P1 · Parts and the whole
Name the quantities. Show one whole group. Label what your ratio compares. Label what your fraction’s whole means.
An unsegmented horizontal bar leaves the learner free to partition a whole. Below it, seven labelled empty writing boxes are arranged in two columns.
Blank fields, in reading order:
- Component one and unit
- Component two and unit
- Component three, if useful
- Whole total and unit
- Part-to-part comparison
- Part-to-whole comparison
- Fraction of the whole
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P2 · A rate with two units
Name both quantities and units. Decide what one unit of the denominator means. Predict another amount only under your stated assumption. Check whether the units answer your question.
Seven labelled empty writing boxes are followed by a four-row blank table with input quantity/unit and output quantity/unit columns.
Blank fields, in reading order:
- Numerator quantity and unit
- Denominator quantity and unit
- Rate: ___ per ___
- Target amount and unit
- Predicted output and unit
- Constant-rate assumption
- My units check
Table headers: Input quantity and unit / Output quantity and unit. Four rows are blank.
Keep the accompanying complete notices with this resource.
P3 · The whole order
Find the cheapest sufficient whole-unit order for each supplier. Add an order fee once. Compare complete totals with the budget. Explain whether spare quantity is allowed.
Two columns compare A on the left and B on the right, with the need and budget above the aligned eight supplier fields. Two final empty boxes record a recommendation and an assumption or spare-quantity condition. Every box is empty.
Blank fields, in reading order:
- Need and unit
- Budget
- A: pack size and unit
- B: pack size and unit
- A: price per pack
- B: price per pack
- A: price per item
- B: price per item
- A: whole packs
- B: whole packs
- A: quantity supplied
- B: quantity supplied
- A: order fee
- B: order fee
- A: total cost
- B: total cost
- A: spare quantity
- B: spare quantity
- My recommendation
- Assumption and spare permission
Keep the accompanying complete notices with this resource.
P4 · Signed changes and order
Show the sign and direction of each change. Keep brackets with the group they change. Explain a multiplication sign with a pattern or a model. Check a division with multiplication.
An unnumbered line has arrowheads at both ends and no preset endpoint. Eight labelled empty writing boxes follow in two columns. A blank two-column pattern table below the boxes has Multiplier and Product headers and four empty rows.
Blank fields, in reading order:
- Start and unit
- First signed change
- Second signed change
- Final amount and unit
- Expression and brackets
- My sign-pattern explanation
- Quotient and divisor
- Multiplication check
Pattern table headers: Multiplier / Product. Four rows are blank.
Keep the accompanying complete notices with this resource.
P5 · Exact rational work
For addition or subtraction, use the same whole and equal-size parts. For multiplication or division, keep the factor or divisor’s meaning. Prefer an exact fraction to a short rounded decimal. Interpret an exact quotient before choosing a full-object count.
Two equally long unsegmented whole bars sit side by side. Eight labelled empty writing boxes follow. No denominator, partition or answer is supplied.
Blank fields, in reading order:
- Named whole and unit
- Original expression
- Equivalent fractions or factors
- Exact result and unit
- An estimate
- Inverse or second-method check
- Amount, amount per group or count
- My interpretation
Keep the accompanying complete notices with this resource.
P6 · Keep, test and review
Keep your first model. Change only the information that changed. Recalculate affected quantities. Retain or revise your decision with a reason. Name a limit the calculation alone cannot settle.
Ten labelled empty boxes preserve original and later information separately. A final optional strip has My decision / Support I used / My next question.
Blank fields, in reading order:
- My useful question
- Quantities and units
- Assumptions
- Original expression
- Original result and decision
- New information
- Unchanged information
- Affected calculation
- Revised result and decision
- What I would test physically
Optional blank strip: My decision / Support I used / My next question.
Keep the accompanying complete notices with this resource.