The Tenths and Hundredths ConnectionActivities & Teaching Strategies
This topic thrives on visual and hands-on learning because decimals are an abstract concept that become concrete when students see and touch them. Shading grids and manipulating blocks turn abstract numbers into tangible parts of a whole, making the connection between tenths and hundredths clear and memorable.
Learning Objectives
- 1Compare the fractional and decimal representations of tenths and hundredths using visual models.
- 2Explain the relationship between fractions with denominators of 10 or 100 and their equivalent decimal forms.
- 3Justify the equivalence of decimals with trailing zeros, such as 0.5 and 0.50, based on place value.
- 4Identify and provide examples of where tenths and hundredths are used in decimal form in everyday contexts.
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Grid Shading Relay: Tenths to Hundredths
Pairs shade 10x10 grids for given decimals like 0.37, first as tenths then subdividing for hundredths. One partner shades while the other times and checks accuracy. Switch roles and compare grids to discuss equivalences.
Prepare & details
Explain how a decimal is another way of writing a fraction with a denominator of 10 or 100.
Facilitation Tip: During Grid Shading Relay, circulate and ask pairs to explain their shading choices before moving to hundredths, ensuring they see the direct relationship between tenths and hundredths.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Base Ten Trades: Decimal Builds
In small groups, students build decimals using flats for tenths and rods of 10 units for hundredths. Trade 10 hundredths for one tenth to model 0.5 as 0.50. Record builds on worksheets and share one trade with the class.
Prepare & details
Justify why 0.5 is equivalent to 0.50 despite having different numbers of digits.
Facilitation Tip: For Base Ten Trades, model how to trade 10 hundredths cubes for 1 tenth flat out loud to reinforce the base ten system.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Money Decimal Sort: Real-Life Match
Provide cards with fraction amounts like 3/10 dollar and decimal cards like 0.35. Pairs sort matches into categories of tenths and hundredths, then justify one pair using drawings. Extend by creating their own money problems.
Prepare & details
Analyze where decimals are used in daily life more frequently than fractions.
Facilitation Tip: In Money Decimal Sort, ask students to justify their matches by explaining the value of each coin in terms of tenths and hundredths.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Number Line Partners: Tenths and Hundredths Jumps
Draw number lines from 0 to 2. Partners take turns jumping tenths then adding hundredths, like from 0 to 0.7 to 0.72. Label jumps and explain the path to verify equivalence.
Prepare & details
Explain how a decimal is another way of writing a fraction with a denominator of 10 or 100.
Facilitation Tip: On Number Line Partners, have students physically stand on the number line at their assigned decimal to internalize the size of tenths and hundredths.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Teaching This Topic
Teachers should prioritize connecting decimals to fractions and visual models from the start, as this deepens understanding beyond procedural rules. Avoid rushing to abstract notation before students can explain what a decimal represents in real terms. Research supports using multiple representations (grids, blocks, number lines) to build flexible thinking and address misconceptions early.
What to Expect
Successful learning looks like students confidently translating between decimals, fractions, and visual models. They should articulate why 0.4 and 0.40 are equal, compare decimals like 0.7 and 0.75 accurately, and explain the fraction-decimal relationship using grids, blocks, or number lines without hesitation.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Grid Shading Relay, watch for students who believe 0.5 and 0.50 are different because they have different numbers of digits.
What to Teach Instead
Have students shade a 10x10 grid for 0.5 (5 tenths) and another for 0.50 (50 hundredths) on the same board, then compare the shaded areas to see they are identical. Ask them to articulate why the zeros do not change the value.
Common MisconceptionDuring Number Line Partners, watch for students who think 0.09 is larger than 0.1 because it has more digits after the decimal point.
What to Teach Instead
Ask students to sort decimal cards on a number line, starting with 0.1 and 0.09. Have them explain why 0.09 is closer to zero and discuss the role of place value in determining size.
Common MisconceptionDuring Base Ten Trades, watch for students who see decimals and fractions as unrelated number types.
What to Teach Instead
After trading base ten blocks, have students write the fraction and decimal for the amount they built, such as 4 tenths cubes and 2 hundredths cubes becoming 0.42 or 42/100. Ask them to explain the connection between the blocks and the notation.
Assessment Ideas
After Grid Shading Relay, present students with a 10x10 grid. Ask them to shade 3 tenths, then write the decimal and fraction for the shaded amount. Next, ask them to shade 15 hundredths and write the decimal and fraction for that amount.
During Base Ten Trades, pose the question: 'Why is 0.7 the same as 0.70?' Have students discuss in pairs using base ten blocks or drawings to justify their answers, then share their reasoning with the class.
After Money Decimal Sort, give each student a card with a decimal (e.g., 0.3, 0.45, 0.9). Ask them to write the equivalent fraction and draw a visual representation (like a shaded rectangle) for their decimal. Collect these to check understanding of the fraction-decimal connection.
Extensions & Scaffolding
- Challenge early finishers to create a 10x10 grid where 0.25 of the grid is one color and 0.15 is another, then write the combined decimal and fraction for the entire shaded area.
- Scaffolding for struggling students: Provide pre-shaded tenths grids and ask them to count the squares aloud to build confidence before moving to hundredths.
- Deeper exploration: Have students research and present how decimals are used in real-world contexts like sports statistics or science measurements, tying the concept to their lives.
Key Vocabulary
| Decimal | A number expressed using a decimal point, representing parts of a whole based on powers of ten. |
| Tenths | One of ten equal parts of a whole, represented as 1/10 or 0.1. |
| Hundredths | One of one hundred equal parts of a whole, represented as 1/100 or 0.01. |
| Place Value | The value of a digit based on its position within a number, such as ones, tenths, or hundredths. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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