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Partial Progress - Circles (browser only)
Puzzles and Problems
Objectives
To use reasoning to solve a problem.
Resources
Abacus Workbook 2 | 📄 Triangle totals | 📄 Triangle totals 2
Vocabulary
problem | solve | add | total
Today's Lesson
Introduction
Show your student 📄 Triangle totals. Explain that you can write the numbers 1 to 6 in the circles, using each number only once.
Using a pencil, write 1 to 6 in any order on the triangle, and ask your student to write the total of each side of the triangle in the squares.
Say:
- We are aiming to make each of the 3 sides have the same total.
Ask your student to suggest how you might move numbers around to make this the case. Try out their ideas, rubbing out and moving numbers accordingly until you have one solution.
For example:
Main Activity
Using 📄 Triangle totals 2, challenge your student to make a triangle with all sides having the same total.
Then challenge them to find the smallest side total possible and the largest side total possible (all sides of the triangle must have the same total).
After they have had the chance to experiment, ask them if it makes a difference which numbers are on the corners.
Ask:
- What happens if we put the bigger numbers on the corners?
- What happens if we put the smaller numbers on the corners?
- What happens if we put the even numbers on the corners? Or the odd numbers?
Extra Challenge
Challenge your student to find all the possible totals such that the total of each side is the same. (Totals of 9, 10, 11 and 12 are possible.)
At the end, ask them to share what they found.
For example: a way of making 10 on each side; the smallest total possible; the largest total possible; whether the numbers on the corners affected the totals.
Workbook
To help your student recap upon previous learning from this course, please ask them to complete the activities on page 41 of Abacus Workbook 2.