Serving advanced learners (and their teachers) since 2012.
In these math problems, the solution is already given. But another number is missing!
Sets of multiplication and division practice problems. But the unknown isn’t where you expect it to be!
Four sets of 2-digit and 3-digit addition and subtraction practice. But the unknown isn’t where you expect it to be!
Students calculate averages using negative temperatures.
First, students note the average monthly highs in the North and South Poles.
Then, they graph those temperatures on a multi-line graph.
Next, they find the highs and lows and calculate the annual temperature range at each location.
Then, they calculate the average temperature in each season for both poles.
Finally, they communicate their Polar Weather Report.
Students will explore the rules of how adding and subtracting evens and odds leads to either evens or odds. They’ll try to explain the why and also answer the question: which has more power, evens or odds?
Students explain why adding two evens always leads to an even.
Students find the rules for even+odd, odd+even, and odd+odd and attempt to explain why these are rules.
They do the same for subtraction: what happens when we subtract even-even, even-odd, odd-even, and odd-odd? Why?
Finally, your students will consider, after all this, which has more power: evens or odds?
Students will work with mathematical language and apply their understanding of the associative and commutative properties to their own mathematical operation.
Students consider mathematical language for the inputs and outputs of two existing operations.
Next, they try to determine the rules of my operation, the Byrdle.
They create their own operation, including its name, symbol, terms for inputs and outputs, and the rule that it follows.
Does their operation follow the commutative property?
Finally, does their operation follow the associative property?
Students learn to group numbers by increasingly large groups of ten rather than going to hundreds or thousands.
Students decide how they’ll read 340, 621, 835, and 999 if there were no “hundreds” place.
Students predict how to read 999 + 1.
Students predict how to read 9999 and 10000.
Students learn that in other cultures, people do indeed group their larger numbers differently.
Students will estimate the number of parking spots in Disneyland’s parking structure and then calculate how much money the structure brings in each year.
Students create three guesses: too high, too low, and a reasonable guess. This is a low-anxiety starting point that anyone can attempt.
Using a high-contrast version of the photo, students generate a few strategies for estimating the number of spots. They will note the potential inaccuracies with each strategy.
Upon learning that the structure has six levels, students will revise their best estimate.
Students learn the real answer and then attempt to calculate how much money the parking structure brings in per year.
After learning the real answer, students are left with a final question: how many people park in the lot. And how much money do they generate in ticket sales?
Students uncover patterns with exponents and make predictions about the powers of 0 and 1.
Students identify two patterns about exponents.
I reveal some possible patterns and show the correct predictions. Then students predict the 0th and 1st powers.
I unveil the solutions for the 0th and 1st powers and conclude with a tantalizing tease about negative exponents.
I reveal the shocking truth about negative exponents.
Using calculators, students will note patterns when multiplying decimals.
Students multiply 15 times 100, 10, 1, 0.1, and 0.01 and then predict the product of 15 × 0.001. They look for a pattern.
Using the same idea from step one, students work with multiplying by 0.02 and 0.05. They’re honing their pattern from step one.
Finally, students practice predicting decimal multiplication problems and checking with their calculators.
In this video, we’ll investigate how to round to numbers other than multiples of ten. Sure, we could round 16 to the nearest ten, but what if we wanted to round 16 to the nearest 9? Or 12, 52, or 75? We take the routine math skill of rounding and force students to truly think about why a number rounds up or down.
Round 15 to the nearest 9. Should it round up to 18 or down to 9?
Create a rule for rounding up to the next 9. Round three more numbers to the nearest 9.
Create a rule for rounding up to the next 7, 15, and 18.
See how to expand this rule to round to any number.
To help students understand place value, we venture beyond our typical decimal number system and explore a Base 9 system. Students will be exposed to ancient Babylon’s Base 60 system and computers Binary and Hexadecimal before creating their own number system.
Students consider what a “numeral” is and just how many we actually use.
We discuss our ten numerals and how the base 10, or decimal, system works. Then we introduce base 9, pondering what 8 + 1 would equal in a system without a symbol for 9.
We dig further into Base 9, asking students to complete a worksheet transforming base 9 numbers into base 10.
After correcting the worksheet, we explore real world number systems: Babylonian, Binary, and Hexadecimal. Finally, students develop their own, non-base-10 system and create two-digit numbers using this worksheet.
Students will decide when mean vs median best summarizes data.
First, they decide which works better, mean or median when Bill Gates enters the group.
Next, students calculate the mean and median when Bill Gates has $5000 and $10 000.
Now, they determine how low their final test score can be to still earn a 90% in a class.
After revealing that there’s no way to not get an A when the median is used, students pick their one data to analyze with mean and median.
Students will use their understanding of percents to make calculations about credit card purchases.
Students will find a credit card and note the APR.
Next, they’ll “purchase” an expensive item and calculate the cost of interest after one year.
Then, students will calculate the cost of interest after minimum payments for the first three months.
Finally, using this interest calculator, they’ll determine how long it would take to pay off the debt using only minimum payments.
Students will determine what mistake this calculator is making when multiplying.
First, students will identify the mistake in a faulty calculator’s multiplication answers and write down their ideas.
Next, students will predict the results of three multiplication problems using a broken calculator that only multiplies digits.
Finally, students checked their multiplication predictions using a broken calculator that provided incorrect answers for various math problems.
Students will determine what mistake this calculator is making when adding.
First, students will identify the repeated mistakes made by a calculator when adding numbers.
Next, students will predict the incorrect results for three addition problems.
Finally, we reveal the answers.
Students determine the error in these subtraction problems.
Students analyze three incorrect subtraction problems and explain the error.
Then, using the error, they answer how the broken calculator would do it.
We reveal the answers to the final three problems.
Students will find multiple solutions to a single fraction subtraction statement by filling in the blanks.
Students fill in the blanks to find as many solutions as possible. They’ll also note any patterns that they used to help them find those solutions.
I reveal my 16 solutions as well as a pattern that I used.
Students will find multiple solutions to a fraction addition statement by filling in the blanks.
Students will find multiple solutions to a single fraction division statement by filling in the blanks.
First, students look for as many possible solutions as they can find. They’ll also note any patterns they spotted.
I explain a pattern that I used and reveal the number of solutions I found.
Students will find multiple solutions to a single math statement by filling in the blanks.
First, students look for as many possible solutions as they can find. They will also note any patterns they see.
I reveal my solutions as well as the patterns I discovered.
Students will find multiple solutions to this fraction division math statement by filling in the blanks.
First, students look for as many possible solutions as they can find. They’ll also note any patterns that help them find those solutions.
Then, I reveal my solutions and a pattern that helped me.
Students will find multiple solutions to this fraction multiplication statement by filling in the blanks.
First, students look for as many possible solutions as they can find.
Then, they create three to five categories from those solutions (using any criteria they’d like) and then give each category a name.
Finally, they write down a new idea they had while working through this task.
Students will find multiple solutions to this fraction subtraction problem by filling in the blanks.
First, students look for as many possible solutions as they can find. They’ll also jot down any patterns they spot.
I share a pattern I noticed and reveal how many solutions I found.
Students will analyze partially complete, multi-digit addition problems and find as many solutions as possible.
Students will analyze partially complete, multi-digit subtraction problems and find the one solution that will complete the problems.
Students will analyze partially complete, multi-digit subtraction problems and find multiple solutions that complete the problems.
Students will find multiple solutions to a single math statement by filling in the blanks.
First, students look for as many possible solutions as they can find.
Now, they search for which digits didn’t appear in any solutions. Why didn’t they work?
I reveal my reasoning behind the three digits that won’t appear in any solutions.
Students will find multiple solutions to a single math statement by filling in the blanks.
First, students look for as many possible solutions as they can find.
Then, they look for patterns in their findings and give each pattern a name.
Finally, which of those patterns would hold true if we changed from subtraction to addition on the right side of the equation?
Students will find multiple solutions to a single math statement by filling in the blanks.
First, students look for as many possible solutions as they can find.
Then, they look for which digits don’t appear in any solutions and explain why those digits don’t work.
I explain why 0, 5, and 7 don’t appear in any solutions.
Students will find multiple solutions to a single math statement by filling in the blanks.
First, students look for as many possible solutions as they can find.
Next, they look for the largest possible exponent that will work.
I explain my findings.
Students will find multiple solutions to a single math statement by filling in the blanks.
First, students look for as many possible solutions as they can find.
Then they explain why there are so few odd numbers in the dividend of the solutions.
I explain the main reasons why there are so few odds.