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Puzzles and Problems
Objectives
To count back in 4s to solve a problem.
To add 2-digit numbers.
To use trial and improvement.
Resources
Abacus Workbook 1 | 📄 Sandcastles problem
Vocabulary
problem | solve | investigate | explain
Today's Lesson
Introduction
Look at and read the 📄 Sandcastles problem together.
Ask:
- How long was Lisa on holiday for? (We don’t know.)
- Who was she on holiday with? (We don’t know.)
- How old is Lisa? (We don’t know.)
- So, if we don’t know these things, what do we know?
Ask your student to repeat back the facts given in the puzzle.
Ask:
- And what do we need to find out?
- Do you have any ideas about how we might make a start?
If necessary, model your thinking.
For example:
- Let’s pick a number to try for day 1 and see how we get on.
- How many shall we try?
- Let’s record that number.
- Write your student’s suggestion (even if it clearly isn’t going to work) under a ‘Day 1’ heading.
- If Lisa made this many on day 1, how many would she have made on day 2 (4 fewer)?
- And on day 3 / 4 / 5?
- So, how many sandcastles is this altogether?
- Hm, that’s too many/ few. What do we need to do to the starting number?
Your challenge is to find the number that Lisa DID make on day 1, and the other days of course, to give a total of 80 sandcastles over the 5 days.
Main Activity
Ask your student to continue to work on the 📄 Sandcastles problem from where the video finishes.
Consolidate
As you conclude the activity, agree the answer. (24+20+16+12+8)
Do you see how 80 = 5x the ‘middle’ number?
Ask your student to discuss with you how they got to the answer, drawing out trial and improvement. Point out how ‘wrong’ answers weren’t really wrong but were helpful steps in working towards the puzzle’s solution.
Extra Challenge
Lisa’s brother, Mark, started with a different number to Lisa, and made 3 fewer sandcastles each day.
Over 5 days he made 75 sandcastles.
On which day did he and Lisa make the same number of sandcastles? (Day 4: 21+18+15+12+9)
Do you see how 75 = 5x the ‘middle’ number?
Workbook
To help your student recap upon previous learning from this course, please ask them to complete the activities on page 7 of Abacus Workbook 1.