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Texas Grab-and-Go Substitute Packet

Multiplication and Fair Shares

Grade: 3 Subject: Mathematics Time: ~45 min core + ~15 min extension Work mode: Independent · pencil + packet Math

Start Here

This is a paper math packet about equal groups and fair shares. Work by yourself with a pencil. You do not need a calculator, but a basic calculator is allowed if you have one. Show your work — you may draw dots, circles, or arrays to help you. Everything you need is printed right here, including a picture that shows how it works. If a problem is hard, skip it and come back. Circle your final answer.

Start Warm-Up 5 min

Get your brain ready. These are easy on purpose.

1Skip-count by 5. Fill in the two missing numbers on the line.

5,   10,   15,   ____,   ____

2How many in all? Here are 3 groups. Each group has 4 dots. Count all the dots and write how many there are in all.

Three equal groups with four dots in each group Three ovals side by side. Each oval holds four dots arranged in a small square, so there are four dots in the first group, four dots in the second group, and four dots in the third group. Group 1 Group 2 Group 3
Figure 1. Three groups of four dots.

Build Study the Math 5–10 min

What you need to know

Equal groups. When every group has the same number in it, you can multiply. "4 groups of 3" means 4 groups that each hold 3. You can add (3 + 3 + 3 + 3) or you can multiply (4 × 3). Both give 12.

What × means. In 4 × 3 = 12, the 4 is how many groups, and the 3 is how many in each group. The answer, 12, is how many in all. Careful: the groups must be equal to multiply.

Arrays. An array lines things up in rows and columns (a rectangle of dots). You multiply rows × columns. A 3-by-4 array has 3 rows and 4 in each row, so 3 × 4 = 12.

What ÷ means (fair shares). Division shares things into equal groups. "Share 12 into 3 equal groups" is 12 ÷ 3 = 4 — each group gets 4. Division and multiplication are opposites: 3 × 4 = 12, so 12 ÷ 3 = 4.

Watch out: multiplying is not the same as adding one time. And groups must be equal — if they are not, you cannot just multiply.

Worked Example — equal groups and an array

Find 4 × 3 (4 groups of 3).

Step 1 — draw the groups: Make 4 groups. Put 3 dots in each group.

Step 2 — count in all: 3 + 3 + 3 + 3 = 12. So 4 × 3 = 12.

Step 3 — see it as an array: The same 12 dots can line up in 3 rows of 4. That is 3 × 4 = 12. The picture below shows the array.

A three by four array of dots equal to twelve A rectangle of dots with three rows and four columns. Each row has four dots and there are three rows, so there are twelve dots in all. The rows are labeled Row 1, Row 2, and Row 3 on the left. Above the columns it says four in each row. Below the array it reads three rows times four equals twelve. 4 in each row (4 columns) Row 1 Row 2 Row 3 3 rows × 4 = 12
Figure 2. A 3 × 4 array: 3 rows with 4 dots in each row make 12 in all. Drawn in black so it reads clearly in grayscale.

3Using the worked example as your guide, find 5 × 2 (5 groups of 2). You may draw the 5 groups and then count. Show how you found the answer.

Apply Use What You Know 20–25 min

Show your work in every item. You may draw dots or an array to help.

4Equal groups story. There are 5 bags. Each bag has 4 apples. How many apples are there in all? Write a multiplication sentence and find the answer.

5Array match. Look at the array below. Write the number of rows, the number in each row, and the multiplication sentence with the answer.

An array with two rows and six columns of dots A rectangle of dots with two rows. Each row has six dots, so there are six dots in the top row and six dots in the bottom row.
Figure 3. An array of dots.

Rows: ______    In each row: ______    Multiplication sentence: ____ × ____ = ____

6Fair-share story (division). Mia has 15 crayons. She shares them equally among 3 friends. How many crayons does each friend get? Write a division sentence and find the answer. You may draw 3 groups and share the crayons one at a time.

7Find and fix the mistake. A student counted the picture below and said the groups show 3 × 4 = 12. But look carefully — the groups are not equal. Tell what is wrong, and write the correct number of dots in all.

Three groups with different numbers of dots Three ovals. The first oval has four dots, the second oval has three dots, and the third oval has four dots. The groups do not all have the same number. Group 1 Group 2 Group 3
Figure 4. Three groups — look closely at how many are in each one.

What is wrong, and how many dots are there in all?

Explain Tell How You Know 5–10 min

Question 8. In problem 6, Mia shared 15 crayons among 3 friends. Explain how you know each friend gets a fair share. Use the boxes below: write your Answer, a Picture or numbers that shows it, and Why it is fair.

Sentence starters you may use: "Each friend gets ___ crayons." · "I drew 3 groups and put ___ in each." · "It is fair because every group has the ___ number." · "I know because ___ × 3 = 15."

Answer (how many each friend gets)
Picture or numbers
Why it is a fair share

Close ACE Wrap-Up 5 min

Articulate

In your own words, tell what equal groups means.

Connect

Point to one item in this packet where you multiplied. Write its number.

Extend

Write your own multiplication fact using equal groups that was not in this packet (for example, 2 groups of 5).

Continue Early Finisher optional · ~15 min

If you finish early (no new materials needed):

Draw the groups. On the back of this page, show 6 × 2 (6 groups of 2). Draw 6 groups, put 2 dots in each, and write how many there are in all. Then draw the same dots as an array (2 rows of 6) and write that multiplication sentence too.

Turn in: Hand in this whole packet with your name, class, and date filled in. Make sure questions 1–8 and the ACE box are answered with your work shown. The early-finisher challenge is optional, but turn it in too if you did it.
G03_MATH_MultiplicationShares_01 — Multiplication and Fair Shares Student Packet