Mathematics · Grade 4

Active learning ideas

The Tenths and Hundredths Connection

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.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.NF.C.5
• CCSS.MATH.CONTENT.4.NF.C.6

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 25 min · Pairs

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.

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.

What to look for

Present students with a 10x10 grid. Ask them to shade 3 tenths and then write the decimal and fraction for the shaded amount. Then, ask them to shade 15 hundredths and write the decimal and fraction for that amount.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 35 min · Small Groups

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.

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.

What to look for

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.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 30 min · Pairs

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.

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.

What to look for

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.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 40 min · Pairs

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.

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.

What to look for

Present students with a 10x10 grid. Ask them to shade 3 tenths and then write the decimal and fraction for the shaded amount. Then, ask them to shade 15 hundredths and write the decimal and fraction for that amount.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• During Grid Shading Relay, watch for students who believe 0.5 and 0.50 are different because they have different numbers of digits.

  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.

• During Number Line Partners, watch for students who think 0.09 is larger than 0.1 because it has more digits after the decimal point.

  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.

• During Base Ten Trades, watch for students who see decimals and fractions as unrelated number types.

  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.

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Methods used in this brief

• Gallery Walk