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# Breanna’s Buttons

Practices
Explaining and justifying
Noticing and using mathematical structure
Topics
Division
Multiplication
3
4
Use an App
Number Frames
22BQ-E25H
Pattern Shapes
4RXV-Q52A
Number Line
4848-NSLC

What relationships can be found with equal groups and leftovers?

Breanna has a button collection.

• When she puts her buttons in 3 or 7 equal groups, there are 2 buttons left over.
• When she puts the buttons into 2 equal groups, there is 1 button left over.

How many buttons could Breanna have?

How could you get started?
• Does Breanna have an even or odd number of buttons? How do you know?
• To start, choose a number between 11 and 20 and see if the clues she gave are true for the number you chose. If not, how can you change the total to make them true?
• Find other possible numbers of buttons that would work with the clues Breanna gave. What pattern do you see?
• For a different set of buttons, Breanna kept the first clue the same and changed just the second clue to say, “When the buttons are in 2 equal groups, there are no buttons left over.” How could you use the work that you have done to help you find the number of buttons in this set?