Choose what a remainder means for the job
Use the same division record to decide whether to open another container, keep a leftover or divide a measurable quantity into fractional shares.
Math investigations
Start with a diagnostic, work through an example and use four levels of practice to choose the next teaching step.
Each lesson includes a teaching sequence, discussion prompts and separate student and teacher materials.
Find the place-value error in a product
Audit a whole-number multiplication algorithm by naming each partial product, repairing its place value and checking the result against a useful bound.
Use a stated rule to predict and prove a pattern
Generate a sequence from an explicit rule, count the changes needed for a distant term and justify an odd-or-even property beyond the displayed terms.
Find when two delivery cycles meet again
List multiples of two small cycle lengths, find the first shared positive return time and convert it to a clock reading from an explicit common start.
Compare metric records written in different units
Build a common-unit record before comparing lengths, masses or capacities, and explain why changing the unit changes the number but preserves the measurement.
Recover a missing rectangle side and check the boundary
Use area and one known side to recover a missing dimension, then test whether the complete rectangle meets a separate perimeter limit.
Choose a protractor scale from the baseline zero
Read labelled dual-scale protractor records by locating the vertex and baseline zero, then check the reading against the angle's opening.
Account for every part of a joined solid
Partition a stepped solid into non-overlapping rectangular prisms, add their volumes and distinguish a shared face from a region counted twice.
Follow a grid route and repair a reversed coordinate
Build a first-quadrant route record with ordered pairs, repair a coordinate reversal and account for each horizontal or vertical leg.
Connect two generated patterns with ordered pairs
Generate two patterns from supplied rules, pair corresponding terms and use a table and coordinate graph to explain their relationship.
Sort quadrilaterals by the properties they inherit
Classify an exact six-card collection in an inclusive shape hierarchy, keeping squares in both the rectangle and rhombus categories.
Translate a story into a grouped numerical expression
Write numerical expressions from short supply stories and explain how parentheses distinguish repeating a whole group from adding an amount once.
Need a shorter start?
Explore 15-minute math workshops or browse the fraction lesson collection.