Mathematics · Year 4

Active learning ideas

Fractions to Decimals (Tenths and Hundredths)

Active learning helps students grasp fractions to decimals because visual and hands-on tasks make place value concrete. When students shade grids or handle money, they see why 7/10 becomes 0.7 and not 0.10. Movement and discussion also reduce abstract confusion about tenths and hundredths.

• National Curriculum Attainment Targets
• NC.MA.4.F.6

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

Activity 01

• Think-Pair-Share
• 35 min · Pairs

Grid Shading: Tenths and Hundredths

Provide 10x10 grids. Students shade fractions like 4/10 or 37/100, then write the decimal equivalent. Partners check each other's work and discuss place value positions. Extend by converting back from given decimals.

Analyze the pattern when converting fractions like 7/10 to decimals.

Facilitation Tip

During Grid Shading, circulate and ask students to describe how many squares equal one tenth before shading begins.

What to look for

Present students with a set of cards showing fractions (e.g., 3/10, 65/100) and another set showing decimals (e.g., 0.3, 0.65). Ask students to match the equivalent fraction and decimal pairs. Observe which students can correctly identify the relationships.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Small Groups

Decimal Arrow Cards: Matching Game

Prepare cards with fractions (e.g., 23/100), decimals (0.23), and place value diagrams. In small groups, students match sets and explain why they fit. Time challenges add pace.

Predict the decimal equivalent of 45/100.

What to look for

On a small slip of paper, ask students to write the decimal for 8/10 and the fraction for 0.42. Also, ask them to explain in one sentence why 0.5 is the same as 5/10.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 40 min · Whole Class

Money Line: Fraction Shopping

Use play money in tens and pennies. Whole class lines up decimals on a number line, then converts to fractions like 37p = 37/100. Discuss real purchases to reinforce.

Justify why 0.6 is the same as 6/10.

What to look for

Pose the question: 'If you have 10 apples and eat 3, what fraction of the apples did you eat? How would you write that as a decimal? What if you had 100 apples and ate 30?' Facilitate a class discussion comparing the decimal representations and place value.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 30 min · Small Groups

Prediction Relay: Convert and Justify

Teams predict decimal for a fraction, run to board to write it, then justify to teacher. Correct teams score; rotate roles. Covers key questions directly.

Analyze the pattern when converting fractions like 7/10 to decimals.

What to look for

Present students with a set of cards showing fractions (e.g., 3/10, 65/100) and another set showing decimals (e.g., 0.3, 0.65). Ask students to match the equivalent fraction and decimal pairs. Observe which students can correctly identify the relationships.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach this topic by connecting fractions to familiar contexts like money and grids, which build on prior place value knowledge. Avoid rushing to rules—let students discover patterns through structured exploration. Research shows manipulatives paired with discussion deepen understanding of equivalent values.

Successful learning looks like students confidently converting fractions to decimals and back, explaining their reasoning with place value language. They should use terms like tenths and hundredths correctly during activities and justify equalities such as 0.3 = 3/10 without hesitation.

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Watch Out for These Misconceptions

• During Grid Shading, watch for students who count each small square as a tenth instead of grouping ten squares as one tenth.

  Pause the activity and ask students to outline a row of ten squares, labeling it as one whole before shading. Have them recount the shaded portion together using the outlined group.

• During Decimal Arrow Cards, watch for students who place 45/100 next to 4.5 instead of 0.45.

  Have students lay out the arrow cards for 45/100 and physically separate the 4 and 5, placing the 0.4 card and 0.05 card end to end to show 0.45.

• During Money Line, watch for students who treat 0.6 as 6 cents instead of sixty cents.

  Use real coins to show that 0.6 equals 60 cents, then ask students to place the fraction 6/10 on the same spot on the money line to reinforce equivalence.

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Methods used in this brief

• Think-Pair-Share