“This was the best money I have ever spent on a teaching tool.” ~ a teacher in Wisconsin
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 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.
Students investigate how subtracting even and odd numbers results in even or odd sums using drawings to explain their findings.
Finally, your students will consider, after all this, which has more power: evens or odds?
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 read and learn how different cultures group numbers, like Japan’s use of 10,000 instead of 1,000.
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 make three guesses about how many cars can park in Disneyland’s Mickey and Friends parking lot.
Students develop various strategies to estimate the number of parking spots using multiplication and identify any potential problems.
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.
Students calculate potential revenue generated by the Disneyland parking structure and consider the average number of people per car.
Using calculators, students will note patterns when multiplying decimals.
Students use calculators to multiply fifteen by whole numbers, observing patterns and predicting results when multiplying by decimals.
Students use their calculators to find products of fifteen multiplied by various numbers and write patterns they observe.
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.
Students round fifteen and twenty-two to the nearest nine, noting any patterns they observe during the process.
Students identify numbers that round to eighteen and complete the rounding rule for nines using nearby multiples.
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.
Students learn about the decimal system and how grouping numerals creates place value to represent numbers beyond nine.
Students calculate the value of base nine numbers by grouping and using base blocks to visualize their quantities.
Students learn how different number systems represent values, focusing on base nine, base sixty, binary, and hexadecimal systems.
Students will fill in the blanks to find division expressions that equal exactly 5.
Students fill in the blanks of the equation using each digit from zero to nine only once to find solutions.
Round pairs of decimals to the nearest tenth and discover that two numbers the same distance apart don’t always round to the same number.
Students round four pairs of decimals to the nearest tenth and mark which pairs round to the same number.
Students find pairs of numbers that round to the same or different values while testing distances from the rounding cutoff.
Students will decide which of a broken calculator’s decimal comparisons are right or wrong, figure out the single rule it follows, and discover that the same rule makes it accidentally right sometimes.
Students identify correct and incorrect answers on the worksheet and analyze the mistaken rule used by the calculator.
Students predict the broken calculator’s responses for three decimals and decide if the answers are right or wrong.
We check the predictions together and reveal which comparisons the calculator got right or wrong.
Students will fill in the blanks so three fractions add to exactly 1.07, then discover that the hundredths must end in 7 because two tenths can only add tens of hundredths, never the ones place.
Students fill in the blanks so three fractions add to exactly 1.07, using each digit one through nine only once.
Students will fill in the blanks to place a fraction and a decimal exactly two hundredths apart.
Students fill in the blanks to create pairs of fractions and decimals that are two hundredths apart without repeating digits.
Students will fill in the blanks to find decimal pairs with a product of exactly 9.
Students fill in the blanks of the equation using each digit from zero to nine only once to find solutions.
Students will fill in the blanks to find decimal pairs with a difference of exactly 7.5.
Students fill in the blanks of an equation using each digit from zero to nine only once to find solutions.
Students will fill in the blanks to find decimal pairs that add to exactly 5.
Students fill in the blanks of an equation with unique digits to create true mathematical statements.
Using calculators, students will note patterns when multiplying decimals.
Students use calculators to multiply fifteen by whole numbers, observing patterns and predicting results when multiplying by decimals.
Students use their calculators to find products of fifteen multiplied by various numbers and write patterns they observe.
Finally, students practice predicting decimal multiplication problems and checking with their calculators.
In this math project, students will design and furnish suites and rooms in a hotel. Then they will use their talents to sell their hotel in a presentation.
First, your students will plan the big picture of their hotel: what will make it special?
Students start shopping for furnishings using a worksheet to track spending for their hotel’s regular rooms and suites.
They’ll break their spending down into five categories of their choosing.
Finally, they’ll determine their hotel’s potential profitability.
Students create a presentation that highlights their hotel’s features, aiming to attract specific types of guests and investors.
Students use authentic data to determine how much money they’d have if they sold an original iPod compared to selling an equivalent amount of Apple stock.
Students identify the information needed to compare the value of the first iPod to an investment in Apple stock.
Students use the iPod’s 2001 price to calculate what an equivalent Apple investment would be worth today.
Students create three ways to show the difference between the current values of an iPod and Apple stock today.
Students repeat their investigation for another product or company (or twice if you’d like!).
Students create a persuasive project using examples and data to argue whether to buy products or invest in companies.
Students will fill in a two-digit number times a fraction to make the smallest product.
Students fill in the equation’s blanks with digits one through nine, using each digit only once to find solutions.
Students label their three solutions from smallest to largest and notice the pattern that affects the product’s size.
Students create the smallest fraction by placing the smallest digit, one, on top and the largest, nine, on the bottom.
Students will fill in the blanks to find a whole number times a fraction that equals exactly 3.
Students fill in the blanks of an equation using each digit from zero to nine only once to create true statements.
Students will determine what mistake this calculator is making when simplifying fractions.
First, students will identify the mistake in a faulty calculator’s fraction simplification and write down their ideas.
Students understand how the broken calculator incorrectly simplifies fractions by subtracting the same number from both parts.
Finally, students check their predictions against the calculator’s wrong answers and the correctly simplified fractions.
By analyzing examples and spotting patterns, students will learn to add fractions.
Students analyze three examples of adding fractions to find a pattern and apply it to a new problem.
Students revise their addition pattern for fractions with unlike denominators and solve a new example.
I reveal the solutions and then leave students with three practice problems.
Students convert fractions to a common denominator and add them to find the correct answers for the given problems.
Students will analyze examples of fraction multiplication and determine the pattern. Then they’ll apply that pattern to new examples.
Students examine examples of multiplying fractions and identify patterns to understand how the multiplication process works.
Students identify patterns in multiplying fractions by multiplying the numerators and denominators from the given examples.
We rewrite our pattern to include the “simplify” step and then students practice with three examples.
I give the solutions and then leave students with one final, even more complex fraction problem!
Students will find multiple solutions to a single fraction subtraction statement by filling in the blanks.
Students fill in the blanks with digits 0 through 9 to make the math statement true in multiple ways.
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 fill in the blanks with digits 0 through 9 to create true math statements using each digit once.
Students identify patterns in their solutions and share different strategies for finding equivalent fractions based on their discoveries.
Students will find multiple solutions to a single fraction division statement by filling in the blanks.
Students fill in the blanks with digits 0 through 9 to make the math statement true without repeating any digits.
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.
Students fill in the blanks with the digits 0 through 9, making math statements true using each digit only once.
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.
Students fill in the blanks with digits 0 through 9, finding multiple ways to make the math statement true.
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.
Students group their solutions into three to five categories and name each category based on patterns they notice.
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.
Students fill in the blanks with digits 0 through 9 to find multiple ways to make the math statement true.
I share a pattern I noticed and reveal how many solutions I found.
Students will decompose a fraction and then recompose the pieces until they’re back to the starting point.
Students decompose 1/8 into three fractions.
They’ll recompose five fractions into two fractions and then recompose those back to our original fraction.
Students decompose a fraction into pieces and then recompose it back to the original fraction following their chosen path.
Students can use the fraction equivalence app to check their sets of fractions.
Students determine which has more power: a fraction’s numerator or its denominator.
First, they consider when comparing fractions, which has more power: the numerator or denominator.
Then, they consider adding and subtracting fractions.
They consider multiplying and dividing fractions.
Students decide which is more powerful, the numerator or the denominator, and explain their reasoning through creative projects.
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.
Students group their solutions into three to five categories, label them, and create a symbol for each category.
I reveal my reasoning behind the three digits that won’t appear in any solutions.
Students will use their understanding of how to order sets of fractions to work through a Fraction Ordering Tournament.
First, students work through the initial round of the tournament.
Then, they complete the remaining rounds and decide on their winner!
Write a short story about a fraction who needs to go undercover and fit in with a group of unlike fractions.
Students will develop a higher-level understanding of what happens when we multiply fractions.
Students will multiply a whole number by a fraction, ending with 1/3 × 6.
Then, they’ll multiply a fraction times a fraction, ending with 3/4 × 1/2.
We’ll check their answer for 3/4 × 1/2.
Students construct fractions from a limited number of digits in order to reach a given solution.
First students will try to create fractions that will get them to 0.
Now, using the same digits, students will try to create fractions that will get them to 1.
Students try to get as close as possible to 1/2 – without actually reaching it.
Now they’ll try to get as close as possible to 0 – without actually reaching it.
Then they try to get as close as possible to 1 – without actually reaching it.
Finally, students chose their own denominators to try to add up to 1/5.
Students will develop a stronger conceptual understanding of what happens when we divide by a fraction.
Students visually divide 8 by 1/2
Students visually divide 8 by 1/4
Students visually divide 8 by 3/4
Students visually divide 8 by 1 1/2
Students visually divide 8 by 1 1/3
We wrap up with the final answer.
Students split up a grid into seven unequal pieces and express their sizes using fractions.
Students will pick a theme for their land and then divide it into seven differently-sized pieces.
They find the fraction that represents each piece’s size and then simply all of the fractions.
They try to create two equal halves (or as close as they can get).
Students order their pieces from largest to smallest and explain the reasons for their choices in size.
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 work with negative numbers and a grid to get their car around a track first.
Find every pair of two-digit numbers that adds to 170 using each digit only once, then explain why there are exactly four.
Launch: the rules, a broken example, and the hunt.
Reveal: all four pairs, the swaps, and the 177 challenge.
Students will fill in the blanks to find every pair of numbers that adds to exactly 50, using each digit only once.
Fill the blanks so two two-digit numbers add to 50, using each digit only once, and find every way.
See the four regular ways and how swapping doubles them, then a hidden question: what if a number starts with a zero?
Reveal six sneaky leading-zero pairs. That makes ten pairs in all, or twenty when you count each order. Then try the same puzzle for 70.
Students count in a circle, paying attention to multiples of 2 and 3.
Students sit in a circle and count, replacing every two with “fizz” to make the game more exciting and challenging.
Students skip count by threes and say “buzz” instead of the numbers that are multiples of three.
Students combine the words “fizz” and “buzz” for numbers that are both two and three numbers, like six.
Students will fill in the blanks to make a division with a remainder of 5, using each digit once, then discover that every solution comes in a pair.
Students fill in the blanks of an equation to find all the possible solutions with a remainder of five.
Students find every whole-number division that equals 5 with no repeated digit, then meet a target that has fewer solutions and work out what rules the missing ones out.
Find every way to make the division equal 5, using each digit no more than once.
Predict whether making it equal 6 gives more solutions or fewer, then find them all.
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 check their predictions against the calculator’s answers.
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.
In these math problems, the solution is already given. But another number is missing!
Practice math fluency with this dice-based calculation game.
Learn the basic rules of Contig.
Now, let’s think about how to spice it up!
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 will quickly recognize whether a number is divisible by 3 or 5 (or both!).
Students will learn this numerical grid-based math game.
Students will analyze partially complete, multi-digit addition problems and find as many solutions as possible.
Students fill in missing digits in addition problems using numerals 0 through 9, making sure to include given numbers.
Students will analyze partially complete, multi-digit subtraction problems and find multiple solutions that complete the problems.
Students fill in missing digits to solve a subtraction problem using each digit from 0 to 9 only once.
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.
Students investigate how subtracting even and odd numbers results in even or odd sums using drawings to explain their findings.
Finally, your students will consider, after all this, which has more power: evens or odds?
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 read and learn how different cultures group numbers, like Japan’s use of 10,000 instead of 1,000.
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 make three guesses about how many cars can park in Disneyland’s Mickey and Friends parking lot.
Students develop various strategies to estimate the number of parking spots using multiplication and identify any potential problems.
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.
Students calculate potential revenue generated by the Disneyland parking structure and consider the average number of people per car.
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.
Students check patterns to see which ones remain true when changing subtraction to addition on the right side.
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.
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.
Students round fifteen and twenty-two to the nearest nine, noting any patterns they observe during the process.
Students identify numbers that round to eighteen and complete the rounding rule for nines using nearby multiples.
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.
Students learn about the decimal system and how grouping numerals creates place value to represent numbers beyond nine.
Students calculate the value of base nine numbers by grouping and using base blocks to visualize their quantities.
Students learn how different number systems represent values, focusing on base nine, base sixty, binary, and hexadecimal systems.
Students will develop a winning strategy for this simple math game.
Students learn the rules of the game.
Then, they develop a strategy guide.