Foundations of Mathematical Thinking · 1st Year

Active learning ideas

The Power of Ten: Grouping

Active learning works well for grouping because students need to physically manipulate objects to build an intuitive sense of how numbers combine. Moving items into groups of ten helps them see the structure of our number system, which makes estimation more meaningful and less abstract.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Algebra

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 20 min · Individual

Format Name: Tens Frame Counting

Students use a ten-frame mat and counters. They place counters one by one, filling the frame. Once full, they create a 'tens stick' and start a new frame, reinforcing the grouping concept.

Explain why it is easier to count objects when we group them in tens.

Facilitation Tip

During Collaborative Investigation: The Benchmark Box, circulate and ask guiding questions like, 'How does this group compare to the box of ten we saw earlier?' to keep students anchored to their benchmark.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 25 min · Small Groups

Format Name: Place Value Building Blocks

Using base-ten blocks (units and rods), students build given numbers. They can also be given a pile of units and asked to make as many tens as possible, then state the total number.

Analyze how the digit 1 changes its meaning when it moves from the units place to the tens place.

Facilitation Tip

In Think-Pair-Share: Is it Reasonable?, model how to explain your thinking by saying, 'I think it’s about 30 because I see three groups of ten and a few extra.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 15 min · Whole Class

Format Name: Number Line Jumps

Students use a large number line. They practice making 'jumps' of ten to reach different numbers, visually demonstrating the power of grouping by ten for counting.

Predict what happens to a number if we have more than nine units.

Facilitation Tip

At Estimation Stations, set a timer for each station so students move quickly and rely on their benchmark sense rather than counting every item.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach this by starting with concrete examples and gradually moving toward abstract thinking. Avoid rushing to symbols; let students verbalize their reasoning first. Research shows that students who practice estimating with visual benchmarks develop stronger number sense and are more accurate in their calculations later.

By the end of these activities, students should confidently use groups of ten to estimate and check quantities. They will explain their reasoning using benchmarks and recognize when an estimate is reasonable, not just exact.

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Watch Out for These Misconceptions

• During Collaborative Investigation: The Benchmark Box, watch for students who feel their estimate is wrong if it isn’t the exact number. Redirect them by saying, 'Your estimate of 25 is great because it’s between 20 and 30, which is close to our benchmark of ten.'

  Remind students that estimates are about range, not precision. Use the box of ten to show that any estimate within the same group of tens (e.g., 20-29) is reasonable.

• During Estimation Stations, watch for students who shout out random numbers without looking at the objects. Redirect them by saying, 'First, let’s count how many are in this small group to use as our guide.'

  Stop the class and model comparing the unknown quantity to the benchmark by holding up a group of ten items and asking, 'How many groups of ten do you see here?' before they guess.

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Methods used in this brief

• Stations Rotation