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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 Math

Overview

This is a self-contained, low-tech substitute packet in which Grade 3 students practice multiplication as equal groups and arrays and division as fair sharing, using small, friendly numbers within 100. Working alone with a pencil (a calculator is not required, though a basic one is allowed), students skip-count and count equal groups, study a worked example that shows 4 × 3 as groups and as a 3 × 4 array, and then apply the ideas to an equal-groups apple story, an array match, a fair-share crayon problem, and a find-the-mistake item about unequal groups. They finish by explaining why a share is fair.

At a glance

Grade: 3

Subject: Mathematics

Time: about 45 minutes core plus a 15-minute optional extension

Materials: printed packet and a pencil; a calculator is not required, though a basic calculator is allowed (no computer, internet, or physical manipulatives — students draw to model)

Work mode: independent

Standards (provisional): 19 TAC §111.5 (Grade 3 Mathematics) — representing multiplication as equal groups and arrays, and representing division as fair sharing into equal groups. Provisional — pending educator verification against the current official TAC source. Standards are paraphrased, not quoted.

Accessible version of the student activity

The full student activity is reproduced below in plain, screen-reader-friendly HTML. It reflows on phones and at 200% zoom. Write your answers on the printed packet, and show your work — you may draw dots or arrays.

Start (5 minutes) — Warm-up

  1. Skip-count by 5. Fill in the two missing numbers: 5, 10, 15, ___, ___.
  2. How many in all? There are 3 equal groups, and each group has 4 dots. Count all the dots and write how many there are in all. (Three groups of four dots.)

Build (5–10 minutes) — Study the math

Equal groups. When every group has the same number, you can multiply. "4 groups of 3" means 4 groups that each hold 3; you can add 3 + 3 + 3 + 3 or multiply 4 × 3, and both give 12. What × means: in 4 × 3 = 12, the 4 is how many groups, the 3 is how many in each group, and 12 is how many in all. Arrays line things up in rows and columns; you multiply rows × columns, so a 3-by-4 array is 3 × 4 = 12. What ÷ means (fair shares): division shares a total into equal groups — "share 12 into 3 equal groups" is 12 ÷ 3 = 4, so each group gets 4. Multiplication and division are opposites: 3 × 4 = 12, so 12 ÷ 3 = 4. Careful: groups must be equal to multiply.

Worked example — equal groups and an array

Find 4 × 3 (4 groups of 3). Step 1, draw 4 groups with 3 dots in each. 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 make 3 rows of 4, so 3 × 4 = 12.

A three by four array of dots. It has three rows, and each row has four dots, so there are twelve dots in all. Row labels on the left read Row 1, Row 2, and Row 3; above the columns it says four in each row; below it reads three rows times four equals twelve.
Figure 2 description and numbers. A grayscale array of dots with 3 rows and 4 columns. Each row has 4 dots, and there are 3 rows, so there are 4 + 4 + 4 = 12 dots in all. The rows are labeled Row 1, Row 2, and Row 3 down the left side, the columns are labeled "4 in each row" across the top, and the array shows 3 rows × 4 = 12. In the printed packet this is a labeled black-and-white figure of plain dots that reads clearly in grayscale.
  1. Using the worked example as a guide, find 5 × 2 (5 groups of 2). You may draw the 5 groups and then count. Show how you found the answer.

Apply (20–25 minutes) — Use what you know

  1. Equal groups story: there are 5 bags, and each bag has 4 apples. How many apples in all? Write a multiplication sentence and find the answer.
  2. Array match: an array has 2 rows with 6 dots in each row. Write the number of rows, the number in each row, and the multiplication sentence with the answer.
  3. Fair-share story (division): Mia has 15 crayons and shares them equally among 3 friends. How many does each friend get? Write a division sentence and find the answer.
  4. Find and fix the mistake: a student said three groups show 3 × 4 = 12, but the groups are not equal — Group 1 has 4 dots, Group 2 has 3 dots, and Group 3 has 4 dots. Tell what is wrong and write the correct number of dots in all.

Explain (5–10 minutes) — Tell how you know (Answer, Picture or numbers, Why)

Question 8. In problem 6, Mia shared 15 crayons among 3 friends. Explain how you know each friend gets a fair share. Write your Answer (how many each friend gets), 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.".

Close (5 minutes) — ACE

Continue (optional, ~15 minutes) — Early finisher

Draw the groups: show 6 × 2 (6 groups of 2). Draw 6 groups with 2 dots each and write how many in all. Then draw the same dots as an array (2 rows of 6) and write that multiplication sentence too.

Turn in

Hand in the whole packet with your name, class, and date, with questions 1–8 and the ACE box answered and your work shown. Include the optional challenge if you did it.

G03_MATH_MultiplicationShares_01 — Multiplication and Fair Shares Accessible landing page