Math Workshop
Demo/test data only. Diagnostic recommendations and demonstrated practice mastery are local sample evidence, not real student grades.
Prerequisite skill library
Algebra tools
Factoring
Find two numbers whose product is the constant and whose sum is the middle coefficient.
x² + 7x + 12 = (x + 3)(x + 4): 3 × 4 = 12 and 3 + 4 = 7.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Number tools
Negative integer arithmetic
Track signs: subtracting a negative adds; multiplying unlike signs gives a negative.
−6 − (−4) = −6 + 4 = −2.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Number tools
Fractions
Use a common denominator for addition; multiply numerators and denominators for products.
1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Graph tools
Slope
Slope is change in y divided by change in x. Keep the same point order in both differences.
Through (1, 2) and (4, 8): slope = (8 − 2)/(4 − 1) = 2.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Graph tools
Coordinates
An ordered pair is (x, y): horizontal position first, vertical position second.
At (−2, 5), x = −2 and y = 5. For y = 2x + 1 at x = 3, y = 7.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Decision tools
Percentages
Convert a percentage to a decimal by dividing by 100, then multiply by the base amount.
15% of $80 = 0.15 × 80 = $12. After a 15% discount: $80 − $12 = $68.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Decision tools
Ratios and unit rates
Divide by the number of units to compare rates. Equivalent ratios multiply both quantities by the same factor.
$12 for 3 notebooks is $4 per notebook. A 2:3 mix scales to 4:6.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Number tools
Order of operations
Calculate parentheses, powers, multiplication/division, then addition/subtraction.
3 + 2 × (5 − 1) = 3 + 2 × 4 = 11.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items
Data tools
Statistical summaries
Mean is sum divided by count; median is the middle of sorted values; range is maximum minus minimum.
For 2, 4, 9: mean = 15/3 = 5, median = 4, range = 7.
3 diagnostic items · 2 guided practice items · 2 transfer mastery items