Tutor Sheet: Grades 6–8 Math (US)

Targets: Rational numbers · Ratios/Proportion/Percent · Expressions & Equations · Linear graphs · Geometry basics · Stats/Prob

Quick diagnostics → Fast fixes

[IntegerSigns] Negatives & order

• Check: −7−(−5)-7 - (-5)−7−(−5) and order these: −3,−5,2,−1-3,-5,2,-1−3,−5,2,−1.
• Fix: Number line first; “minus of a minus = plus”; circle the operation before computing.

[PropAdditive] Proportion vs add-on thinking

• Check: Is 3:2 the same as 6:5? (trap)
• Fix: Proportion = same multiplier; test by cross-multiplying or scaling both terms by one factor.

[PercentOf] Percent meaning

• Check: 30% of 50? Is it the same as 50% of 30?
• Fix: “Of = ×”; 10% anchors (10% of 50 = 5 → ×3); commutativity shows 30% of 50 = 50% of 30.

[AlgebraBalance] Move/solve errors

• Check: Solve 3(x−2)=213(x-2)=213(x−2)=21; 2y+5=−112y+5= -112y+5=−11. Watch for sign drops.
• Fix: Inverse-operations column method: show both sides each step; box variable on LHS, constants RHS.

[TwoStepEqn] Word → equation

• Check: “A number doubled then decreased by 7 is 11.”
• Fix: Underline verbs (doubled, decreased); write skeleton 2x−7=112x-7=112x−7=11 → solve → answer sentence.

[Slope/Intercept] Linear models

• Check: From y=2x−5y=2x-5y=2x−5: slope? intercept? Graph 2 points. From a graph, find equation.
• Fix: Slope = change in yyy/change in xxx; intercept = where it hits axes; use (0,b)(0,b)(0,b) and (1,m+b)(1, m+b)(1,m+b).

[AngleChasing] Angle relations

• Check: Transversal diagram: find missing angles using linear pair/vertical/alt. interior.
• Fix: Mark pairs with colors; write the rule next to each equality.

[VolumeUnits] Mensuration units

• Check: Rectangular prism 3 cm×4 cm×5 cm3\text{ cm} \times 4\text{ cm} \times 5\text{ cm}3 cm×4 cm×5 cm: SA? Volume?
• Fix: Draw & label l,w,hl,w,hl,w,h; SA in cm², Volume in cm³; convert units after computing.

[CenterChoice] Mean vs median

• Check: Data with an outlier: choose center and justify.
• Fix: Skew/outlier → median; symmetric/no outlier → mean. Always say why.

[Equiprobability] Probability bounds

• Check: “P(die shows 7) = ?” “Two heads in one fair-coin toss = ?”
• Fix: Build the sample space; ensure 0≤P≤10 \le P \le 10≤P≤1; use tree/area models for two-step chances.

[DataScale] Graph reading

• Check: Line/bar graph with tricky scale: “How many more?”

Fix: Pre-flight: Title • Axes • Units • Scale • Legend; restate scale aloud before computing.