Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Ordering and Comparing Numbers to 199

Active learning works well here because students need to physically manipulate numbers to grasp place value and magnitude. Moving, sorting, and comparing numbers with hands-on tools makes abstract concepts concrete and memorable for learners at this stage.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1.2
• NCCA: Junior Cycle - Number - N.1.3

• 15–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 35 min · Small Groups

Small Groups: Place Value Card Sort

Provide cards with numbers to 199. Groups sort them into three piles: smallest third, middle third, largest third, using a shared number line. Then, they order all cards smallest to largest and justify with place value talk. Record the final order on chart paper.

What does it mean for one number to be greater than or less than another?

Facilitation Tip

During Place Value Card Sort, circulate to ask guiding questions like 'How did you decide where this card belongs?' to prompt metacognition.

What to look for

Provide students with three numbers (e.g., 75, 132, 98). Ask them to write the numbers in order from smallest to largest and then use the symbols >, <, or = to compare the first two numbers.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Pairs: Symbol Snap Game

Pairs flip number cards and snap pairs needing >, <, or = symbols between them. Correct snaps earn points; discuss place value if wrong. Switch roles after 10 rounds and tally scores.

How can you put a set of numbers in order from smallest to largest?

Facilitation Tip

In Symbol Snap Game, model both correct and incorrect symbol gestures to normalize mistakes and encourage peer correction.

What to look for

Display two numbers on the board (e.g., 145 and 154). Ask students to hold up fingers to show the tens digit of each number. Then, ask them to explain which number is greater and why, focusing on the tens place.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 25 min · Whole Class

Whole Class: Human Number Line

Assign each student a number card up to 199. They line up from 0 to 199 on floor tape, adjusting positions based on peer comparisons. Call out pairs to swap if incorrect, noting place value reasons.

Can you use the symbols > and < to compare two numbers up to 199?

Facilitation Tip

For the Human Number Line, assign starting positions randomly to prevent students from assuming left-to-right order implies increasing value.

What to look for

Pose the question: 'Imagine you have 120 stickers and your friend has 102 stickers. Who has more stickers? How do you know?' Encourage students to use the terms 'greater than' or 'less than' and refer to place value in their explanations.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 15 min · Individual

Individual: Number Line Puzzle

Students cut out number strips to 199 and glue them in order on personal number lines. Check with a partner using > or < symbols between adjacent numbers. Extend by adding missing numbers.

What does it mean for one number to be greater than or less than another?

What to look for

Provide students with three numbers (e.g., 75, 132, 98). Ask them to write the numbers in order from smallest to largest and then use the symbols >, <, or = to compare the first two numbers.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach this topic by alternating between concrete, representational, and abstract stages. Start with base-10 blocks to build numbers, move to drawings or number lines, and finally to symbolic comparisons. Avoid rushing to symbols before students can explain comparisons using models. Research shows that students who verbalize their reasoning while manipulating materials develop stronger number sense than those who only write comparisons.

Students will confidently compare and order numbers up to 199 using place value and comparison symbols. They will justify their reasoning with clear references to tens and ones, and demonstrate understanding through discussions and written comparisons.

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Watch Out for These Misconceptions

• During Place Value Card Sort, watch for students who sort by ones digit alone, ignoring the tens place.

  Ask them to build each number with base-10 blocks and compare the total amounts, then discuss why the tens digit determines the larger value before resorting.

• During Symbol Snap Game, watch for students who misread the direction of < and > symbols.

  Have them use their arms to form the symbol mouth while saying 'the alligator eats the bigger number,' then immediately sort a set of number cards using the correct gesture.

• During Human Number Line, watch for students who assume 100 is smaller than numbers just below it like 99.

  Have them physically walk the line from 99 to 100 while counting tens aloud, then compare the blocks for 99 (9 tens + 9 ones) and 100 (10 tens) to see the increase.

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Methods used in this brief

• Think-Pair-Share