Teacher plan · Day 68
About 35–45 minutes, or several shorter visits. This is an unpiloted planning suggestion, not a QCAA condition or a required dose.
Prepare and access
Prepare scrap paper, suitable large counters and labels. Prices/fees/offers and transport capacities are fictional. Device use is optional. Hide models before individual work.
• Keep the mathematical purpose when changing mode. Do not assume a diagnosis predicts a preferred way to learn.
• Offer a quiet place, one instruction at a time, a preview of the steps, a pause card and a visible finish point. No countdown, flashing rewards or forced sound.
• Provide large text, high contrast, plain borders and a complete text alternative to each visual. Colour must never carry the only meaning.
• For motor access, use a selection-and-destination control rather than drag-only interaction, large physical pieces or an adult moving pieces as directed.
• For language access, explain group, each, total, left, fee, estimate and budget using the current story. Home-language explanations and bilingual notes are welcome; mathematical reasoning is assessed separately from spelling or English fluency.
• Reduce a number range or show part of a model when appropriate, then record the change. These supports do not certify the original task independently completed.
• No translation is represented as verified without a fluent reviewer and a recorded version. No invented First Nations language words, stories or cultural designs; seek the appropriate community’s permission and language guidance before a local cultural adaptation.
Complete day sequence
Day68 · Compare the same amount
Purpose: Compare two whole-pack offers for the same required quantity and explain a whole-dollar unit cost.
Materials: scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.
Demonstration · D68
Offer A is six blank pens for a pretend $18. Offer B is four blank pens for a pretend $16. Exactly 12 pens are required; whole packs only.
Do not compare the ticket prices before reading the pack sizes. Draw the required 12 places. Use two six-packs and three four-packs, then calculate total costs. Find 18 ÷ 6 = 3 dollars per pen and 16 ÷ 4 = 4 dollars per pen as a second check. Label dollars per pen separately from dollars per pack. All divisions have no remainder; do not introduce recurring decimals or real pricing claims. Whole-pack prices are invented, and this is not a recommendation about a retailer.
Model: 2 × $18 = $36; 3 × $16 = $48. Both plans provide exactly 12 pens. Offer A costs $36, which is $12 less. Its unit cost is $3 per pen; B is $4 per pen.
Transfer probe: When a cheaper ticket price buys a smaller pack, it may cost more to buy the same quantity. Ask the learner to show the quantity and money totals side by side.
Watch for: Choosing $16 because it is the smaller ticket price; using one pack of each rather than equal quantities; omitting 'per pen' from unit cost.
Three complete learner briefs
A: Exactly 15 paper cards are required. A has three cards for $9; B has five cards for $20. Whole packs only; all prices pretend.
Teacher example: A:5packs/$45; B:3packs/$60. Both supply exactly15 items. Whole-dollar unit costs A$3/B$4 per item.
B: Exactly 12 labels are required. A has four for $20; B has six for $24. Whole packs only; all prices pretend.
Teacher example: A:3packs/$60; B:2packs/$48. Both supply exactly12 items. Whole-dollar unit costs A$5/B$4 per item.
C: Exactly 24 game cards are required. A has eight for $24; B has six for $24. Whole packs only; all prices pretend.
Teacher example: A:3packs/$72; B:4packs/$96. Both supply exactly24 items. Whole-dollar unit costs A$3/B$4 per item.
Own, check and next
Use W08's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C15/C16 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H08/X08 are optional new settings, not compulsory extra workload.
Complete class routine
• Connect: 3–5 minutes. Read the purpose. Ask what the numbers count and which amount is missing. Permit quiet thinking before replies.
• Model: 7–10 minutes. Use the day’s exact demonstration. Point to every term in the representation. Show the worked answer as a teacher example, then remove it before individual work.
• Try: 10–15 minutes. Learner chooses A, B or C after the teacher checks number demand. Make, draw, explain, sign, point or type; adults may scribe exactly what is dictated. Ask for the contextual unit and one check.
• Compare: 5–8 minutes. Share two strategies with consent. A learner may use an anonymous sample or work privately. Discuss the supplied work, not the person.
• Exit: 3–5 minutes. Use a C item individually. Record mathematical reasoning and the support given. Revisit the matching next-teaching target when needed.
Give the material
Learner day · Full worksheet/three briefs · Supplied teacher model · Full model alternative · Complete written read-aloud
First neutral exit · Second neutral exit · First staff exit · Second staff exit
Full worksheet staff note
Use the complete Day68 plan and C15/C16 exit. Record route and supports. Accept clear equivalent models; drawing neatness and spelling are not maths criteria.