What multiplication and division mean
Math · 3rd grade
Arrays: rows and columns
By the end, Theo will be able to read and build arrays as matching rows and columns and write the multiplication sentence as rows times columns.
About 25 minutes to teach
Teach the idea
An array is equal groups lined up so every row matches and every column matches. Rows go across. Columns go up and down. The multiplication sentence is always rows times columns.
The picture in this lesson is an array. It shows three rows across and five columns up and down.
Here is another array: 2 rows of 6.
2 × 6 = 12
That is 12 in all.
Here is 3 rows of 5.
3 × 5 = 15
That is 15 in all.
It works backward too. Given 4 × 3, build 4 rows of 3. Count them up and you get 12 in all.
Do it together
1. Point to the picture together. Ask Theo how many rows go across and how many columns go up and down. Have him slide one finger across a full row, then up and down a full column, so he can feel the difference.
2. On paper, have Theo draw dots in 2 rows of 3. Ask him to write the multiplication sentence under his drawing and count the total. Check that every row matches and every column matches.
3. Give him a new one to draw: 5 rows of 2. He draws it, writes the sentence, and counts the total. If a row or column is uneven, ask him to fix it before he writes the number.
4. Say 3 × 4 out loud. Have Theo draw 3 rows of 4 on paper, write the sentence, and count how many dots he made. When he is ready, move on to the activity below.
Activity
Together: Build the array. Theo lines up buttons on the table in 4 rows of 5, checking that every row matches and every column matches, and writes 4 × 5 = 20. Theo points to one row going across and one column going up and down. Now work backward: you say 2 × 7, and Theo builds 2 rows of 7 and counts 14. Then you say 2 × 9, and Theo builds it and counts 18.
Tip If Theo mixes up rows and columns, have him trace one full row with a finger across the page, then one full column up and down, before he writes anything. If he finishes fast, invite him to invent one new array on paper and read its sentence to you.
On paper
Worksheet
Arrays
The worksheet, as it prints
Math · Worksheet
Arrays
Count the rows and columns, then write the multiplication sentence and the total.
Name: Theo
Score: ____ / 6
1. Write the multiplication sentence for this array:
2. Write the multiplication sentence for this array:
3. Draw an array for 5 × 3. How many dots did you draw?
4. A window has 3 rows with 6 panes in each row. How many panes are there?
5. An array has 5 rows and 2 columns. Write its multiplication sentence and the total.
6. What would happen to the total if you added one more row to the array in problem 5?
This took Arbor about a minute
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