What is the inverse operation of addition and subtraction? 2) Create a backward thinking problem and explain it using a tape diagram with comparison of forward thinking.

Okay, let's answer these questions.

3 Confirm

1) What is the inverse operation of the following (a) and (b)?

a) $17 + 5$
The inverse operation of addition is subtraction.
If $17 + 5 = 22$, then the inverse operations are:

$$22 - 5 = \boxed{17}$$ $$22 - 17 = \boxed{5}$$

b) $15 - 8$
The inverse operation of subtraction is addition.
If $15 - 8 = 7$, then the inverse operations are:

$$7 + 8 = \boxed{15}$$ $$8 + 7 = \boxed{15}$$

2) Create a backward thinking problem and explain it using a tape diagram with comparison of forward thinking.

Backward Thinking Problem:
"I had some cookies. I ate 4 of them, and now I have 9 cookies left. How many cookies did I have to begin with?"

Explanation with Tape Diagrams:

• Forward Thinking (Subtraction): If you start with an unknown number of cookies ($X$), eat 4, and have 9 left, the equation is $X - 4 = 9$. Tape Diagram for Forward Thinking: [ Total Cookies (X) ] [-----][-------------] [ 4 ][ 9 ] This diagram shows that the total $X$ is made up of the 4 eaten and the 9 remaining.

• Backward Thinking (Addition - Inverse Operation): To solve this problem using backward thinking, you reverse the process. If you ended up with 9 cookies after eating 4, you must add the 4 cookies back to the 9 you have to find the original amount. Equation: $9 + 4 = X$ Tape Diagram for Backward Thinking: [-------------][-----] [ 9 ][ 4 ] [ Total Cookies (X) ] This diagram shows that the 9 cookies you have now, plus the 4 you ate, make up the total you started with.

  $$9 + 4 = \boxed{13}$$

  So, you had 13 cookies at the beginning.

4 Practice

1) Read the Grade 3 textbook (p. 18) and do all exercise.
As an AI, I cannot read physical textbooks or complete exercises from them.

2) Read teacher's manual (p.22-23) to understand how to teach it.
As an AI, I cannot read physical manuals.

3) Practice demonstrating the solving of addition and subtraction by using tape diagrams.

a) Addition using a tape diagram (e.g., $6 + 7$):
Problem: "A gardener planted 6 rose bushes and 7 tulip bulbs. How many plants did the gardener put in total?"

Tape Diagram:
First, draw a tape for the rose bushes.
[ Rose Bushes (6) ]

Then, extend the tape for the tulip bulbs.
[ Rose Bushes (6) ][ Tulip Bulbs (7) ]

The total length of the tape represents the sum.
[ Rose Bushes (6) ][ Tulip Bulbs (7) ]
[---------------------------------]
[ Total Plants ( ? ) ]

From the diagram, we add the lengths:

$$6 + 7 = \boxed{13}$$

The gardener planted 13 plants in total.

b) Subtraction using a tape diagram (e.g., $16 - 9$):
Problem: "There are 16 birds on a branch. 9 of them fly away. How many birds are left on the branch?"

Tape Diagram:
First, draw a tape for the total number of birds.
[---------------------------------]
[ Total Birds (16) ]

Then, mark off the portion for the birds that flew away.
[ Birds Flew (9) ][ Birds Left ( ? ) ]
[---------------------------------]
[ Total Birds (16) ]

The remaining part of the tape represents the number of birds left.
To find the unknown part, we subtract the known part from the total:

$$16 - 9 = \boxed{7}$$

There are 7 birds left on the branch.