Scale and Lever Logic
Warm up the skills and intuition that algebra requires by balancing scales and measuring weights.
Explore how algebra works and why it matters, and build a strong foundation of skills across many algebra topics including equations, rates, ratios, and sequences.
By the end of this course, you’ll know both traditional algebraic techniques and many unique problem-solving approaches that aren’t typically covered in school. You'll also more generally have improved algebraic intuition, honed for the strategic thinking that you need when approaching difficult problems.
Supercharge your algebraic intuition and problem solving skills!
Save time with this clever thinking.
Learn some clever techniques to simplify problems, saving yourself time and effort.
In this strategic shortcut, use an easy number as a test case and then update to find the true answer.
These problems can be quickly solved in your head if you find the trick to each of them.
Practice using rearrangement of terms, factoring, distribution, canceling, and any other tricks you know!
Representing an algebraic identity geometrically can lead to deep insights.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 can be mentally evaluated faster than you might expect!
Manipulate these odd arrays of dots to find another useful summation shortcut.
Extend the tricks from triangular and square numbers to the next two sets of polygonal numbers.
These problems require creative combinations of all the shortcuts that you've seen so far.
Puzzles that are like Sudoku, but trickier!
Is it possible to fill these grids so that the sums of the rows and columns are all correctly predicted?
What if, instead of specific target sums, you only know that all of the sums need to match?
In this exploration, the digits need to be filled in around the perimeter of each shape.
It's like Sudoku except that each specified region must obey a specific arithmetical rule.
Do this round of puzzles to get warmed up!
Go a bit meta to explore some of the mathematics at work 'behind the scenes' of Calcdoku.
Now you're prepared for some intense 4x4 Calcdoku challenges!
These are the most advanced Calcdoku puzzles in this unit — good luck!
The unification of logic and algebra.
Explore several types of balance puzzles and learn some strategies for approaching them.
Simplify systems combining the shapes that balance on one scale with those that balance on another.
First isolate a shape on one side of a scale, then use this equivalency to make substitutions elsewhere.
When fractional shapes or numbers are involved, a few additional steps are required to isolate variables.
Extend your thinking to cases where there are more, different unknowns in each puzzle.
Apply what you've learned balancing scales to the scientific application of balancing chemical equations.
2, 5, 10, 17, 26... What comes next?
Explore, describe, and then predict the patterns in these sequences.
Practice describing sequences in three different ways: by property, recursively, and explicitly.
Focus in on this one sequence type and learn a few tricks that take advantage of its steady behavior.
Now focus in on these sequences that evolve using recursive multiplication instead of addition.
Apply what you know about geometric sequences visualize the formation of fractal figures.
Solve challenging problems that employ recursively-described sequences such as the Fibonacci sequence.
If 4 cows make 4 gallons of milk in 4 days, how much milk do 8 cows make in 8 days?
Explore rates and ratios in some of the real-life situations in which they show up.
Hone your skills solving problems that employ proportionality and inverse proportionality.
In this exploration, multiple variables can change simultaneously, all contributing to an overall effect.
Explore how scaling an object can counter-intuitively affect other properties of that object.
Understand why quantities related by physical and geometric laws have non-linear relationships.
Extend the rates and ratio strategies in this unit to solve a sequence of challenging mixing puzzles.