Mission 1 · Unit 1

Factors and Multiples

6.NS.B.4 · Unit 1
Today's objective: Find the greatest common factor and use the distributive property.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The school kitchen needs to pack 120 granola bars and 84 juice boxes into identical snack bags for Field Day. Every bag must have the same number of granola bars and the same number of juice boxes, with nothing left over. Your team must figure out every possible bag size, recommend the best option, and prove it works using factors, the GCF, and the distributive property.

BAG 1 BAG 2 ... Field Day Snack Packing 120 granola bars + 84 juice boxes GCF = ? bags x = 120 84

Team Roles

Facilitator Reads the snack-packing problem aloud, makes sure everyone lists factors before the team picks a bag size, and watches the timer.
Model Builder Draws factor rainbows or T-charts for 120 and 84, circles common factors, and writes the distributive property equation.
Precision Checker Verifies that each factor pair multiplies correctly, checks that items divide evenly into bags, and confirms no leftovers.
Reporter Prepares the defense: states the recommended bag size, shows the GCF evidence, and explains one mistake the team caught.

Investigation

The Problem

The school kitchen has 120 granola bars and 84 juice boxes. They need to make identical snack bags for Field Day. Each bag must have the same number of granola bars and the same number of juice boxes. No items can be left over.

Your tasks:

  1. Find all possible bag sizes (how many bags can you make?).
  2. For each bag size, tell how many granola bars and juice boxes go in each bag.
  3. Recommend the best bag size and explain why.
  4. Use the distributive property to verify: GCF x (items per bag) = total items.
Factors of 120 1 120 2 60 3 40 4 30 5 24 6 20 8 15 10 12 Factors of 84 1 84 2 42 3 28 4 21 6 14 7 12

Step-by-Step Investigation Guide

  1. List all factor pairs of 120 Start with 1 x 120. Check 2, 3, 4, and keep going until the factors repeat. Use a T-chart to organize your pairs.

    How do you know when you have found all the factor pairs?

  2. List all factor pairs of 84 Do the same for 84. Start with 1 x 84 and check every number up to the square root.

    Which small numbers do NOT divide evenly into 84? How can you tell quickly?

  3. Circle the common factors Compare both lists. Mark every number that appears as a factor of BOTH 120 and 84. These are the possible bag sizes.

    How many common factors did you find? Which one is the greatest?

  4. Find the GCF and calculate items per bag The Greatest Common Factor tells you the most bags you can make. Divide: 120 / GCF = granola bars per bag. 84 / GCF = juice boxes per bag.

    Does your answer make sense? Are both quotients whole numbers?

  5. Write the distributive property equation Show that GCF x (granola bars per bag + juice boxes per bag) = total items. For example: 12 x (10 + 7) = 12 x 10 + 12 x 7 = 120 + 84 = 204.

    Why does the distributive property help prove your answer is correct?

  6. Choose the best bag size and defend it Think about what is practical. Too few bags means too many items per bag (heavy!). Too many bags means only 1 item each. What is the best balance?

    If a parent says "That bag is too heavy for a 6th grader," how would you change your recommendation?

Language Support

Key Vocabulary

Factor: A number that divides evenly into another (no remainder)
Multiple: The result when you multiply a number by a whole number
GCF: Greatest Common Factor - the biggest number that divides into two or more numbers
Distributive Property: a x (b + c) = a x b + a x c
Factor pair: Two numbers that multiply to give a product
Divide evenly: No remainder (leftover) when you divide

Sentence Frames

  • "___ is a factor of ___ because ___ divides into ___ with no remainder."
  • "The common factors of ___ and ___ are ___."
  • "The GCF is ___ because it is the largest factor they share."
  • "Using the distributive property: ___ x (___ + ___) = ___."

Multiple Representations

T-Chart

List factor pairs in two columns. Circle shared factors in both charts.

Factor Rainbow

Write factors in order. Draw arcs connecting pairs that multiply to the number.

Equation

GCF x (items per bag) = total. Use distributive property to verify.

Work Space

Factors of 120:



Factors of 84:



Common Factors:


GCF:


Distributive Property Equation:


Recommendation and Defense: