- Look across a single row first. - Add the same row amount once for each row.

1. There are \(3\) rows of \(2\) dots. 2. Repeated addition is \(2+2+2=6\). 3. Multiplication is \(3\times2=6\).

There are \(3\) rows. \(2+2+2=6\) and \(3\times2=6\).

- Picture both trays side by side. How could you count all their cookies? - Try using each equation to find the total. Do they match the cookies you pictured?

1. There are two equal groups of four cookies. 2. Both \(4+4=8\) and \(2\times4=8\) describe them.

Both are correct. There are \(2\) groups of \(4\), for \(8\) cookies.

- Look only at the top color for now. - How can you describe that small part using rows and columns?

1. The top part has \(1\) row with \(4\) squares. 2. Its multiplication fact is \(1\times4=4\). The factors count rows and squares per row.

\(1\times4=4\). There is \(1\) row with \(4\) squares in it.

- Find the number of equal rows and the number of objects in each row. - A multiplication equation can represent “number of groups \(\times\) amount in each group.” - The product should describe the total number of objects in the display.

1. Seven rows with six stars in each row are represented by \(7 \times 6\). 2. \(7 \times 6=42\). 3. The factor \(7\) represents the number of rows, the factor \(6\) represents the number of stars in each row, and the product \(42\) represents the total number of stars.

a) \(7 \times 6=42\) b) \(7\) is the number of rows, \(6\) is the number of stars in each row, and \(42\) is the total number of stars.

- What is the amount that repeats in this addition? - How could you show the repeated amounts as equal groups? - If the multiplication fact is unfamiliar, think of a group of \(12\) as \(10\) and \(2\).

1. There are \(7\) equal groups of \(12\) cents. 2. Write \(7\times12\,\text{cents}\). 3. The total is \(7\times12=84\) cents.

\(7\times12\,\text{cents}=84\,\text{cents}\).

- Find the number of rows and the dots in each row. - Use a multiplication fact for each array and compare the products.

1. Array a) has \(4\) rows of \(6\) dots, so \(4 \times 6 = 24\). 2. Array b) has \(3\) rows of \(8\) dots, so \(3 \times 8 = 24\). 3. Each array is organized into equal groups whose multiplication fact has a product of \(24\).

a) \(4\times6=24\) b) \(3\times8=24\) The products are equal because both multiplication facts equal \(24\).

- Compare more than the number of rows. - How many dots are in each row of each array?

1. Array a) has \(4\) rows with \(5\) dots in each row, so it shows \(4 \times 5 = 20\). 2. Array b) has \(4\) rows with \(8\) dots in each row, so it shows \(4 \times 8 = 32\). 3. Mara’s statement is incorrect. The number of rows alone does not find the multiplication equation; the number of dots in each row must also match.

Mara is incorrect. Array a) shows \(4 \times 5 = 20\), while array b) shows \(4 \times 8 = 32\). The row count and the number of dots per row must both match.

- Count the rows, not every dot. - Look at how many dots from one half appear in a single row. - Your explanation should say what both factors mean in the picture.

1. The array has \(6\) rows. Each row has \(4\) dots in the left half, so the left half has \(6 \times 4 = 24\) dots. 2. Each row also has \(4\) dots in the right half, so the right half has \(6 \times 4 = 24\) dots. 3. In each equation, \(6\) represents the number of rows and \(4\) represents the number of dots from that half in each row.

a) \(6 \times 4 = 24\) b) \(6 \times 4 = 24\) c) The factor \(6\) is the number of rows, and the factor \(4\) is the number of dots in that half of each row.

- In each picture, compare the number of counters in every row. - Equal groups must all have the same number of counters. - Write a multiplication equation only when the groups are equal.

1. Picture a) has \(3\) equal groups of \(4\), so \(3\times4=12\). 2. Picture b) has \(4\) equal groups of \(3\), so \(4\times3=12\). 3. Picture c) does not show equal groups because one row has fewer counters than the others.

a) Pictures a) and b) b) a): \(3\times4=12\); b): \(4\times3=12\) c) Picture c) has groups of different sizes, so it does not show equal groups.

- How many dots are in one row? How many rows are there? - Look at the columns. What is different about how you count?

1. There are \(3\) rows with \(4\) dots each, giving \(4+4+4=12\). 2. There are \(4\) columns with \(3\) dots each, giving \(3+3+3+3=12\). 3. Both sums count every dot exactly once, just in a different direction.

Rows: \(4+4+4=12\). Columns: \(3+3+3+3=12\). They count the same dots in different directions.

- In each story, what counts the bags? - What counts the balls in each bag? - Compare the totals after writing the equations.

1. Mia packs \(5\times3=15\) balls. 2. Ben packs \(3\times5=15\) balls. 3. The total is the same, but the number of bags and balls in each bag have switched.

Mia: \(5\times3=15\). The \(5\) counts bags, and the \(3\) counts balls per bag. Ben: \(3\times5=15\). The \(3\) counts bags, and the \(5\) counts balls per bag. Yes, both pack \(15\) balls.

- Use the picture to count the rows and the number of tiles in one row. - For the total, think of each row as one equal group. - For part c, look for how the filled tiles repeat within every row.

1. The array has \(8\) rows with \(8\) tiles in each row. 2. The total number of tiles is \(8 \times 8 = 64\). 3. Each row has \(4\) filled tiles, and there are \(8\) rows. Thus, \(8 \times 4 = 32\) filled tiles.

a) \(8\) rows and \(8\) tiles in each row b) \(8 \times 8 = 64\) c) \(32\) filled tiles; each of the \(8\) rows contains \(4\) filled tiles.

- Use the row and column counts from the grid rather than counting individual tiles. - Removing the outside border removes two rows and two columns from the dimensions of the interior. - Find the whole and interior products before finding the border count.

1. The array has \(7\) rows and \(8\) columns, so the whole array has \(7 \times 8=56\) tiles. 2. Removing the top and bottom rows and the left and right columns leaves \(5\) interior rows and \(6\) interior columns, so the interior has \(5 \times 6=30\) tiles. 3. Subtract the interior from the whole array: \(56-30=26\). 4. Therefore, there are \(26\) border tiles.

a) \(7 \times 8=56\) b) \(5 \times 6=30\) c) \(56-30=26\) border tiles

- Look at two neighboring rows together. - In the second row, the \(5\) and \(4\) switch places. - How many of each kind are in one pair of rows?

1. In one row, the counts are \(5\) and \(4\). In the next row, they switch. 2. Each pair of rows has \(9\) squares of each kind. 3. There are \(4\) pairs of rows, so each kind appears \(4 \times 9=36\) times.

Each pair of rows has \(9\) squares of each kind. There are \(4\) row pairs, so each kind appears \(4 \times 9=36\) times.