Mathematics · Grade 2 · Number Sense and Place Value Patterns · Term 1

Comparing Numbers to 200

Students will compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols.

• Ontario Curriculum Expectations
• 2.NBT.A.4

About This Topic

Skip counting is a foundational skill that bridges the gap between simple addition and the beginnings of multiplicative thinking. In Grade 2, students are expected to skip count by 2s, 5s, 10s, and 25s up to 200, starting from various points. This aligns with the Ontario Algebra and Number strands, focusing on identifying and extending patterns. It is not just about rote memorization; it is about recognizing the rhythmic and visual patterns that emerge on a hundred chart or number line.

Skip counting is also culturally significant, as it is used in traditional games, music, and counting systems across many cultures, including Indigenous storytelling and French nursery rhymes. It is a practical skill for counting currency, like nickels, dimes, and quarters. This topic comes alive when students can physically model the patterns through movement, rhythm, and collaborative games.

Key Questions

1. How can you tell which of two numbers up to 200 is greater?
2. What do you look at first when comparing two three-digit numbers?
3. Can you put a set of numbers up to 200 in order from least to greatest on a number line?

Learning Objectives

• Compare two three-digit numbers up to 200 using the greater than (>), less than (<), and equal to (=) symbols.
• Explain the process of comparing two three-digit numbers by analyzing the hundreds, tens, and ones digits from left to right.
• Identify the greater or lesser number in a pair of numbers up to 200 based on place value.
• Order a set of numbers up to 200 from least to greatest on a number line.

Before You Start

Comparing Numbers to 100

Why: Students need prior experience comparing two-digit numbers to build understanding for three-digit numbers.

Understanding Place Value to Hundreds

Why: A solid grasp of the value of hundreds, tens, and ones digits is essential for comparing three-digit numbers.

Key Vocabulary

Greater than (>)	A symbol used to show that the number on the left is larger than the number on the right.
Less than (<)	A symbol used to show that the number on the left is smaller than the number on the right.
Equal to (=)	A symbol used to show that two numbers have the same value.
Place Value	The value of a digit based on its position within a number, such as ones, tens, or hundreds.
Hundreds Digit	The digit in the third position from the right in a three-digit number, representing the number of hundreds.

Watch Out for These Misconceptions

Common Misconception

Thinking skip counting only starts at zero.

What to Teach Instead

Students often struggle to skip count by 10s if they start at 3 (3, 13, 23...). Using a hundred chart during a 'Think-Pair-Share' allows students to see the vertical jump, helping them realize the ones digit stays the same while the tens digit increases.

Common Misconception

Losing track of the count when crossing a hundred (e.g., 90, 100, 110).

What to Teach Instead

This is a place value error. Active movement, like jumping across a line on the floor while calling out the numbers, helps students physically feel the transition into the next hundred, reinforcing the sequence through muscle memory.

Active Learning Ideas

Stations Rotation: Pattern Detectives

Set up stations with different tools: a hundred chart with counters, a long floor number line, and a set of Canadian coins. At each station, students must skip count by a different interval (2, 5, 10, or 25) and record the 'ending digit' patterns they notice.

45 min·Small Groups

Think-Pair-Share: The Broken Calculator

Tell students their '+' key only works for one number (e.g., +5). Ask pairs to figure out how many 'clicks' it takes to get from 0 to 50, and then from 5 to 55. They share their strategies for keeping track of the counts.

15 min·Pairs

Gallery Walk: Pattern Posters

Groups create a visual representation of a skip counting sequence (e.g., counting by 2s starting at 1). They highlight the pattern in the ones place. Students walk around with sticky notes to comment on patterns they see in other groups' work.

30 min·Small Groups

Real-World Connections

• Grocery store clerks compare prices of items to ensure customers are charged correctly, using symbols like '>' or '<' when discussing sales or discounts for items under $200.
• Librarians organize books by their Dewey Decimal System numbers, which are numerical. They might compare two numbers to determine which book comes first on a shelf, ensuring items are ordered correctly.
• Construction workers might compare measurements for building materials, ensuring lengths are correct. For example, they might check if a piece of wood is greater than, less than, or equal to a required length of 150 cm.

Assessment Ideas

Exit Ticket

Provide students with three pairs of numbers up to 200 (e.g., 135 and 153, 102 and 120, 188 and 188). Ask them to write the correct comparison symbol (>, <, =) between each pair.

Quick Check

Display two numbers on the board, such as 172 and 165. Ask students to hold up fingers to represent the hundreds digit, then the tens digit, then the ones digit for each number. Then, ask them to use their hands to show the '>' or '<' symbol to compare the numbers.

Discussion Prompt

Present students with the numbers 148 and 142. Ask: 'Which digit do you compare first? Why? What happens if the hundreds digits are the same? What happens if the tens digits are also the same?' Guide them to explain their reasoning for comparing the ones digits.

Frequently Asked Questions

Why is skip counting by 25s important in Grade 2?

In Canada, the quarter is a common coin. Learning to skip count by 25s (25, 50, 75, 100) is a practical life skill for handling money and introduces students to the idea of quarters of a whole, which helps with future fraction work.

How does skip counting lead to multiplication?

Skip counting is essentially repeated addition. When a student counts 5, 10, 15, they are discovering that three groups of five make fifteen. This builds the conceptual framework for the 'groups of' language used in Grade 3 multiplication.

What are some fun ways to practice skip counting at home?

Use a ball to play 'catch and count,' where each person says the next number in the sequence. You can also count steps while walking, or use a deck of cards to flip and skip count based on the number shown.

How can active learning help students understand skip counting?

Skip counting is inherently rhythmic. Active learning strategies like 'Human Number Lines' or rhythmic clapping games engage the body's kinesthetic sense. When students move their bodies to the count, they are more likely to internalize the pattern and notice the regularity of the sequence compared to just writing numbers on a page.