Square roots & basics Pythagoras (t2steun)

Square roots

& basic Pythagoras

May 19th, 2021

extra math t2

lesson 3 of 8

13:30

Cameras ON

1 / 29

Slide 1: Slide

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This lesson contains 29 slides, with interactive quizzes and text slides.

Lesson duration is: 60 min

Items in this lesson

Square roots

& basic Pythagoras

May 19th, 2021

extra math t2

lesson 3 of 8

13:30

Cameras ON

Slide 1 - Slide

Schedule

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

Slide 2 - Slide

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

Slide 3 - Slide

Intended learning outcomes

Last lesson

At the end of the lesson you could...

Square, add, multiply, and factorise square roots

Slide 4 - Slide

Review question 1:
Simplify.

3 \sqrt ​ 5 ​ ​ ​ - 7 \sqrt ​ 5 ​ ​ ​

4 \sqrt ​ 5 ​ ​ ​

- 4 \sqrt ​ 5 ​ ​ ​

- 4

Cannot be simplified

Slide 5 - Quiz

Review question 2:
Simplify.

5 \sqrt ​ 5 ​ ​ ​ + 3 \sqrt ​ 7 ​ ​ ​

8 \sqrt ​ 12 ​ ​ ​

8 \sqrt ​ 35 ​ ​ ​

15 \sqrt ​ 12 ​ ​ ​

Cannot be simplified

Slide 6 - Quiz

Review question 3:
Simplify.

3 \sqrt ​ 2 ​ ​ ​ \cdot 4 \sqrt ​ 6 ​ ​ ​

7 \sqrt ​ 8 ​ ​ ​

7 \sqrt ​ 12 ​ ​ ​

12 \sqrt ​ 8 ​ ​ ​

12 \sqrt ​ 12 ​ ​ ​

Slide 7 - Quiz

Review question 4:
Factorize.

\sqrt ​ 50 ​ ​ ​

25 \sqrt ​ 2 ​ ​ ​

2 \sqrt ​ 25 ​ ​ ​

5 \sqrt ​ 2 ​ ​ ​

2 \sqrt ​ 5 ​ ​ ​

Slide 8 - Quiz

Review question 5:
Factorize and simplify.

\sqrt ​ 50 ​ ​ ​ + \sqrt ​ 18 ​ ​ ​

8 \sqrt ​ 2 ​ ​ ​

34 \sqrt ​ 2 ​ ​ ​

\sqrt ​ 68 ​ ​ ​

Cannot be simplified

Slide 9 - Quiz

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

Slide 10 - Slide

Single brackets

Letters

Square roots

Slide 11 - Slide

Double brackets

Letters

Square roots

Slide 12 - Slide

Simplify.

\sqrt ​ 2 ​ ​ ​ (3 \sqrt ​ 5 ​ ​ ​ + 4)

6 \sqrt ​ 5 ​ ​ ​ + 4

6 \sqrt ​ 5 ​ ​ ​ + 4 \sqrt ​ 2 ​ ​ ​

3 \sqrt ​ 10 ​ ​ ​ + 4

3 \sqrt ​ 10 ​ ​ ​ + 4 \sqrt ​ 2 ​ ​ ​

Slide 13 - Quiz

Simplify. Write it down!

(\sqrt ​ 3 ​ ​ ​ + 2) (\sqrt ​ 3 ​ ​ ​ - 2)

- 1

1

\sqrt ​ 3 ​ ​ ​ - 4

\sqrt ​ 3 ​ ​ ​ - 2

Slide 14 - Quiz

Pythagoras

First some basics

Then some bingo

Slide 15 - Slide

Right-angled triangles

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

The hypotenuse is always opposite the right angle

Slide 16 - Slide

Pythagoras's theorem

Take any right-angled triangle
Stick a square to each side
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!

Slide 17 - Slide

Pythagoras's theorem

Take any right-angled triangle
Stick a square to each side
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!

Slide 18 - Slide

What is the area of the
green square?

6.5

102

Slide 19 - Quiz

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

6.5

8.5

10.3

42.0

Slide 20 - Quiz

A bit more mathematical...

Slide 21 - Slide

A bit more mathematical...

A B^{​ 2 ​ ​} + A C^{​ 2 ​ ​} = B C^{​ 2 ​ ​}

Slide 22 - Slide

A bit more mathematical...

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

How do you calculate BC?

A B^{​ 2 ​ ​} + A C^{​ 2 ​ ​} = B C^{​ 2 ​ ​}

Slide 23 - Slide

AB = 3 and AC = 4.
Calculate BC.

B C = \sqrt ​ 5 ​ ​ ​

B C = 7

B C = 5

B C = 1

Slide 24 - Quiz

Slide 25 - Slide

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

Slide 26 - Slide

Bingo

Only horizontal or vertical
counts as a bingo!

Slide 27 - Slide

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

b . 4 \sqrt ​ 3 ​ ​ ​ + 6 \sqrt ​ 7 ​ ​ ​ - 5 \sqrt ​ 3 ​ ​ ​

b . 4 \sqrt ​ 3 ​ ​ ​ + 6 \sqrt ​ 7 ​ ​ ​ - 5 \sqrt ​ 3 ​ ​ ​

Slide 28 - Open question

Bingo questions

PowerPoint

Slide 29 - Slide

Square roots & basics Pythagoras (t2steun)

Items in this lesson

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Slide 5 - Quiz

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Slide 19 - Quiz

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Slide 24 - Quiz

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Slide 28 - Open question

Slide 29 - Slide

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