← Reasoning

Grade 5-2

45 problems

Count distinct arrangements up to rotation
Number Arrangements
Find the hidden rule, then place numbers
Number Arrangements
Fill the grid under row-column-region rules
Number Arrangements
Angles between segments drawn on a cube
Exploring the Cube
Cross-sections cut from a cube
Exploring the Cube
Top, front, and side views of drawn lines
Exploring the Cube
Build a cuboid from six rectangles
Rectangular Prisms
Cut and fold edges of a net
Rectangular Prisms
Longest and shortest perimeter of a net
Rectangular Prisms
Fair games and comparing likelihoods
Counting Cases
Permutations versus combinations
Counting Cases
Addition and multiplication counting rules
Counting Cases
Best and worst case draws for a pair
The Pigeonhole Principle
People needed for three shared birthdays
The Pigeonhole Principle
Pigeonhole applied to digit-card numbers
The Pigeonhole Principle
Two-coloring decides domino tiling
Parity
Decide odd or even without computing
Parity
Flip count parity pins down hidden faces
Parity
Recover a missing count from the mean
Averages
Move the mean by adding a value
Averages
Sum evenly spaced runs via the middle
Averages
Solve using lines with equal sums
Foundations of Magic Squares
Largest and smallest line sum
Foundations of Magic Squares
Solve using the sum of one line
Foundations of Magic Squares
Complete a 4 by 4 magic square
Varieties of Magic Squares
Magic sums on the edges of a cube
Varieties of Magic Squares
Magic star built from paired sums
Varieties of Magic Squares
Move a triangle onto its congruent twin
Congruent Figures
Cut an equilateral triangle into congruent triangles
Congruent Figures
Which conditions force two triangles congruent
Congruent Figures
Figures turned through 180 degrees
Line-Symmetric and Point-Symmetric Figures
Line-symmetric and point-symmetric figures
Line-Symmetric and Point-Symmetric Figures
Figures reflected in a mirror
Line-Symmetric and Point-Symmetric Figures
Cut a point-symmetric figure into congruent halves
Using Symmetry
Shortest path that must touch a line
Using Symmetry
Symmetric numbers written in digital numerals
Using Symmetry
How many different cube nets exist
Nets of a Cube
Draw cube nets inside a bounded grid
Nets of a Cube
Find opposite faces on a cube net
Nets of a Cube
Deduce the pattern on a hidden face
Nets of a Patterned Cube
Slide a face to an equivalent net
Nets of a Patterned Cube
Transfer segments from cube to net
Nets of a Patterned Cube
Complete a die from several views
Dice
Greatest and least dice pip totals
Dice
Rolling a die along a path
Dice