DoAssignment study guide

C1.4 · Create patterns showing whole-number and decimal relationships

Learn to create patterns showing whole-number and decimal relationships through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Algebra

Ontario Grade 6 Mathematics — C1.4

A pattern is a set of numbers arranged according to a rule. The rule tells how the numbers are connected. A whole number is a number such as 3 or 18, with no decimal part. A decimal is written with a decimal point, such as 1.5 or 0.25. You can make a pattern by changing each number in the same way. You can show a pattern in a list, a table, or a graph. In each case, the reader should be able to see the rule and the relationship between the numbers.

What you will learn

Create whole-number and decimal patterns by following a clear rule.
Show how two sets of numbers are related.
Check that each term or pair follows the chosen rule.

Build a pattern from a rule

Imagine putting counters into groups. Suppose you begin with 3 counters and add 3 more each time. The counts are 3, 6, 9, and 12. Each count is connected to the one before it because you add 3 to get the next number.

One number in a pattern is called a term. In the list 3, 6, 9, 12, the first term is 3 and the next term is 6. To continue the pattern, use the same rule again. Since 12 plus 3 is 15, the next term is 15.

A pattern can also show how one number is connected to another. You can choose an input, use a rule, and find an output. The input is the number you start with. The output is the number you get after using the rule. For example, if the rule is “add 4,” an input of 2 has an output of 6.

When you create a pattern, state the rule in words first. Then make the terms or choose inputs and find their matching outputs. A matching pair belongs together because the output comes from applying the rule to that input.

3, 6, 9, 12, 15

A pattern follows a rule.
A term is one number in a pattern.
Use the same rule each time.
Keep each input with the output made from it.

Show and check the relationship

A list is helpful when you want to show the order of terms. A table is helpful when you want to match inputs and outputs. Put each input and its output on the same row. This makes the connection easy to follow.

A coordinate graph can also show number pairs. A coordinate is a pair of numbers that tells where to place a point. The first number tells the position from left to right. The second tells the position from bottom to top. The graph’s horizontal line is the horizontal axis, and its vertical line is the vertical axis. Label the axes so a reader knows what the numbers mean.

Decimals can follow a rule just like whole numbers. The digits after the decimal point show parts of one whole. For example, 0.5 means five tenths, and 0.25 means twenty-five hundredths. When adding decimals, line up the decimal points. This helps keep tenths with tenths and hundredths with hundredths.

After making a pattern, check every step or pair. For a list, ask whether each term follows the rule. For a table, check that every output matches its input. For a graph, check that every point shows a pair from your table. If one value does not fit, correct it before sharing the pattern.

Use a list to show terms in order.
Use a table or graph to show paired numbers.
Label the parts of a table or graph.
Check every number against the rule.

Practice making your own pattern

Start by choosing a relationship that you can describe clearly. For example, you could decide that each output is 4 greater than its input. Choose a few inputs, apply the rule to each one, and record the pairs. The rule should work for every row.

You can also make a pattern with a decimal rule. Choose a starting decimal and decide how much to add each time. Keep the decimal points lined up as you add. Write each new term carefully, then check that the same amount was added at every step.

A multiplication rule can connect whole-number inputs and outputs as well. If the rule is “multiply the input by 3,” each output is three equal groups of its input. Apply that rule to every chosen input. Do not switch to another rule partway through the table.

Before you finish, read the pattern as if you were seeing it for the first time. Can you tell what the rule is? Can you see which numbers belong together? A clear title, labels, and an accurate list, table, or graph help someone else understand the relationship.

Choose and state one rule.
Apply it consistently to each term or input.
Use labels to explain what the numbers show.
Review the completed pattern for errors.

Two rules using the same inputs

Input	Output: add 4	Output: multiply by 3
1	5	3
2	6	6
3	7	9
4	8	12

Worked example

A whole-number input-output pattern

Create a pattern in which each output is 4 more than its input. Show the first four pairs using inputs 1, 2, 3, and 4.

Inputs and outputs: add 4

Each plotted point shows one input and its output. The horizontal axis is the input; the vertical axis is the output.

State the rule
The output is 4 more than the input. Add 4 to each input to make its output.
Use the chosen inputs
Begin with the four inputs in the question. Apply the same rule to each one. For example, adding 4 to 1 gives 5.
$1, 2, 3, 4$
Find and record the outputs
Add 4 to each input. The resulting outputs are 5, 6, 7, and 8. The table keeps every input beside its matching output.
$5, 6, 7, 8$
Check the pairs
Read across each row. Each output is 4 greater than its input, so all four pairs follow the rule.

Answer: The rule is to add 4 to the input. The pairs are (1, 5), (2, 6), (3, 7), and (4, 8).

Check: Each output is exactly 4 greater than its matching input.

Worked example

A decimal pattern that grows

Create a decimal pattern that starts at 0.25 and increases by 0.25 each time. Show four terms.

Term number and term value

The points show the four decimal terms in order. The horizontal axis is the term number; the vertical axis is the term value.

Identify the rule
The first term is 0.25. Add 0.25 each time to find the next term.
Continue the pattern
Add 0.25 to 0.25 to get 0.50. Add 0.25 again to get 0.75. One more addition gives 1.00.
$0.25, 0.50, 0.75, 1.00$
Check the decimal addition
The decimal points line up, so hundredths are added to hundredths. Writing 1.00 keeps two decimal places and shows the same value as 1.
$0.75 + 0.25 = 1.00$

Answer: The four terms are 0.25, 0.50, 0.75, and 1.00.

Check: Each term after the first is 0.25 greater than the term before it.

Worked example

A multiplication relationship

Create a pattern in which each output is 3 times its input. Use inputs 1, 2, 3, and 4.

Inputs and outputs: multiply by 3

Each plotted point shows an input and its output. The horizontal axis is the input; the vertical axis is the output.

Describe the rule
Each output is three equal groups of its input. Multiply each input by 3 to find its output.
Make the pairs
For input 1, three equal groups make 3. For input 2, three equal groups make 6. Continue in the same way for inputs 3 and 4. 1 \to 3, 2 \to 6, 3 \to 9, 4 \to 12
Check every pair
Each output is three times its matching input. The same rule works for all four pairs.

Answer: The pairs are (1, 3), (2, 6), (3, 9), and (4, 12).

Check: Each output is 3 equal groups of its input.

Common mistakes and how to avoid them

Changing the rule partway through a pattern.

Correction: Choose one rule and use it for every term or pair.

Matching an output with the wrong input.

Correction: Keep each input and its output in the same row.

Adding decimals without lining up their decimal points.

Correction: Line up the decimal points before adding so matching place values stay together.

Leaving a graph without labels.

Correction: Label the axes so the reader knows what each set of numbers means.

Lesson summary

A pattern follows a rule that connects its numbers.
Patterns can use whole numbers or decimals.
Lists, tables, and coordinate graphs can show patterns.
Check that every term or pair follows the same rule.

Check your understanding

Question 1

A pattern starts at 6 and adds 5 each time. What are its first four terms?

6, 11, 16, 21
6, 10, 14, 18
5, 11, 17, 23
6, 11, 15, 20

Show answer and explanation

6, 11, 16, 21

Adding 5 each time gives 6, 11, 16, and 21.

Question 2

A pattern starts at 0.4 and adds 0.2 each time. What is the third term?

Show answer and explanation

0.8

The terms are 0.4, 0.6, and 0.8, so the third term is 0.8.

Question 3

Which rule connects inputs 2, 3, and 4 to outputs 8, 12, and 16?

Add 6 to each input.
Multiply each input by 4.
Add 4 to each input.
Multiply each input by 3.

Show answer and explanation

Multiply each input by 4.

Each output is four times its input: 2 gives 8, 3 gives 12, and 4 gives 16.

Key terms

Pattern: A set of numbers arranged according to a rule.
Term: One number in a pattern.
Input: A number you start with when using a rule.
Output: The number you get after using a rule on an input.
Coordinate: A pair of numbers that tells where to place a point on a graph.
Axis: A numbered line on a graph.

Continue through Grade 6 Math

View the complete Grade 6 Math Ontario Grade 6 Mathematics curriculum and lessons

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation C1.4. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

Report a correction or ask a question