Activity 01
Manipulative Build: Tenths and Hundredths Blocks
Distribute base-ten blocks to small groups. Instruct students to build one whole, then represent 0.1 with one flat and 0.01 with one small square. Extend to building and comparing 0.3 and 0.30, noting they use the same total area. Groups record findings on charts.
Explain how a decimal point is like a mirror between whole numbers and parts.
Facilitation TipDuring Manipulative Build, circulate to ask each pair to verbalize how the tenths flat relates to the hundredths square before they start building.
What to look forGive students a base-ten grid. Ask them to shade in a representation for 0.4 and then write the equivalent representation using hundredths (e.g., 0.40). Then, ask them to draw a line and explain what the decimal point separates.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→· · ·
Activity 02
Grid Shading: Decimal Equivalents
Provide decagonal grids for tenths and hundred grids for hundredths. Pairs shade 0.4 on the decagon and 0.40 on the hundred grid, then compare coverage. Discuss why the shaded areas match despite different grids. Pairs create their own examples.
Compare the value of a tenth to a hundredth.
Facilitation TipWhile students shade grids in Grid Shading, remind them to mark the decimal point first so the mirroring across the point stays clear in their work.
What to look forDisplay two base-ten blocks: one representing a tenth and one representing a hundredth. Ask students to hold up fingers to indicate which is larger (1 finger) and which is smaller (2 fingers). Then, ask them to write the decimal value for each.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→· · ·
Activity 03
Comparison Mats: Decimal Showdown
Set up mats with place value charts. Pairs draw cards with decimals like 0.2 and 0.20, then build both on mats using blocks or sketches. They explain comparisons to the group. Rotate cards for multiple rounds.
Construct a visual representation of 0.3 and 0.30.
Facilitation TipOn Comparison Mats, have students write the decimal value below each mat area so the symbolic and visual representations stay connected as they debate size.
What to look forPose the question: 'Imagine you have a chocolate bar divided into 10 equal pieces, and another identical chocolate bar divided into 100 equal pieces. If you eat 3 pieces from the first bar, and your friend eats 30 pieces from the second bar, who ate more chocolate?' Facilitate a discussion using base-ten blocks or drawings to justify their answers.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→· · ·
Activity 04
Number Line Placement: Visual Ordering
Give students blank number lines from 0 to 1. In small groups, they mark and label tenths and hundredths like 0.3, 0.30, 0.07. Groups order a set of decimals and justify positions. Share on class board.
Explain how a decimal point is like a mirror between whole numbers and parts.
What to look forGive students a base-ten grid. Ask them to shade in a representation for 0.4 and then write the equivalent representation using hundredths (e.g., 0.40). Then, ask them to draw a line and explain what the decimal point separates.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→A few notes on teaching this unit
Teachers should first let students explore the blocks and grids without guidance to surface misconceptions naturally. Then, direct comparisons between students’ constructions help them articulate the systematic structure of the base-ten system across the decimal point. Avoid rushing to rules—build the understanding through repeated, purposeful manipulation and discussion.
By the end of these activities, students will confidently represent tenths and hundredths using blocks and grids, explain the role of the decimal point in mirroring place values, and compare decimals with precision. Their reasoning will include clear references to the size of the unit parts they have constructed and measured.
Watch Out for These Misconceptions
During Manipulative Build, watch for students who declare 0.3 larger than 0.30 because the latter has more digits after the decimal.
Have them build 0.3 using three tenths flats and 0.30 using thirty hundredths squares, then place the tenths flat directly over the group of ten hundredths squares to see they cover the same area. Ask them to explain the equivalence aloud before moving on.
During Manipulative Build, watch for students who treat the decimal point as just a separator with no role in place value.
After they build a number like 1.4, ask them to slide the ones cube to the tenths side and the tenths flat to the ones side, noting how the value changes. The physical mirroring across the point should reveal the systematic relationship.
During Grid Shading, watch for students who believe a hundredth is larger than a tenth because the grid has more squares.
Ask them to shade one tenth on a 10x10 grid and then overlay ten hundredths squares on top of it, counting as they go. The overlay should show that ten hundredths exactly cover one tenth, clarifying the size relationship.
Methods used in this brief