Mathematics · Grade 2 · Algebra: Patterns and Relationships · Term 3

Patterns on Number Lines and Charts

Use number lines and hundreds charts to find and explore interesting number patterns, like skip counting.

TL;DR:Turn your students into pattern detectives as they explore the hidden rules and structures within numbers. This topic uses familiar tools like number lines and hundreds charts to make abstract patterns visible and fun.

• Ontario Curriculum Expectations
• Ontario Curriculum (2020): Grade 2 - Algebra - C1.3

About This Topic

This topic introduces Grade 2 students to the foundational concepts of algebraic thinking by exploring patterns within our number system. In line with Canadian mathematics curricula, which emphasize patterning and number sense as key pillars, this unit moves students beyond simple rote counting. It encourages them to become mathematical detectives, using tools like number lines and hundreds charts to visualize and analyze the structure of numbers. The focus is on identifying relationships and understanding rules, such as those created by skip counting.

By investigating the visual patterns of skip counting by 2s, 5s, and 10s on a hundreds chart, students develop a deeper understanding of place value and number properties, such as even and odd. The number line serves as a powerful model for representing growing patterns as a series of 'jumps' or intervals, reinforcing the concept of repeated addition. This exploration lays the critical groundwork for more complex mathematical concepts, including multiplication, division, and algebraic reasoning, that students will encounter in later grades. It fosters curiosity and the ability to make predictions based on observed data, a key skill in all areas of mathematics.

Key Questions

1. Analyse the patterns made by skip counting by 2s, 5s, and 10s on a hundreds chart.
2. Explain how a number line can show a growing pattern.
3. Compare the pattern of even numbers to the pattern of odd numbers.

Learning Objectives

• Identify and describe a variety of growing patterns on number lines and hundreds charts.
• Create and extend number patterns involving repeated addition (skip counting).
• Compare the visual and numerical patterns of even and odd numbers.
• Determine the rule for a given pattern and use it to find missing elements.
• Verbally explain how a number pattern is growing or changing.

Key Vocabulary

Pattern	A set of numbers or objects that are arranged following a specific rule.
Skip Counting	Counting forwards or backwards by a number other than one.
Number Line	A straight line with numbers placed at equal intervals, used to visualize number order and operations.
Hundreds Chart	A 10-by-10 grid containing the numbers 1 to 100 in order.
Even Number	A whole number that can be divided into two equal groups with none left over. These numbers end in 0, 2, 4, 6, or 8.
Odd Number	A whole number that has one left over when divided into two equal groups. These numbers end in 1, 3, 5, 7, or 9.
Rule	The procedure that is repeated to create a pattern, such as 'add 2 each time'.

Watch Out for These Misconceptions

Common Misconception

Skip counting must always start with the number you are counting by (e.g., counting by 5s must begin at 5).

What to Teach Instead

A skip counting pattern is simply repeated addition, and it can start from any number. Practice starting counts from various numbers, for example, 'Let's start at 3 and count by 5s: 3, 8, 13, 18...'

Common Misconception

When using a number line, the starting number is counted as the first 'jump'.

What to Teach Instead

Clarify that the 'jump' or 'hop' represents the interval or the space between two numbers. Model this by placing a finger on the starting number and then physically hopping to the next number while counting 'one jump'.

Common Misconception

Students describe the visual pattern on a hundreds chart without connecting it to the numerical rule.

What to Teach Instead

Explicitly bridge the visual and the numerical by asking guiding questions. For example, 'You noticed the pattern for 10s makes a straight column. What do you notice about the tens digit as you go down the column? What does that tell us we are doing each time?'

Active Learning Ideas

Stations Rotation

Hundreds Chart Detectives

Students use transparent counters or different coloured markers to cover numbers on a hundreds chart as they skip count by 2s, 5s, and 10s. They then describe the visual patterns they see, such as vertical columns for 10s or alternating columns for 2s.

20 min·Pairs

Stations Rotation

Human Number Line

Create a large number line on the floor with tape. Students take turns starting at a given number and physically jumping along the line according to a skip counting rule provided by the teacher or another student.

15 min·Whole Class

Stations Rotation

Pattern Paths

Students are given a starting number and a rule (e.g., 'Start at 11, add 3'). They write out the first five numbers of the pattern and draw the corresponding jumps on a blank number line.

20 min·Individual

Real-World Connections

• Counting collections of Canadian coins like nickels (5s), dimes (10s), and toonies (2s).
• Reading the minutes on an analog clock, which are marked in intervals of five.
• Looking at house numbers on a street, where one side is typically odd numbers and the other is even.
• Finding a date on a calendar, where moving down one column is a pattern of adding 7.
• Setting out plates and cutlery for a family dinner, creating a repeating pattern for each person.

Assessment Ideas

Peer Assessment

Observe students during partner work, listening for their use of vocabulary to describe patterns. Ask them to 'turn and talk' to explain the pattern they found to their partner.

Quick Check

Provide a worksheet with several number sequences that have missing numbers. Students must fill in the blanks and write the rule for each pattern (e.g., 'The rule is add 10').

Exit Ticket

Give students an exit ticket with a simple pattern. Ask them to circle a smiley face, neutral face, or sad face to show how confident they feel about finding the next number in the pattern.

Frequently Asked Questions

Why are patterns important in math?

Patterns are the building blocks of math. Learning to recognize them helps us solve problems more quickly, make predictions, and understand how numbers work together. It's the first step towards learning bigger ideas like multiplication and algebra.

How is a number line different from a hundreds chart for showing patterns?

A number line is great for showing a pattern as a series of 'jumps' in one direction, which helps us see the size of the steps. A hundreds chart organizes numbers in a grid, which helps us see different kinds of patterns, like columns and diagonals, and how they relate to place value.

Can patterns go backwards?

Absolutely! A pattern can use subtraction, too. This is like skip counting backwards. For example, starting at 50 and counting back by 10s gives you the pattern 50, 40, 30, and so on.