- Read the array as \(8\) equal groups. - How many dots are in one group?

1. Read the array as \(8\) equal rows. 2. Each row contains \(6\) dots, so each bowl receives \(6\) beads. 3. The division equation is \(48 \div 8 = 6\).

\(6\) beads per bowl; \(48 \div 8 = 6\). The array has \(8\) equal rows with \(6\) dots in each row.

- Cover all but one row. What useful count can you read now? - How could you check the shares by putting them back together?

1. The picture has \(3\) rows with \(4\) crayons in each row. 2. Each child gets \(4\) crayons, so \(12\div3=4\).

\(4\) crayons each; \(12\div3=4\).

- Imagine filling one group. How could you tell when it is full? - How can you check that all the cubes have been used?

1. Each group contains \(5\) cubes. 2. \(15\div5=3\), so there are \(3\) groups.

\(3\) groups; \(15\div5=3\).

- In A, ask what the \(4\) counts. - Do the same for B. - The division answer is \(3\) in both situations, but it tells you something different each time.

1. \(12 \div 4=3\). 2. In B, \(4\) is the number of marbles in each bag, so the answer \(3\) tells the number of bags. 3. In A, \(4\) is the number of bags, so the answer \(3\) tells the number of marbles in each bag.

a) \(3\) b) B c) A

- Think of each row as one group of \(7\) dots. - Ask how many equal groups of \(7\) make \(42\). - Use the related multiplication fact to check the answer.

1. Find how many groups of \(7\) make \(42\): \(42 \div 7 = 6\). 2. The array has \(6\) rows. 3. The related multiplication equation is \(6 \times 7 = 42\).

\(6\) rows; \(42 \div 7 = 6\) and \(6 \times 7 = 42\).

- Distinguish the number of groups from the size of each group. - Use the multiplication equation \(6 \times 9 = 54\).

1. The array has \(6\) rows with \(9\) dots in each row. 2. \(54 \div 6 = 9\) answers: How many dots are in each of the \(6\) rows? 3. \(54 \div 9 = 6\) answers: How many rows of \(9\) dots are there?

\(54 \div 6 = 9\): the number of dots in each row. \(54 \div 9 = 6\): the number of rows.

- First find how many dots are in one row. - Divide \(36\) by the number of dots in one row. - The answer is the number of rows.

1. In array a), each row has \(9\) dots, so \(36 \div 9 = 4\) rows. 2. In array b), each row has \(6\) dots, so \(36 \div 6 = 6\) rows. 3. In array c), each row has \(4\) dots, so \(36 \div 4 = 9\) rows.

a) \(36 \div 9 = 4\) b) \(36 \div 6 = 6\) c) \(36 \div 4 = 9\)

- Picture the stickers being spread evenly across the pages. - Once the stickers have been shared, what could you count on just one page?

1. The number of pages is already known: \(5\). 2. \(20\div5=4\). 3. The \(4\) counts stickers on each page, not pages.

\(20\div5=4\) stickers per page. Mei is wrong: \(5\) is the page count; \(4\) counts stickers on one page.

- The shells in each bag are fixed. - Think about what must multiply by the bag size to make the total.

1. \(18\div6=3\), so Arlo makes \(3\) bags. 2. The check is \(3\times6=18\).

\(18\div6=3\) bags; check: \(3\times6=18\).

- In A, the \(6\) tells how many groups there are. - In B, the \(6\) tells how many marbles go in each group. - Explain what the answer \(3\) counts in each situation.

1. In situation A, the number of groups is known, and the number in each group is unknown: \(18 \div 6 = 3\). Each friend gets \(3\) marbles. 2. In situation B, the size of each group is known, and the number of groups is unknown: \(18 \div 6 = 3\). Leon fills \(3\) bags. 3. The division equation is the same, but the answer represents marbles per friend in A and number of bags in B.

A) \(18\div6=3\). The \(6\) friends are the known groups, so each friend gets \(3\) marbles. B) \(18\div6=3\). Each bag must hold \(6\) marbles, so Leon can fill \(3\) bags. The same division fact answers two different questions: how many are in each group, or how many groups can be made.

- In a), the number of groups is known. Find how many tulips go in each group. - In b), the size of each group is known. Find how many groups can be made. - The calculation is the same, but the answer counts something different in each situation.

1. One possible sharing question is, “How many tulips go in each vase if \(80\) tulips are shared equally among \(4\) vases?” 2. One possible grouping question is, “How many bouquets can be made if each bouquet uses \(4\) tulips?” 3. In both cases, \(80 \div 4 = 20\). The first answer is \(20\) tulips per vase, and the second is \(20\) bouquets.

a) Example: “How many tulips go in each vase if \(80\) tulips are shared equally among \(4\) vases?” b) Example: “How many bouquets can be made from \(80\) tulips if each bouquet has \(4\) tulips?” c) \(20\) tulips per vase; \(20\) bouquets

- In each story, ask what the \(4\) counts. - Then ask what the answer \(3\) counts. - One story gives the number of groups. The other gives the size of each group.

1. In A, the \(4\) is the number of bags. The answer \(3\) is the number of rolls in each bag, so this is equal sharing. 2. In B, the \(4\) is the number of rolls in each bag. The answer \(3\) is the number of bags, so this is finding the number of groups. 3. The same division equation can therefore represent different meanings for the number you divide by and answer.

A) \(4\) is the number of bags. \(3\) is the number of rolls in each bag. We are finding how many are in each group. B) \(4\) is the number of rolls in each bag. \(3\) is the number of bags. We are finding how many groups there are.

- In each situation, decide whether you know the number of groups or the number in each group. - Write a division equation for each diagram. - Explain what each answer counts.

1. Situation A asks for the number in each group: \(36 \div 6 = 6\), so each child gets \(6\) dots. 2. Situation B asks for the number of groups: \(36 \div 9 = 4\), so there are \(4\) groups. 3. Both situations use division, but A gives the number of groups and asks for the size of each group, while B gives the group size and asks for the number of groups.

A: Each child gets \(6\) dots because the number of groups is known. B: There are \(4\) groups because the size of each group is known.