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.

• 1st Year
• Foundations of Mathematical Thinking
• 3 activities
• 15 min–25 min

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.'

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.'

What to Teach Instead

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.

Common Misconception

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.'

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Collaborative Investigation: The Benchmark Box, give students 23 counters and ask them to make as many groups of ten as possible. Observe whether they can form two groups of ten and identify the remaining three units.

Exit Ticket

During Think-Pair-Share: Is it Reasonable?, give each student a card with a number (e.g., 15, 27). Ask them to draw the number using tens and units (e.g., one stick for ten, one dot for a unit). Then, ask: 'If you had 12 units, how many tens and units would you have?' Collect their drawings to check for accuracy.

Discussion Prompt

After Estimation Stations, show students two arrangements of the same number of objects—one grouped in tens and one scattered. Ask: 'Which arrangement is easier to count and why? How does seeing the groups of ten help you know the total number faster?' Listen for explanations that mention benchmarks and efficiency.

Extensions & Scaffolding

• Challenge: Give students a set of 87 objects and ask them to estimate the total in three different ways, each time using a different benchmark (e.g., groups of 5, groups of 10, groups of 20). Record all estimates and discuss which was most accurate and why.
• Scaffolding: For students struggling, provide pre-made groups of ten and ask them to count how many are left over, then write the total as a number.
• Deeper exploration: Have students create their own estimation challenge for a partner, using objects in the classroom, and discuss why certain arrangements make estimation easier or harder.