Lesson 3 — Adding and Subtracting Decimals with Money

Summary

Learners add and subtract decimals by lining up the decimal points and working place by place, regrouping when needed. They practice in a market context — totaling purchases and giving change with money — and check that every answer makes sense with the amounts they started with.

Objectives

• Add and subtract decimals in a real money context, lining up place values and regrouping as needed. (D05.S1.05.02)

Connection

You are at a market with 5.00. You buy rice for 2.50 and fruit for 1.75. How much do you pay, and how much change do you get back? Adding and subtracting decimals is exactly the math of buying and selling — the same skill a seller uses to give the right change in a market in Lagos, a shop in Lima, or a floating market in Bangkok. Money works in many currencies, but the place-value idea — line up the points, work place by place — is the same everywhere.

Materials

• Market price tag cards
• Decimal money recording page
• Play money or paper coins

Preparation

• Copy price tag cards for pairs and the recording page for each learner.
• Set up play money or paper coins for groups.
• Have a worked example ready: 2.50 + 1.75 = 4.25; change from 5.00.

Facilitator note

This lesson is written to the learner (“you”). The skill to carry is aligning the decimal points so tenths add to tenths and hundredths to hundredths, then regrouping exactly as with whole numbers (ten hundredths make a tenth; ten tenths make a one). Because this is a foundational skill, model a worked example step by step, then guide a second together before independent practice (Kirschner, Sweller & Clark, 2006). Common slips to watch for: lining up numbers on the right edge instead of at the decimal point, and forgetting to write the decimal point in the answer. Retrieval: ask learners to recall last lesson’s rounding rule and reuse it to estimate (“about 2.50 + 1.75 ≈ 4.25, so the answer should be near 4”). Using real local currency is fine; keep the math generic so it works with any currency, and avoid assuming one currency is the “default.” The arithmetic is evidence; the habit of giving exact change so no one is cheated is a fairness value (docs/philosophy.md §4).

Procedure

1. Gather (5 min). Recall: how do you round 4.36 to the nearest tenth? Today you use decimals to add and subtract — the math of money.
2. The rule (5 min). When you add or subtract decimals, line up the decimal points, then work place by place, just like whole numbers. The decimal point in the answer sits right under the others.
3. Worked example — add (10 min). A customer buys rice (2.50) and fruit (1.75). Write 2.50 and 1.75 with the points lined up. Add hundredths: 0 + 5 = 5. Add tenths: 5 + 7 = 12 tenths → write 2, carry 1 one. Add ones: 2 + 1 + 1 = 4. The total is 4.25.
4. Worked example — subtract (10 min). The customer pays 5.00. Subtract 4.25 to find the change. Line up the points: 5.00 − 4.25. Hundredths: borrow from the tenths — 10 − 5 = 5. Tenths: 9 − 2 = 7. Ones: 4 − 4 = 0. The change is 0.75.
5. Practice at the market (15 min). With a partner, pick two or three price tags, total them, and find the change from an amount you choose. Use play money to act it out, then check each other’s work — did you line up the points? Is the change right?
6. Close (5 min). Adding and subtracting decimals is a daily-life skill. When the points line up, the math is as easy as whole numbers — and you can always estimate first to check your answer is sensible.

Differentiation

• Support: Use amounts with only tenths (2.5, 1.7) and no regrouping at first; keep the place-value chart visible and describe each step aloud. Provide tactile markers so learners with low vision can follow.
• Extension: Solve multi-item totals with several regroupings, estimate the change mentally first, and compare your estimate to the exact answer.

Assessment

• Formative (observation/self): Can the learner line up decimal points, add and subtract with regrouping, and give correct change in a market task?
• Self-check: The learner asks, “Did I line up the decimal points, and does my answer make sense for the amounts I started with?”

Home connection

Next time something is bought, help figure out the total or the change, and line up the decimal points to do it.

Resources

• Decimal addition/subtraction by place-value alignment is standard in elementary mathematics; see John A. Van de Walle, Elementary and Middle School Mathematics (10th ed., 2019). The claim that giving exact change so no one is cheated is a fairness value (docs/philosophy.md §4).