# Fractions and Decimals: Connecting Two Ways to Show Parts Discover how fractions and decimals are two languages for the same idea. ![Figure 1: A baker's kitchen with a mixing bowl on a counter](https://goa-cc-uat-aili-app-001.azurewebsites.net/api/generate/bd58d402-003a-4beb-8fe8-ec15fa7a13c4/asset/993) ## Learning intentions We are learning to understand that fractions and decimals represent the same numbers and to convert between them. ## Success criteria I can express a fraction as a decimal number when the denominator is 10 or 100 ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30059)). I can express a decimal number as a fraction ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30059)). I can identify the place value of tenths and hundredths in a decimal number ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30031)). I can recognize that fractions and decimal numbers can represent the same number ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30057)). ## Curriculum alignment Students apply place value to decimal numbers ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30027)). Students apply equivalence to the interpretation of fractions ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30051)). Decimal numbers are fractions with denominators of 10, 100, etc. ([Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30030), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30030)). Fractions and decimal numbers can represent the same number ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30057)). ## Materials - Base-10 blocks or grid paper (10 × 10 squares printed or drawn) - Fraction strips (paper or card showing tenths and hundredths) - Number line (0 to 2, marked in tenths) on poster or whiteboard - Index cards with decimal and fraction pairs - Coins (real or play) for money examples - Worksheet with grid squares (hundredths grids) ## Lesson sequence ### 1. Hook (5 minutes) Show two containers of juice. One is labeled 1/10 full. The other is labeled 0.1 full. Ask the class: Are these the same amount, or different? Take responses. Do not confirm yet. Say: By the end of this lesson, you will know the answer and why. ### 2. Direct instruction: Tenths (8 minutes) Draw a rectangle on the board. Divide it into 10 equal parts. Shade one part. Say: This shape is divided into 10 equal parts. One part is shaded. We can write this as a fraction: 1/10 (one-tenth). We can also write it as a decimal: 0.1. Write both on the board side by side: 1/10 = 0.1 Shade 3 more parts. Say: Now we have 4 parts shaded out of 10. That is 4/10 (four-tenths). As a decimal, we write 0.4. Write: 4/10 = 0.4 Point to the decimal point. Say: The decimal point separates the whole number from the parts. In 0.4, there are zero wholes and four-tenths ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30029)). Ask: What fraction and decimal does this show? (Shade 7 parts.) Wait for responses. Confirm: 7/10 = 0.7. ### 3. Direct instruction: Hundredths (8 minutes) Display a 10 × 10 grid (100 small squares). Say: This grid has 100 equal squares. If we shade one square, we have 1/100 (one-hundredth). As a decimal, we write 0.01. Write: 1/100 = 0.01 Shade 25 squares in a block. Say: We have 25 squares shaded out of 100. That is 25/100 (twenty-five hundredths). As a decimal, we write 0.25. Write: 25/100 = 0.25 Point to the decimal. Say: The first digit after the decimal point is tenths. The second digit is hundredths ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30031)). In 0.25, the 2 means two-tenths, and the 5 means five hundredths. Together they make twenty-five hundredths. Shade 50 squares. Ask: What fraction and decimal does this show? (Wait for responses.) Confirm: 50/100 = 0.50. Say: Notice that 50/100 is the same as 5/10. Both equal 0.5. Fractions and decimals that look different can be the same number ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30057)). ### 4. Guided practice: Fraction to decimal (7 minutes) Display a number line from 0 to 1, marked in tenths (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0). Say: I will name a fraction. You point to where it sits on the number line and tell me the decimal. Call out: 3/10. (Students point to 0.3.) Confirm: 3/10 = 0.3. Call out: 6/10. (Students point to 0.6.) Confirm: 6/10 = 0.6. Call out: 8/10. (Students point to 0.8.) Confirm: 8/10 = 0.8. Now show a 10 × 10 grid on the board. Shade 35 squares. Say: How many squares are shaded? (35.) How many squares are there altogether? (100.) So the fraction is 35/100. What is the decimal? Guide students to say: 0.35. Write: 35/100 = 0.35 Shade a different grid to show 72 squares shaded. Ask: What is the fraction? (72/100.) What is the decimal? (0.72.) Confirm both. ### 5. Guided practice: Decimal to fraction (5 minutes) Say: Now I will name a decimal. Students apply place value to decimal numbers. Say: 0.4. What fraction is this? (4/10.) Confirm: 0.4 = 4/10. Say: 0.7. What fraction is this? (7/10.) Confirm: 0.7 = 7/10. Say: 0.15. What fraction is this? (15/100.) Confirm: 0.15 = 15/100. Say: 0.60. What fraction is this? (60/100.) Confirm: 0.60 = 60/100. Can we simplify this? Yes, 60/100 = 6/10. ### 6. Independent practice (5 minutes) Hand out a worksheet with the following tasks: **Task 1:** Draw a grid and shade it to show 0.3. Write the fraction. **Task 2:** Write the decimal for 7/10. **Task 3:** Write the fraction for 0.45. **Task 4:** Draw a 10 × 10 grid and shade it to show 0.82. Write the fraction. **Task 5:** Look at this grid (show 6/10 shaded). Write the decimal. Circulate. Ask students to explain their thinking as they work. ### 7. Consolidation (2 minutes) Gather the class. Numbers, including decimal numbers, can be composed in various ways by using place value. Ask: Are 1/10 and 0.1 the same? (Yes.) Why? (Because 1/10 means one part out of ten, and 0.1 means one-tenth.) Say: Fractions and decimals are two different ways to write the same number. When the denominator is 10 or 100, it is easy to change between them ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30059), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30057)). ## Differentiation **Support** Provide pre-drawn grids (10 × 1 and 10 × 10) so students focus on counting and naming, not drawing. Use only tenths (denominators of 10) in the first lesson. Introduce hundredths in a follow-up lesson. Pair students with a peer or adult to read decimal notation aloud together. Emphasize the word "and" to mark the decimal point: "zero and four tenths" for 0.4 ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30029)). **Extension** Ask: If 0.5 = 5/10, what other fractions equal 0.5? (50/100, 1/2.) Discuss equivalent fractions. Introduce money: $0.35 is 35/100 of a dollar, or 35 cents. Have students write amounts in dollars and cents using decimal notation. Pose a comparison question: Which is larger, 0.6 or 0.59? Draw grids to show why ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30031)). ## Assessment **Formative check during independent practice:** Observe students completing Task 3 (write the fraction for 0.45). **What to look for:** Student writes 45/100 (correct). Student writes 0.45 as the fraction (misunderstanding; needs clarification that 0.45 is already a decimal). Student writes 45/10 (place-value error; review which position is tenths and which is hundredths). If a student struggles, ask: How many parts is the grid divided into? (100.) How many are shaded? (45.) So the fraction is... (45/100). Repeat the same process with a visual grid to anchor understanding. --- *AILI rapid lesson · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id bd58d402-003a-4beb-8fe8-ec15fa7a13c4* ### Sources - node:n1: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can place value facilitate interpretation of number? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30027) - node:n2: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can understanding of addition and subtraction be extended to decimal numbers? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30033) - node:n3: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can place value facilitate interpretation of number? › Students apply place value to decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30029) - node:n4: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can place value facilitate interpretation of number? › Students apply place value to decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30031) - node:n5: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can place value facilitate interpretation of number? › Students apply place value to decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30030) - node:n6: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can understanding of addition and subtraction be extended to decimal numbers? › Students add and subtract within 10 000, including decimal numbers to hundredths. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30035) - node:n7: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can understanding of addition and subtraction be extended to decimal numbers? › Students add and subtract within 10 000, including decimal numbers to hundredths. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30037) - node:n8: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can understanding of addition and subtraction be extended to decimal numbers? › Students add and subtract within 10 000, including decimal numbers to hundredths. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30036) - node:n9: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can fractions be characterized in different ways? › Students apply equivalence to the interpretation of fractions. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30059) - node:n10: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can fractions be characterized in different ways? › Students apply equivalence to the interpretation of fractions. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30057) - node:n11: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can fractions be characterized in different ways? › Students apply equivalence to the interpretation of fractions. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30058) - node:n12: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can place value facilitate interpretation of number? › Students apply place value to decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30030) - node:n13: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can percentages standardize part-whole relationships? › Students interpret percentages. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30064) - node:n14: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can fractions be characterized in different ways? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30051) - node:n15: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can percentages standardize part-whole relationships? › Students interpret percentages. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30065) - node:n16: Mathematics › Mathematics (K–6) › Grade 4 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can place value facilitate interpretation of number? › Students apply place value to decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30029)