Embedded Files
Introduction
Introduction
Watch the video for an introduction to the lesson.
Activity 1 - Evaluating numbers with indices
Activity 1 - Evaluating numbers with indices
Task 1
Task 1
Watch the video, Math Antics - Intro To Exponents (aka Indices).
Use the embedded Geogebra interactive to view numbers in index and expanded notation.
Note: Use the Number and Letter base buttons to look at lots of different indices.
Math Antics - Intro To Exponents (aka Indices)
Duration: 10:04
Task 2 - Indices battle bots
Task 2 - Indices battle bots
We're going to play a game! Look at the interactives below. They represent 2 armies of battle bots.
Each Battle bot will fight the one next to it and the one with the biggest number will win. Use the blue turn button to see the results of the fight and then use the arrow to move to the next fight.
The first three fights, the winner and loser are labelled but after that you have to figure it out for yourself.
Now it's your turn!!
Read the Google slides template for instructions.
Then use the button to make a copy of the Google Slides template to create two armies of your own and battle them!
Click on the button to open a new tab and view the Google Doc.
Click on the Use Template button to create a copy for you to edit.
After playing the game a few times, answer the following questions in your exercise book or folder:
What was the best strategy? Explain why?
To increase your likelihood of winning, what number should you put as the exponent and why?
Can there ever be a battle that ties? If so, which soldiers are played? Are they the same cards or different ones?
Activity 2 - Approximating square roots
Activity 2 - Approximating square roots
Task 1
Task 1
Use the Geogebra applet, Visualising square roots, to investigate the relationship between the side length and area of a square, which is the basis for the operation square root.
Use the slider to change the size of the square and the check boxes to reveal the values.
Task 2
Task 2
Use the Geogebra app from task 1 to help you answer the questions in the Approximating square roots Google Doc activity.
Click on the button to open a new tab and view the Google Doc.
Click on the Use Template button to create a copy for you to edit.
Task 3
Task 3
Look closely at the diagram.
How could we approximate the value of the √40?
Task 4
Task 4
Knowing a square root is the side length of the square when the area is a certain number, approximate the following square roots.
Answer the following questions in your exercise book or folder:
Using the geogebra applet at the beginning of the activity, find the approximates for √5, √32, and √70.
Would the √2 be closer to √1 or √4? Explain your answer.
Activity 3 - Discovering the order of operations
Activity 3 - Discovering the order of operations
Completing steps or tasks in the correct order is really important.
Task 1
Task 1
What consequences can you imagine could happen if the steps in Task 1 happened out of order?
When solving mathematical problems the order in which we complete steps is very important.
Mathematicians call this the order of operations.
Operations are actions like add, subtract, multiply, divide, squaring, etc.
Just like the driving steps in Task 1, mathematical equations have an order in which they occur.
Task 2
Task 2
Watch the video, Math Antics - Order Of Operations to learn more about the order of operations.
Use information from the video to help you complete the questions in the embedded Geogebra interactive.
Write each question into your exercise book or folder and show all your working.
When you have answered all 8 problems use the tick boxes to check your answers.
Math Antics - Order Of Operations
Duration: 9:39
Activities too hard?
Activities too hard?
Choose and complete the POW and SQRT levels to practice your knowledge on evaluating numbers with indices and square roots.
Activities too easy?
Activities too easy?
Task 1 - Indices Puzzle
Task 1 - Indices Puzzle
Visit the Power Countdown page on the NRICH maths website.
Watch the video and then try using the numbers to make the targets.
How many different ways can you find to make each target?
Task 2
Task 2
Use Heron’s method for approximating square roots.
Find two square numbers, so that one is almost double the other.
Such as 25 and 49.
Take their square root values.
√25 = 5 and √49 = 7
Divide the larger from the smaller.
7 ÷ 5 = 1.4
This is an approximation for √2. The √2 ≈ 1.414…
Try this method for √3 by finding square numbers that are almost triple times each other and √5 by finding square numbers that are almost five times each other.
Note: This activity is modified from fraction approximations to square roots by Don Steward.
Task 3 - The four 4’s problem
Task 3 - The four 4’s problem
Can you find every number between 1 and 20 using only four 4’s and any operation?
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
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