Lead the Place-Value Journey
A 90-minute introduction followed by two 60-minute workshops.
Preparation
Bring counters, bundling materials, base-ten drawings, one-meter strips, hundred-grids, and graph paper. Pair teachers across grades. Decide what represents one whole before using any model; the same physical block may have a different value if the designated whole changes.
Session 1 · Experience the Story (90 minutes)
0–10: See five counters as different decompositions. Compare counting with recognizing parts; avoid speed-based judgments.
10–30: Chapters 1–3: build 34, unbundle one ten, and explain why the total stays fixed. Compare the values of repeated digits and locate rounding benchmarks.
30–55: Chapters 4–5: compare 0.6 and 0.58 in hundredths; explain 0.4 × 0.6 and 4.8 ÷ 0.6 with units. Contrast a trailing zero with multiplication by ten.
55–70: Chapters 6–7: distinguish signed order from distance and a negative exponent from a negative number. Explain one scientific-notation normalization.
70–90: Return to the map. Identify one prerequisite, a breakpoint supported by evidence, and one future connection from “A Glimpse Ahead.”
Session 2 · Understand Your Chapter (60 minutes)
0–10: Revisit the six breakpoint hypotheses in the overview.
10–25: Grade teams map the chapter onto local expectations. Annotate a correct example: what unit does each digit count?
25–40: Compare two valid strategies, diagnose the first incorrect inference, and complete the faded reasoning before checking the key.
40–55: Attempt a new-context transfer task independently. Upper-grade teams may investigate a “Think Like a Mathematician” challenge.
55–60: Choose one evidence-based change to an existing lesson.
Session 3 · Teach the Story (60 minutes)
0–10: Share a student explanation, useful representation, or unresolved question.
10–35: Adapt a lesson using a context, explicit whole/unit, organized model, precise language, and symbolic method. Include worked and contrasting examples, error analysis, partial reasoning, and independent practice; fade support.
35–50: Cross-grade review checks quantities, unit changes, developmental placement, estimate size, notation, and workspace.
50–60: Plan an immediate exit task and a new-context check 1–2 weeks later.
Teacher field guide
- What is one whole, and what is the unit in each place?
- Which quantity is fixed, and which is being scaled?
- What decomposition or exchange reveals the structure?
- What estimate or benchmark checks the answer?
- Which correct method and plausible error will students explain?
- Which support will be faded before independent work?
- What later task will test transfer and retention?
Classroom practice and evidence
Each chapter has two-page core practice and a separate teacher key. Grades 6–8 add an optional challenge page. Read developmental notes before choosing tasks; use oral responses and objects for early learners.
Track computation accuracy, conceptual explanation, and independent transfer separately. Ask students to rename a number, compare a changed representation, and justify a new computation. A correct digit placement without an explanation may conceal a fragile unit concept.
Facilitator cautions
Do not reduce place value to naming columns. Distinguish exchanges that preserve quantity from operations that scale it. A trailing zero after the decimal preserves value; adding a zero elsewhere may change it. Negative signs, absolute values, and negative exponents have different roles. Signed order begins before Grade 7; scientific notation belongs to the later connection. For rounding ties, state the convention rather than assuming all tools use the same one.