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15 guides
Grade 1 · Grade 2 · Grade 3 · Number and operations · Patterns and algebra
Doubling makes two equal copies; halving reverses that action when a quantity can be split into two equal whole-number groups.
Skills: Double and halve whole-number quantities · Reason about odd and even numbers
Grade 2 · Grade 3 · Grade 4 · Measurement
Treat time as a distance between two moments, using friendly jumps in hours and minutes instead of fragile clock arithmetic.
Skills: Solve elapsed-time problems
Grade 2 · Grade 3 · Grade 4 · Number and operations
Use multiplication to combine equal groups and division to reverse the relationship by finding a group size or a number of groups.
Skills: Multiply equal groups · Divide equal groups
Grade 4 · Data and probability
Expected value describes the average outcome over many repetitions, so it can be meaningful even when it is not a possible result of one trial.
Skills: Interpret a non-whole expected value
Grade 12 · Patterns and algebra · Calculus and analysis
Translate each formula before calculating, then use repeated totals as checksums that can expose and locate a corrupted entry.
Skills: Evaluate advanced symbolic expressions · Use overlapping checks to locate an error
Grade 2 · Grade 3 · Grade 4 · Number and operations
A fraction names equal-sized parts of one whole; the denominator names the partition and the numerator counts selected parts.
Skills: Represent a fraction of a whole · Find one tenth of a quantity
Grade 1 · Grade 2 · Grade 3 · Number and operations · Patterns and algebra
Use the chart's fixed row and column structure: horizontal moves change by 1, while vertical moves change by 10.
Skills: Use hundred-chart structure
Grade 2 · Grade 3 · Grade 4 · Number and operations
Turn a longer situation into a short chain of questions, keep track of what each number means, and check the final result against the story.
Skills: Add and subtract whole-number quantities · Solve a multi-step word problem
Kindergarten · Grade 1 · Grade 2 · Grade 3 · Number and operations · Geometry
Track an ordered position by fixing a direction, using equal steps, and distinguishing a location from the distance traveled to reach it.
Skills: Use number-line structure · Model relative positions
Grade 1 · Grade 2 · Grade 3 · Number and operations
Understand a three-digit number as equivalent collections of hundreds, tens, and ones that can be regrouped without changing the total.
Skills: Compose and decompose whole numbers to 1,000
Grade 2 · Grade 3 · Grade 4 · Measurement · Geometry
Keep two measurements distinct: area counts square units covering the inside, while perimeter measures length around the boundary.
Skills: Find rectangle area by multiplication · Find rectangle perimeter
Grade 1 · Grade 2 · Grade 3 · Grade 4 · Patterns and algebra
Find the smallest repeating unit, locate positions within the cycle, and count complete cycles before handling any leftover positions.
Skills: Identify a position in a repeating cycle · Count categories in a repeating pattern
Grade 2 · Grade 3 · Data and probability
Use the graph key as a multiplication rule: each picture may represent several objects rather than just one.
Skills: Interpret a scaled picture graph
Kindergarten · Grade 1 · Number and operations
Build early number sense by matching one count word to each object, recognizing the total, comparing collections, and composing a number from smaller parts.
Skills: Count and compare within 20 · Compose and decompose within 5
Grade 4 · Measurement · Geometry
Connect the volume formula to counting unit cubes: find cubes in one rectangular layer, then multiply by the number of equal layers.
Skills: Find rectangular-prism volume by multiplication
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