Witches – lesson plan

This was used in Primary School to address problem solving, and looking at the different approaches that could be used in solving the problem. This activity was used to encourage the systematic approach.

Objectives

Solve mathematical problems or puzzles, generalise and predict

Suggest extensions by asking “What if…?…

Know when all possible answers have been found

Organise the recording of possibilities, e.g. in an ordered list or table

Vocabulary

Odd, even, multiple, times, continue, number pairs, total, altogether, equals, list, rule, combinations

Prior Knowledge

Recall multiples of 3 and 4

Addition facts within 24

Working in pairs?

Level 2

Odd and even

Level 3

Tables – 2,3,4,5,10

Questions?

Draw a spider

Draw a mouse, a bat

Difference between insect… how many legs?

Quick way of finding 4 times table

What numbers of legs is it impossible to make

Other than odd numbers

How many legs went into the pot?

Just a few lines from the 3 witches in Macbeth – ACT 1V – scene 1

Double, double toil and trouble, fire burn and cauldron bubble

Fillet of a fenny snake

In the cauldron boil and bake

Eye of newt and toe of frog

Wool of bat and tongue of dog

Adder’s fork and blind-worm’s sting

Lizard’s leg and howlet’s wing

For a charm of powerful trouble

Like a hell-broth boil and bubble

Double, double toil and trouble, fire burn and cauldron bubble

Read out loud to the class and ask them to count the number of legs…

THE WITCHES CAULDRON

Meg the witch has

Lost her spell book.

She has to make a spell

But cannot remember how.

Meg has only three ingredients

Spiders Mice Bats

8 legs4 legs 2 legs

1)Meg knows that her first spell only has mice and bats.

She knows that the total number of legs in this spell comes to 16.

How many spells could she make?

2)Meg’s next spell is made up of spiders and bats.

She knows that the total number of legs in this spell comes to 24.

How many spells could she make?

3)The last spell is made up of spiders, mice and bats.

She remembers that this spell has a total of 24 legs.

How many spells could she make?

Spell using mice and bats
16 legs /
4 legs /
2 legs
1 / 4 mice = 16 legs / 0 bats = 0 legs
2 / 3 mice = 12 legs / 2 bats = 4 legs
3 / 2 mice = 8 legs / 4 bats = 8 legs
4 / 1 mouse = 4 legs / 6 bats = 12 legs
5 / 0 mice = 0 legs / 8 bats = 16 legs
Spell using spiders and bats 24 legs /
8 legs /
2 legs
1 / 0 spiders = 0 legs / 12 bats = 24 legs
2 / 1 spiders = 8 legs / 8 bats = 16 legs
3 / 2 spiders = 16 legs / 4 bats = 8 legs
4 / 3 spiders = 24 legs / 0 bats = 0 legs
Spell using spiders, mice and bats
24 legs /
8 legs /
4 legs /
2 legs
1 / 3 spiders = 24 legs / 0 mice = 0 legs / 0 bats = 0 legs
2 / 2 spiders = 16 legs / 2 mice = 8 legs / 0 bats = 0 legs
3 / 2 spiders = 16 legs / 1 mice = 4 legs / 2 bats = 4 legs
4 / 2 spiders = 16 legs / 0 mice = 0 legs / 4 bats = 8 legs
5 / 1 spiders = 8 legs / 4 mice = 16 legs / 0 bats = 0 legs
6 / 1 spiders = 8 legs / 3 mice = 12 legs / 2 bats = 4 legs
7 / 1 spiders = 8 legs / 2 mice = 8 legs / 4 bats = 8 legs
8 / 1 spiders = 8 legs / 1 mice = 4 legs / 6 bats = 12 legs
9 / 1 spiders = 8 legs / 0 mice = 0 legs / 8 bats = 16 legs
10 / 0 spiders = 0 legs / 6 mice = 24 legs / 0 bats = 0 legs
11 / 0 spiders = 0 legs / 5 mice = 20 legs / 2 bats = 4 legs
12 / 0 spiders = 0 legs / 4 mice = 16 legs / 4 bats = 8 legs
13 / 0 spiders = 0 legs / 3 mice = 12 legs / 6 bats = 12 legs
14 / 0 spiders = 0 legs / 2 mice = 8 legs / 8 bats = 16 legs
15 / 0 spiders = 0 legs / 1 mice = 4 legs / 10 bats = 20 legs
16 / 0 spiders = 0 legs / 0 mice = 0 legs / 12 bats = 24 legs
Spell using mice and bats
16 legs /
4 legs /
2 legs
mice = legs / bats = legs
mice = legs / bats = legs
mice = legs / bats = legs
mice = legs / bats = legs
mice = legs / bats = legs
mice = legs / bats = legs
Spell using spiders and bats 24 legs /
8 legs /
2 legs
spiders = legs / bats = legs
spiders = legs / bats = legs
spiders = legs / bats = legs
spiders = legs / bats = legs
spiders = legs / bats = legs
spiders = legs / bats = legs
Spell using spiders, mice and bats
24 legs /
8 legs /
4 legs /
2 legs
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