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3rd Grade · 3.OA.A.1

Equal groups in 3rd grade

Equal groups are groups that each hold the same number of things, like 6 cups with 2 crackers in each. In 3rd grade, your child learns multiplication as equal groups: 4×64 \times 6 means 4 groups of 6, and the answer is the total number of things.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

What it means, in plain words

Multiplication is a quick way to find the total when every group has the same number of things. The first number says how many groups there are. The second number says how many things are in each group. So 4×64 \times 6 is 4 groups of 6, and 6×46 \times 4 is 6 groups of 4. Both make 24, but they describe different pictures.

Equal groups in 3rd grade come in several forms: bags of apples, rows of chairs or jumps of the same size along a number line. An array is a set of objects in rows and columns, where every row has the same number. Each row of an array is one equal group.

Your child also works the other way, from a multiplication to a story. Given 3×83 \times 8, your child should be able to describe a situation it fits, such as 3 packs with 8 crayons in each pack. Telling the story shows that your child knows what each number stands for.

Your child should be able to:

  • Explain that 4×64 \times 6 means 4 groups of 6
  • Write a multiplication for a picture of equal groups or an array
  • Tell a short story that fits a multiplication such as 3×83 \times 8
  • Find the total by skip counting or with a known fact

Example

There are 4 bags with 6 oranges in each bag. Write a multiplication and find how many oranges there are in all.

  1. There are 4 bags, so there are 4 groups.
  2. Each bag has 6 oranges, so each group has 6.
  3. The multiplication is 4×64 \times 6.
  4. Skip count by 6 four times: 6, 12, 18, 24.
  5. There are 24 oranges in all.

Example

Tell a story that fits 2×92 \times 9, then find the total.

  1. The first number is the number of groups, so there are 2 groups.
  2. The second number is how many are in each group, so each group has 9.
  3. One story: 2 teams play soccer, with 9 players on each team.
  4. 2×9=182 \times 9 = 18, so there are 18 players in all.

Where children usually get stuck

  • For 4 bags with 6 oranges in each, your child writes 4+6=104 + 6 = 10.

    Your child sees two numbers and adds them, because adding is what has always worked. The 6 is the count inside each bag, not 6 more oranges.

    What helps. Act it out with 4 cups and some dry beans. Put 6 beans in each cup, then count all the beans together.

  • Your child draws groups of different sizes, such as 5, 6 and 7, and still writes 3×63 \times 6.

    Your child knows multiplication uses groups but has not noticed that every group must hold the same number. With unequal groups there is no single number to multiply by.

    What helps. Before your child writes a multiplication, check each group together and ask "Does every group have 6?"

  • With the groups drawn, your child still counts every object one at a time, all the way to 24.

    Your child sees separate objects, not groups that can be counted as one unit each. Skip counting by the group size is what turns counting into multiplication.

    What helps. Touch each group in turn and say only the running total: 6, 12, 18, 24.

Try four practice questions

Real 3rd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    Liam looked at the picture of equal groups below.
    Liam said: "2 groups of 5." Which statement best matches Liam's claim?
    A
    Liam swapped the number of groups and the number in each group.
    B
    Liam miscounted only the number in each group.
    C
    Liam miscounted only the number of groups.
    D
    Liam described the groups correctly.
    Show the answer and how to solve it

    Liam described the groups correctly. The picture shows 2 groups of 5 stars, and that is exactly what Liam said.

    1. 1Look at the picture. Count the groups: there are 2 groups. Count the stars in each group: each group has 5 stars. So the picture shows 2 groups of 5.
    2. 2Compare this to Liam's claim. Liam said "2 groups of 5." That matches the picture exactly.
    3. 3Liam's description matches the picture exactly. He used the correct group count (2) and the correct items per group (5).

    Common mistake. A common mistake is assuming Liam must have made an error. "2 groups of 5" and "5 groups of 2" look similar but describe different pictures. The first number always tells how many groups; the second tells how many are in each group. Liam's numbers are in the right order.

    The idea underneath. In equal groups, the order of the two numbers matters. The first number tells how many groups; the second tells how many are in each group. Switching them describes a different picture.

  2. 2On level
    Look at the equal groups below. Which multiplication expression matches the picture? Use the number of groups as the first factor and the number in each group as the second factor.
    A
    4×3\displaystyle 4 \times 3
    B
    3×4\displaystyle 3 \times 4
    C
    3×5\displaystyle 3 \times 5
    D
    4×4\displaystyle 4 \times 4
    Show the answer and how to solve it

    The expression 3×43 \times 4 matches the picture because there are 33 groups, and each group has 44 stars.

    1. 1Look at the picture. Count the number of circles. There are 33 circles, so there are 33 equal groups.
    2. 2Now count the stars in one circle. Each circle has 44 stars, and every circle has the same number.
    3. 3When we write a multiplication expression for equal groups, the first number is the number of groups, and the second number is how many are in each group. So 33 groups of 44 stars is 3×43 \times 4.

    Common mistake. A common mistake is writing 4×34 \times 3. That expression means 44 groups of 33, but the picture shows 33 groups of 44. The first factor is always the number of groups.

    The idea underneath. In a multiplication expression for equal groups, the first number tells how many groups and the second number tells how many are in each group. Here, 3×43 \times 4 means 33 groups of 44 — the order matters.

  3. 3On level
    Maya wrote a multiplication for the equal jumps on the number line.
    051015+3+3+3+3+3
    5×3\displaystyle 5 \times 3
    Select the statement that best describes Maya's work.
    A
    The expression matches the jumps.
    B
    The number of jumps is wrong.
    C
    The jump size is wrong.
    D
    Both numbers are wrong.
    Show the answer and how to solve it

    The expression matches the jumps. There are 55 jumps of size 33, and Maya's expression 5×35 \times 3 correctly shows this.

    1. 1First, look at the number line. There are 5 equal jumps. Each jump moves 3 units to the right.
    2. 2For a number line, the multiplication is (number of jumps) × (size of each jump). With 55 jumps of size 33, the correct expression is:
    3. 3Maya wrote 5×35 \times 3. The first number, 55, matches the count of jumps. The second number, 33, matches the jump size. The expression matches the picture.

    The idea underneath. On a number line, the order matters: the first factor counts the jumps, and the second tells the size of each jump. Even though 5×35 \times 3 and 3×53 \times 5 have the same product, only one matches the picture.

  4. 4Stretch
    Which story matches this expression? Use the first number for the number of groups and the second for the number in each group.
    0×7\displaystyle 0 \times 7
    A
    There are 7 baskets, with 0 apples in each basket.
    B
    There are 0 baskets. Each basket would hold 7 apples.
    C
    There are 0 apples.
    D
    There is 1 basket with 7 apples in it.
    Show the answer and how to solve it

    0×70 \times 7 means 00 groups of 77. The matching story is: "There are 00 baskets, with 77 apples in each basket."

    1. 1Look at the expression below.
    2. 2In a multiplication expression, the first number tells how many groups there are, and the second number tells how many things would be in each group.
    3. 3So 0×70 \times 7 means 00 groups, each meant to hold 77 items. There are no groups at all — just zero of them.
    4. 4Find the story that says there are 00 baskets, with 77 apples meant for each basket. That story matches the structure 0×70 \times 7.

    Common mistake. A common mistake is reversing the factor order. The expression 0×70 \times 7 means 00 groups of 77, while 7×07 \times 0 means 77 groups of 00. Both have a product of 00, but they describe different structures.

    The idea underneath. When you see a multiplication like 0×70 \times 7 or 1×71 \times 7, the first number tells how many groups there are, and the second tells how many things would be in each group. The order matters even when one factor is 00 or 11.