Square roots & basics Pythagoras (t2steun)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Square roots

& basic Pythagoras

May 19th, 2021

extra math t2

lesson 3 of 8

13:30

Cameras ON

Schedule

• Programme                                                      5 min
• Review: square roots                                  10 min
    Quiz questions
• Square roots: brackets & powers         15 min
    Practice
• Basic Pythagoras                                         30 min
    Bingo!

Programme

8 weeks:

- 5 ‘normal’ lessons

- 1 ‘practice test’ lesson

- 1 ‘review’ lesson

- 1 ‘retake’ lesson
      (maybe in test week)

1. Square roots

2. Simplifying roots

3. More roots & Pythagoras

4. Applying Pythagoras I

5. Applying Pythagoras II

Intended learning outcomes

Last lesson

At the end of the lesson you could...

• Square, add, multiply, and factorise square roots

Review question 1:
Simplify.

3√​5​​​−7√​5​​​

1. 4√​5​​​
2. −4√​5​​​
3. −4
4. Cannot be simplified

Review question 2:
Simplify.

5√​5​​​+3√​7​​​

1. 8√​12​​​
2. 8√​35​​​
3. 15√​12​​​
4. Cannot be simplified

Review question 3:
Simplify.

3√​2​​​⋅4√​6​​​

1. 7√​8​​​
2. 7√​12​​​
3. 12√​8​​​
4. 12√​12​​​

Review question 4:
Factorize.

√​50​​​

1. 25√​2​​​
2. 2√​25​​​
3. 5√​2​​​
4. 2√​5​​​

Review question 5:
Factorize and simplify.

√​50​​​+√​18​​​

1. 8√​2​​​
2. 34√​2​​​
3. √​68​​​
4. Cannot be simplified

Intended Learning Outcomes

Today

At the end of the lesson you can...

• Work out brackets with square roots in them
• Work out square roots with powers

Single brackets

Letters

Square roots

Double brackets

Letters

Square roots

Simplify.

√​2​​​(3√​5​​​+4)

1. 6√​5​​​+4
2. 6√​5​​​+4√​2​​​
3. 3√​10​​​+4
4. 3√​10​​​+4√​2​​​

Simplify. Write it down!

(√​3​​​+2)(√​3​​​−2)

1. −1
2. 1
3. √​3​​​−4
4. √​3​​​−2

Pythagoras

First some basics

Then some bingo

Right-angled triangles

A right-angled triangle always has two legs and one hypotenuse

The hypotenuse is always opposite the right angle

Pythagoras's theorem

1. Take any right-angled triangle
2. Stick a square to each side
3. The theorem:
   Add up the areas of the squares
   stuck to the legs...
   ...and the answer is the area of the
   square stuck to the hypotenuse!

Pythagoras's theorem

1. Take any right-angled triangle
   
2. Stick a square to each side
   
3. The theorem:
   
4. Add up the areas of the squares
   
5. stuck to the legs...
   
6. ...and the answer is the area of the
   
7. square stuck to the hypotenuse!
   

What is the area of the
green square?

1. 6.5
2. 42
3. 52
4. 102

How long is the leg that the
green square is stuck to?

1. 6.5
2. 8.5
3. 10.3
4. 42.0

A bit more mathematical...

A bit more mathematical...

AB​2​​+AC​2​​=BC​2​​

A bit more mathematical...

Let's say AB = 4 and AC = 6.

How do you calculate BC?

AB​2​​+AC​2​​=BC​2​​

AB = 3 and AC = 4.
Calculate BC.

1. BC=√​5​​​
2. BC=7
3. BC=5
4. BC=1

Bingo

• Make a 3x3 grid
• Fill in 9 numbers from 1 to 16
• Teams: take a picture and upload it here
• Class: have the teacher check it

Bingo

Only horizontal or vertical
counts as a bingo!

Take a picture of your filled-in grid and upload it here.

b.4√​3​​​+6√​7​​​−5√​3​​​

b.4√​3​​​+6√​7​​​−5√​3​​​

Bingo questions

PowerPoint