Minds On

3D objects

Examine the following two images of groups of three-dimensional objects.

Which object appears the most?

The objects are cone, cube, cone, sphere, sphere, and cone.

Press ‘Answer’ to reveal which object appears the most.

Cone

Which object appears the most?

3D Objects. The objects are cone, cube, cone, sphere, sphere, sphere, sphere

Press ‘Answer’ to reveal which object appears the most.

Sphere

What are two conclusions that you can make about the two sets of objects?

Throughout this learning activity, you can record your thoughts digitally, orally, or in print.

Action

Mean and mode

The mode refers to an item or number that appears the most in a set of data.

The mode for the first example in the Minds On was a cone, and the mode for the second example was a sphere.

What is the mode in this group of numbers?

Another way we can compare data is by using the mean.

The mean is the average of a set of numbers.

For example:

  1. Imagine Learner A has 6 markers, Learner B has 4 markers, and Learner C has 5 markers.
  2. To find the mean for the number of markers, the quantities must be “levelled out” or shared again so that each student has about the same number of markers. If Learner A has 6 (the most) we could take one from them and give it to Learner B who has 4 (the least). Now Learner A would have 5 (6-1) and Learner B would have 5 (4+1). Learner C has 5 already so the quantities (number of markers each person has) have been shared more equally.
  3. This is the mean.

Let’s try with numbers.

  1. The numbers from 1 − 10 are recorded in equal-sized squares.

The squares are placed in a container.

Three numbers are picked. They are recorded: 3, 7, 8.

To calculate the mean of these three numbers we must add the numbers.

Then we divide the sum (answer) by 3 (the number of values (numbers) in the data set).

Let’s try it out!

3 + 7 + 8 = 18

18 divided by 3 = 6

The mean of the numbers 3, 7, and 8 = 6

Let’s try a few more!

Task 1

Calculate the mean of these sets of numbers.

Press ‘Hint’ to reveal how to calculate mean.

Add all the numbers in the set and then divide by the number of values (addends). In these examples we add the 4 numbers together and then divide by 4.

4, 6, 1, 5

4

2, 9, 4, 5

5

7, 1, 8, 4

5

Task 2

The following data shows the number of seeds planted after four rounds of gardening by four different gardeners.

Predict whether the mean and mode(s) will be the same for two of the gardeners. Why or why not?

What is the mean for each gardener?

  • Gardener 1: 7, 9, 4, 4
  • Gardener 2: 7, 7, 7, 7
  • Gardener 3: 4, 5, 5, 10
  • Gardener 4: 9, 8, 8, 7

The gardener with the largest mode gets an extra tree to plant in their garden. What is the mode for each set of data?

Record your ideas in a method of your choice.

Consolidation

Precipitation graphs

Here are the annual precipitation graphs for two cities: City A and City B. They show how much it rained each month for a year.

The rain and snow are measured in mm.

Predict if the mean and mode(s) will be the same for both data sets. Why or why not?

Does either set of data have a mode? If so, what is it?

Make three conclusions about the data for one of the two cities.

What are two comparison statements that can be made about the two graphs?

Record your ideas in a method of your choice.

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel…

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.