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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.
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 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?
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 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 will fill in the blanks to place a fraction and a decimal exactly two hundredths apart, then discover why every answer ends in 8 and the decimal always sits just below the fraction.
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.
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 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 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?
Next, students go shopping for furniture to fill their rooms and suites. My class started with IKEA’s catalog, but students liked to use other shops as well.
They’ll break their spending down into five categories of their choosing.
Finally, they’ll determine their hotel’s potential profitability.
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.
Introduce the prompt: What if we bought Apple stock instead of the original iPod? How much money would we have if we sold them both today? Ask “what do we need to know?” to answer this. Students will find this information online.
Students compute the number of Apple shares they could have bought on October 23, 2001. Then they compute the amount of money those shares would be worth now.
They create three interesting ways to express the two amounts: one using a pure math skill (percents, ratio, difference) and two using equivalence (how many Big Macs, tickets to Disneyland, or PlayStations could you buy with the two values).
Students repeat their investigation for another product or company (or twice if you’d like!).
They finally create a big idea about investing vs spending, backing it up with evidence from their research. Their final product can take the form of an essay, presentation, video, website, etc.
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.
Next, students will predict the simplified fractions a broken calculator produces when it subtracts the same number from the numerator and denominator instead of dividing.
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.
First, students look for a pattern when adding like fractions. They try to solve an unfinished example.
Next, we break their pattern by including examples with unlike fractions. Students will attempt to update their pattern and then solve an unfinished example.
I reveal the solutions and then leave students with three practice problems.
After showing the solutions to the practice problems, I leave students with a triple fraction! (Psst. The answer is 7/8.)
Students will analyze examples of fraction multiplication and determine the pattern. Then they’ll apply that pattern to new examples.
First, we let students discover a pattern using three simple examples. They’ll work out a fourth example.
We check the pattern and then complicate things a bit by using three new examples with products that need to be simplified.
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 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 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.
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 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 can then pick their own starting point and create their own path as they decompose and then recompose back to that first fraction.
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.
Finally, students will make an overall decision. Depending on what you’d like to do, students can expand their thinking into an advertisement, story, song, persuasive essay, or other product.
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 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).
Finally, they order their pieces from largest to smallest and explain why those pieces would be those sizes. Then, if you’d like, they can build the actual land!
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.
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.
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.
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 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 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.
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 develop a winning strategy for this simple math game.
Students learn the rules of the game.
Then, they develop a strategy guide.