Decimal Operations Workshop

Overview

Students develop fluency adding and subtracting multi-digit decimals using the standard algorithm. They connect place-value alignment to real-world money and measurement contexts, then explain how they know their answers are reasonable.

Learning intentions

Students will be able to:

• Add and subtract multi-digit decimals using the standard algorithm.
• Align decimal points and use zeros as placeholders when needed.
• Estimate answers to check whether exact calculations are reasonable.
• Explain solutions using place-value language and real-world contexts.

Success criteria

• I can line up decimal points before calculating.
• I can add or subtract digits in the correct place-value columns.
• I can use zeros to complete missing decimal places.
• I can estimate and explain whether my answer makes sense.

Curriculum links

• Number — fluently adding and subtracting multi-digit decimals using the standard algorithm.
• Number — representing rational numbers in real-world contexts, including money, distance, and temperature.
• Number — ordering rational numbers and using a number line to judge whether answers are reasonable.
• Number — understanding the role of zero and the value of digits in decimal place value.

Lesson structure (60 minutes)

1. 0–7 min · Hook and estimate. Open with the opening estimate challenge showing a shopping receipt with prices of $4.75, $12.60, and $3.08; students estimate the total independently, compare estimates with a partner, and explain which whole-number values they used.

2. 7–18 min · Direct teach. Use the place-value teaching slides to model (24.70 + 8.356) and (31.2 - 7.845), emphasizing that decimal points—not the number of digits—must be aligned. Students annotate the examples, identify each place-value column, and help complete missing zeros such as (31.200).

3. 18–28 min · Guided practice. Display the problems from the guided-practice slides: (6.48+13.7), (42.005-8.6), and (105.3-27.846). Students solve on whiteboards, hold them up, and explain one step using a sentence frame: “I aligned ___ because ___ has a value in the ___ place.”

4. 28–43 min · Partner application. Distribute the decimal shopping and measurement worksheet to pairs. Students solve a set of shopping, distance, and temperature problems, first estimating and then calculating exactly. Partners must compare methods, circle the operation used, and check one answer with the inverse operation or an estimate. Circulate and ask, “Which place value controls your regrouping?” and “How do you know your answer is reasonable?”

5. 43–52 min · Error analysis and discussion. Show the examples from the error-analysis slides, including a misplaced decimal point, an omitted placeholder zero, and an incorrect regrouping step. Students identify, correct, and explain each error with a partner, then share the most important correction with the class.

6. 52–60 min · Independent check and exit ticket. Students complete the final problems on the independent check and exit ticket without partner support: (18.06+7.895), (50-16.728), and a brief explanation of why (4.2+0.37) can be written as (4.20+0.37). Close with the summary and exit prompt and collect responses.

Resources

• the decimal operations slide deck
• the decimal shopping and measurement worksheet
• Individual whiteboards or paper
• Dry-erase markers
• Pencils and erasers
• Place-value chart displayed or projected
• Calculators for optional answer checking after work is shown
• Projector or interactive display

Assessment

• Use whiteboard responses during guided practice to check decimal alignment, regrouping, and use of placeholder zeros.
• During partner work, listen for place-value explanations and inspect estimates before exact answers.
• Use the exit ticket to identify students who need support with alignment, subtraction across zeros, or explaining equivalence.

Differentiation

• Provide a place-value chart, grid paper, and preformatted columns for students who need visual or motor support. Allow students to mark decimal points in color.
• Give sentence starters such as “I know the answer is reasonable because…” and explicitly model vocabulary including tenths, hundredths, thousandths, align, regroup, and estimate for multilingual learners.
• Read worksheet directions aloud, reduce the number of practice items without reducing the reasoning demand, and check in privately with students who need additional processing time.
• Extend ready students by asking them to create two different decimal expressions with a difference of (12.5), or to find and explain two possible errors in a worked subtraction problem.