Manipulating powers

﻿Hello everyone. I'm Mr. Lund, and today's lesson is on square and cube numbers. How do you calculate four squared? Let's use an array of counters to help us visualise the problem. Four squared means four multiply by four. If you do that so, you find you get 16. A square number is a number multiplied by itself. Is this statement true or false? Eight is a square number because you can make a square using eight counters. That's false. Eight counters do not make a complete square. Nine counters would. Nine is a square number. Three multiplied by three. So let's calculate 15 squared. 15 squared means multiply 15 by itself twice. I can break that down into two steps. I can say 15 times by 10, plus 15 times by five. That gives me 150 plus 75. In total, that gives me 225. 15 squared equals 225. Have a look at this example, how is it different? In this example, we have a negative number. To calculate negative nine squared. I'm going to start off by multiplying nine by nine. That equals 81. So negative nine times by negative nine is also 81 because two negatives multiplied together gives me a positive answer. Whenever you square a negative number, you find yourself with a positive answer. So how do you think you're going to get along with square numbers? Here are some questions for you to try. Pause the video and come back when you're complete to check your answers. Here are the solutions to questions one and two. Notice negative two squared gives you a positive answer. Any squared number gives you a positive answer. In question two, it is important that you know your square numbers up to 10. So the square of one, the square of two, the square three, all the way up to 10. Good for your exams. How do you calculate four cubed? Here is a cube. I have split the cube into four rows of 16. Calculating four cubed means I multiply the number four by itself, three times. I could start off by multiplying four times by four that gives me an answer of 16 and then multiplying that by four again. 16 times by four gives me an answer of 64. Four cubed equals 64. So how is this question different? This time we're going to cube a negative number. If I multiply the first two numbers I see, I end up with a positive answer of nine. I need to multiply nine by the remaining negative three and that gives me a solution of negative 27. Minus three cubed equals negative 27. Whenever you cube a negative number, you end up with a negative solution. Why don't you check on a calculator, but you must remember to put your negative number inside of brackets before you cube it. Here are some questions for you to try. Pause the video and return to check your answers. Here are the solutions to question number four and five. The very first question, four a, shows you that the cube of one is equal to one. One raise to any power is always equal to one. Why not try these questions? Pause the video and return to check your answers. Here are the solutions for six, seven, and eight. Number six is quite interesting. If you put those in a calculator, you would find that one gives an answer of negative four and the other gives an answer of positive four. That is because of the order of operations. Have a think about that one. Some final questions for you to try. Pause the video and return to check your answers. Here are the solutions to question number nine. Ascending means going from small to large. The range of the numbers is the largest number subtract the smallest number. If you're subtracting a negative number, then it turns those signs into a positive. So nine plus one equals 10. Chopped up!

Evaluate the following numerical expression,

Evaluate the following numerical expression

What is the area of this square?

The side length of a cube is 6cm. What is the volume of this cube?

Square and Cube Numbers

In this lesson, we will investigate the properties of square and cube numbers. We will model what these number categories are using visual models of arrays and stacked cubes, and will pracise calculating squaring and cubing a number.

Lesson overview:Square and cube numbers

Core Content

Types of numbers: