  2. 2

    Split each row into ten and six plants.

    16=10+6

    This split includes all sixteen plants in each row.

  3. 3

    Count each part across three rows.

    3×10=303×6=18

    The ten-plant and six-plant parts are each repeated three times.

  4. 4

    Add the plant totals.

    30+18=48

    The garden contains forty-eight plants altogether.

Answer

48 plants.

EXAMPLE 02

Deal with a leftover

There are 27 pencils. Each full pot holds 4. How many full pots can be filled, and how many pencils remain?

Worked solution

  1. 1

    Find the largest possible number of full pots.

    6×4=247×4=28

    Six pots use no more than twenty-seven pencils, but seven full pots need too many.

  2. 2

    Find the pencils not used in full pots.

    27−24=3

    Six full pots use twenty-four of the twenty-seven pencils.

  3. 3

    Check the grouping and leftover.

    6×4+3=273<4

    The three remaining pencils cannot fill another pot, so there are six full pots and three left.

Answer

6 full pots and 3 pencils left.

03 / YOUR TURN

Try it yourself.

Check your understanding

Find the total in 4 boxes of 13 counters.

Show answer & reasoning

52 counters.

Split each box into 10+3 counters. Four tens make 40 and four threes make 12, so 40+12=52 counters.

Keep practising

6 worksheet questions

Read the questions online
  1. There are 3 bags with 12 shells in each. How many shells altogether?
  2. Four players share 48 cards equally. How many cards does each get?
  3. A theatre has 5 rows with 14 seats in each row. How many seats are there?
  4. Sixty crayons are packed into 5 equal boxes. How many crayons go in each box?
  5. Twenty-nine biscuits are packed into bags of 5. How many full bags are made? How many biscuits remain?
  6. Twenty-nine biscuits must all be packed. A bag can hold at most 5. What is the smallest number of bags needed?
Read the worked solutions
  1. There are 3 bags with 12 shells in each. How many shells altogether?

    3×10+3×2=30+6=36.

    36 shells.
  2. Four players share 48 cards equally. How many cards does each get?

    40÷4=10 and 8÷4=2; 10+2=12.

    12 cards.
  3. A theatre has 5 rows with 14 seats in each row. How many seats are there?

    5×10+5×4=50+20=70.

    70 seats.
  4. Sixty crayons are packed into 5 equal boxes. How many crayons go in each box?

    5×12=60.

    12 crayons.
  5. Twenty-nine biscuits are packed into bags of 5. How many full bags are made? How many biscuits remain?

    5×5=25; 29−25=4.

    5 full bags and 4 biscuits.
  6. Twenty-nine biscuits must all be packed. A bag can hold at most 5. What is the smallest number of bags needed?

    Five bags hold only 25. A sixth bag holds the remaining 4.

    6 bags.
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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Tables 2, 3, 4, 5 and 10; linked division; arrays; one-/two-digit problems.

Official curriculum source ↗

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