Grade 6: Expressions and Equations — Substitute Lesson Plan

Topic: Numeric Expressions and the Distributive Property (Section 6.1a)

Objective

Students will use the distributive property to express a sum of two whole numbers (1–100) that share a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., 36 + 8 = 4(9 + 2)), and will practice translating real-world contexts into equivalent numeric expressions.

Materials

• "Grade 6: Expressions and Equations" resource — printed copies of:
• 6.1a Class Activity: Translating Contexts to Equivalent Numeric Expressions (pp. 19–26)
• 6.0a The Properties of Arithmetic Reference Sheets (pp. 13–17)
• 6.1a Homework: Translating Contexts to Equivalent Numeric Expressions (pp. 27–31) — for extension/if time remains
• Whiteboard or chart paper and marker
• Pencils and notebook paper for each student

Warm-up (~5 min)

1. Write this on the board: 36 + 8 = 4(9 + 2)
2. Ask students: "What do you notice about the two numbers being added on the left side? What number was 'pulled out' on the right side?"
3. Guide students to identify that 4 is the greatest common factor (GCF) of 36 and 8, and that dividing each term by 4 gives 9 and 2 (numbers with no common factor).
4. Briefly define for the class: numeric expression, equivalent numeric expressions, and distributive property (write these terms on the board as a reference for the rest of class).

Main Activity (~25 min)

1. Hand out the 6.1a Class Activity: Translating Contexts to Equivalent Numeric Expressions pages to each student (or pair students up if there are not enough copies).
2. Also distribute the Properties of Arithmetic Reference Sheet so students can check the distributive property and related rules as they work.
3. Have students work through the activity individually or in pairs, focusing on:
4. Finding the GCF of two whole numbers.
5. Rewriting sums using the distributive property (as modeled in the warm-up example).
6. Translating written context/word problems into numeric expressions.
7. Circulate the room while students work. If students get stuck, point them back to the warm-up example (36 + 8 = 4(9 + 2)) as a model they can follow step-by-step:
8. Step 1: Find the GCF of the two numbers.
9. Step 2: Divide each number by the GCF.
10. Step 3: Write the expression as GCF × (sum of the two quotients).
11. Remind students to use the academic vocabulary on the board (numeric expression, equivalent expressions, distributive property) when explaining their reasoning to a partner or writing answers.

Wrap-up / Exit Ticket (~10 min)

Have students complete the following on a sheet of paper to turn in:

1. In your own words, explain what it means for two numeric expressions to be equivalent.
2. Using the example 36 + 8 = 4(9 + 2), explain how you know both sides of the equation name the same number.
3. Identify the GCF used in this example and explain how it was found.

Collect exit tickets as students leave, or collect them at their desks at the end of class.

If Time Remains

• Have students begin the 6.1a Homework: Translating Contexts to Equivalent Numeric Expressions (pp. 27–31) quietly at their desks, continuing to use the distributive property model practiced in class.
• Alternatively, do a quick oral vocabulary review: call out a term from the board (numeric expression, equivalent numeric expressions, distributive property, GCF) and have students give a one-sentence definition or example.