Minds On

Let’s skip count

Let’s skip count from 1.42 to 2.02. You may wish to access a number line to support your thinking.

An image of a number line with the numbers 0, 1, 2 and 3. The number 1.42 and 2.02 are indicated on the number line.

Let’s look at this example.

Consider the following questions and then press each question to reveal its answer.

I am skip counting by 0.10, one tenth.

If I continue to skip count by 0.10, one tenth, the next number would be 2.12.

6 jumps of 0.1, 6 jumps of one tenth.

Do you have any other ideas or thoughts? What would you do differently?

Action

Patterning in Decimals

Patterning in decimals is important because decimals reflect many things in real life.

Here are some examples where decimals are used and needed in real life.

  • Money
  • Weight
  • Length
  • Baking
  • Driving
    (gas and travel)
  • Temperature
  • Sports

Money

One place we use decimals in real life is with money.

Counting by different coins, such as nickels or quarters, reveals a pattern.

Example: If I am counting by quarters, my pattern could be: 0.25, 0.50, 0.75, 1.00…

Term Number

Term Value ($)

1

$0.25

2

$0.50

3

$0.75

4

$1.00

My pattern rule could be: Start at 0.25 and increase by 0.25 each time.

Task 1

For each word problem below, create a table of values and state the pattern rule using a method of your choice.

Word problem #1

A baker has an important ingredient that costs $2.20. The baker is going to pay for it with dimes. They start counting at $0.10 and continues to increase by $0.10 every time they count another dime. Record the pattern that the baker will count until they reach $2.20.

State the pattern rule and create a table of values.

Press ‘Answer’ to reveal a possible solution for the word problem.

Pattern Rule: start at .10 and add .10 each time.

Term Number

Term Value ($)

1

2

3

4

5

6

7

22

0.10

0.20

0.30

0.40

0.50

0.60

0.70

2.20

Word problem #2

An artist is planning to buy a paint brush. It costs $6.75. The artist plans to pay in quarters. The artist counts up by $1.25, starting from $1.25. Record the pattern of the artist counting until they reach $6.75.

State the pattern rule and create a table of values.

Press ‘Answer’ to reveal a possible solution for the word problem.

Pattern Rule: Start at $1.25 and increase by $1.25 each time.

Term Number

Term Value ($)

1 1.25
2 2.50
3 3.75
4 5.00
5 6.25
6 7.50

Baking

Decimals are also used in baking.

Recipes provide precise measurements that require different decimals/fractions to bake properly.

Example: If my recipe requires 100 ml and I have a 25ml measuring cup, my pattern could be: 0.25ml, 0.50ml, 0.75ml, 100ml. I would need to use my 0.25ml measuring cup 4 times before I reached 100ml.

Term Number

Term Value (ml)

1 25
2 50
3 75
4 100

My pattern rule could be: Start at 0.25 and increase by 0.25 each time.

Task 2

For each word problem below, create a table of values and state the pattern rule using a method of your choice.

Word problem #1

A baker is baking a cake. The recipe requires 400ml of oil. The baker only has a small measuring cup (0.33 ml) to use. If they already put in 100ml of oil, how many third cups will the baker need before getting to 400ml?

State the pattern rule and create a table of values.

Press ‘Answer’ to reveal a possible solution for the word problem.

Pattern Rule: Start at 1 cup and increase by one-third cup (0.33) each time.

Term Number

Term Value (ml)

1 100
2 133
3 166
4 200
5 233
6 266
7 300
8 333
9 366

Word problem #2

A baker is baking muffins for the bakery. The muffins require 300ml of fruit juice. The baker has a small cup (25ml) to use. How many cups of 25ml will the baker need to use to reach 300 ml?

State the pattern rule and create a table of values.

Press ‘Answer’ to reveal a possible solution for the word problem.

Pattern Rule: Start at 25ml and increase by 25 ml each time.

Term Number

Term Value (ml)

1 25
2 50
3 75
4 100
5 125
6 150
7 175
8 200
9 225
10 250
11 275
12 300

Task 3: Practice

For each of the four patterns below, answer the following questions by recording your ideas using a method of your choice.

Pattern 1: 12.3, 18.3, 24.3…

Pattern 2: 10.7, 10.2, 9.7…

Pattern 3: 0.56, 0.88, 1.2…

Pattern 4: 7.9, 7.75, 7.6…

Be sure to:

  • determine the pattern rule
  • create a table of values
  • extend the pattern to find the next three terms
  • determine what the 10th and 20th terms would be

After you have tried the questions out for yourself, you may press the patterns to access the answers to check your work.

Pattern rule: Term number × 6 + 6.3

Table of values:

Term Number

Term Value

1 12.3
2 18.3
3 24.3
4 30.3
5 36.3

Next three terms: 42.3, 48.3, 54.3

10th term: 66.3

20th term: 126.3

Pattern rule: Term number × (– 0.5) + 11.2

Table of values:

Term Number

Term Value

1 10.7
2 10.2
3 9.7
4 9.2
5 8.7

Next three terms: 8.2, 7.7, 7.2

10th term: 6.2

20th term: 1.2

Pattern rule: 0.32 × term number + 0.24

Table of values:

Term Number

Term Value

1 0.56
2 0.88
3 1.2
4 1.52
5 1.84

Next three terms: 2.16, 2.48, 2.8

10th term: 3.44

20th term: 6.64

Pattern rule: Term number × (– 0.15) + 8.05

Table of values:

Term Number

Term Value

1 7.9
2 7.75
3 7.6
4 7.45
5 7.3

Next three terms: 7.15, 7, 6.85

10th term: 6.55

20th term: 5.05

Consolidation

Task 1: Saving money

Record your work using a method of your choice.

You have been saving nickels, 2 each day. You have 54 collected. Using the pattern and decimal values:

  • determine the pattern rule
  • create a table of values
  • determine when (term number) there will be $1 worth of nickels
  • when there will be enough collected for $5.

Task 2: Think about your learning

Answer the following questions using a method of your choice.

  • Where do you use decimals in your everyday life?
  • How is patterning the same or different as without decimals?
  • How does understanding fractions help you to understand decimals?

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel…

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

Connect with a TVO Mathify tutor

Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.

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