Maths · three daily practice… | Year 7 Maths · T1 W3–4 · Daily Choices

Pick one A/B/C route for the day. Modes are choices for access and agency, not fixed “learning styles”. The D15/D20 routes are later practice, after a first fresh-check response. All contexts are invented and need no purchase or personal information.

Day 11 · Fraction operations

A · mosaic strip: On one same-size strip, show 1/2+3/8=7/8; explain why the denominator stays eighths after renaming.
B · timing card: A fictional 1-hour animation uses 5/6 of the hour; 1/3 is removed from that planned time. Find the remainder as a fraction of the same hour, with an equivalent-name step.
C · wrong-rule reply: A peer writes 1/2+3/8=4/10. Repair the unit error with eighths, then give a numerical check that your result is below one.

Day 12 · Decimal places

A · design lengths: Add 4.75 m and2.60 m, then find the remainder from10.00 m, with a rounded estimate and inverse.
B · storage readout: Fictional file segments use3.45 GB and1.80 GB of an 8.00 GB allowance. Find used and remaining; check by adding back.
C · path error audit: A fictitious map notes 6.35 km then2.70 km. Critique the claimed total8.105 km; give the correct total and place-value reason.

Day 13 · Fraction of a fraction

A · rectangle overlay: Show 3/4×2/3=1/2 in a 3-by-4 grid; name six of twelve overlapping cells.
B · signal window: A made-up 20-minute signal period is active for 3/4; 2/5 of the active part uses one pattern. Find the part of the whole period (3/10) and minutes (6), with an area or equivalent-fraction reason.
C · counterexample card: Someone claims 2/5×3/4=6/9. Show the correct 3/10 with a 5-by-4 array and explain which denominator was changed wrongly.

Day 14 · Grouping and percentage

A · equal markers: A fictional 2.4-unit track has 0.6-unit intervals. Count intervals, not markers; verify by multiplication.
B · quarter-unit strips: Divide1.5 units into pieces of0.25 unit. Give the piece count and an inverse equation.
C · panels: On a fictional48-panel display, find12.5% by using one eighth; explain why the answer is a number of panels, not 12.5 panels.

Day 15 · Later practice, after fresh check

A · new fraction pair: Solve 3/5+1/10 with tenths and a below-one check.
B · new decimal group: Find 4.8÷0.8 and verify by multiplication.
C · new percent whole: Find20% of70 equal game tokens, naming70 as the whole.

Day 16 · Prime leaves

A · two trees: Start60 as6×10 and3×20; show both end at 2²×3×5 and multiply back.
B · tile packs: Factor84 into prime packs using4×21, then write the product in exponent notation.
C · stop-rule critique: A proposed “prime factorisation” of60 is 4×3×5. Explain which factor is not prime and finish it correctly.

Day 17 · Exponent meaning

A · compare trees: Break72 as8×9 and12×6. Give identical prime-leaf counts and exponent notation.
B · spoken/card product: Build 2³×3² with three 2 cards and two 3 cards, then evaluate. Explain why 2³≠2×3.
C · alternate number: Factor54 into primes and exponent notation, then check by multiplication.

Day 18 · Shared factors

A · original collections: Factor90 and150, circle one shared2,3,5 in each, and show 90/150=3/5.
B · leaf-card explanation: Explain why two copies of a prime cannot be cancelled if one product contains only one. Use the 90/150 leaves and give the correct simplest fraction.
C · false simplification: A peer divides90 by10 but150 by30 to claim 90/150=9/5. Explain why both parts must use the same divisor, then divide both by30 and check the result.

Day 19 · Squares and roots

A · square grid: Explain 12×12=144 and why √144=12; factorise12 and square its prime product to check144.
B · second square: Show 100=2²×5²=10², then state √100 with a multiplication check.
C · false-root reply: A peer says √81=3 because 81=3⁴. Repair the claim using 9²=81 and explain what √ asks.

Day 20 · Later practice, after fresh check

A · new factorisation: Factor120 into primes and exponent notation, then multiply back.
B · new square: Show169 is a perfect square and give its positive root with a product check.
C · exponent editor: Correct 2³×5²=150; evaluate the left side and either repair the value or write a true prime product for150.