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Students will work with equivalence to find meals and activities that equal the calories in one popular meal from a restaurant.
First, students will pick a restaurant and then find how many calories are recommended per day.
Then they’ll create a common meal from that restaurant and calculate the calories in that meal compared to the recommended calories per day.
Now they’ll create several interesting equivalences, showing how the calories in their meal equal the calories in other meals or the calories spent on activities.
They use their information to design a parody ad.
Bonus: They are now hired by the restaurant to create an ad for a low-calorie meal.
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.
Use super cute fruit to introduce algebraic thinking to your young students.
Students will find factors of 161,000 and match them up with a first name.
First, students will answer some warm-up questions about 161,000.
Next, they’ll break 161,000 down into its prime factorization.
Now we begin working with those prime factors to figure out the name(s).
I reveal the answers and issue several new challenges. Can you find a smaller code than IAN?
Students will use the factors of a number to turn that number into words.
First, students encode PIE, BREAD, and BEARD.
Then they’ll find other words that would encode to 720.
Students explore the “Forbidden Letters” of 720, starting with G.
Finally, they look for the longest 720 words possible. BARED, FABLE, AIDED, and DEBAR are other 5-letter words. BALBOA and BABIED are two 6-letter words.
Students will add sets of parentheses to expressions to see how large of a change they can create.
First, I model the process and then give them a sample to try: 7 × 3 + 7 × 2
I show my best answer (see below) and then present four more samples.
I reveal my best answers, then ask students to think about what patterns or rules they spotted to help them place their parentheses. They write these out as 3 to 5 tips to create a guidebook.
In this video, students explore the relationship between multiplication and its inverse, division. They will attempt to “undo” multiplication by dividing once, twice, or even three times.
We begin with the simplest, one-step case. Multiply by a number, then divide by the same number, and you return to where you started. But then, we try a two-step version, such as: 10 × 6 ÷ 3 ÷ 2 = 10.
Now we look at cases where we divide three times to undo multiplication.
Finally, students have a chance to continue practicing this idea with a web app.
Students factor 365 in an attempt to create a better system of months and weeks than our current calendar.
Students are asked (by the Supreme Council for Calendars) to clear up the confusing mess of 28, 30, and 31-day months by factoring 365.
Students will discover that 365 has very few factors: 1, 5, 73, and 365 — not so great for even months. We introduce intercalary days: days outside of any month. Students reserve a few days for a special holiday, then create nice, even months.
Now students will divide those months into even weeks so that the year and each month have nice, whole numbers of weeks.
Finally, we do some naming: what will we call our months? What about our days of the week?
Students will double a single dollar once per day and discover how long it takes to reach $1 million. Along the way, they’ll move from repeated multiplication to using exponents.
Students will use the patterns they find in the first few steps to predict a step much further along.
Students begin by predicting how many pieces there will be at step 5.
After revealing that step 5 has 36 pieces, I ask students to predict step 12.
I reveal that step 12 has 85 squares and challenge students to predict any step. Answers: Step 49: 344, Step 93: 652, Step 728: 5,097
Students will use the patterns they find in the first few steps to predict a step much further along.
Students begin by looking for patterns and predicting the number of squares at step 5.
I reveal the solution (it’s 24) and students work on predicting step 12.
After revealing the solution (it’s 52), I reveal an algorithm to predict any step and challenge students to calculate much larger steps. Answers – Step 63: 64 × 4 = 256 – Step 97: 98 × 4 = 392 – Step 821: 822 × 4 = 3288
Students will use the patterns they find in the first few steps to predict a step much further along.
Students predict the number of squares at step 5.
I reveal the answer (it’s 29) and then ask them to predict step 12.
After confirming that step 12 has 64 squares, I ask students to predict any step! Answers – Step 47: 239 – Step 111: 559 – Step 998: 4994
Students will use the patterns they find in the first few steps to predict a step much further along.
Students predict how many squares there will be at step 5.
I reveal the solution (it’s 29) and ask students to predict step 12.
After showing the answer (it’s 64), I challenge students to predict any step! Answers – Step 50: 453 – Step 101: 912 – Step 999: 8,994
Students will use the patterns they find in the first few steps to predict a step much further along.
Students predict the number of pieces at step 5.
I reveal the solution (32) and ask students to predict step 12.
After revealing that step 12 has 74 pieces, I challenge students to predict any step. Answers – Step 50: 302 – Step 100: 602 – Step 999: 5,996
Students will use the patterns they find in the first four steps to predict the 50th step.
Students look for patterns and predict how many Xs will be at step 10.
I reveal the solution (it’s 31) and ask students to predict step 50.
After showing my solution (there are 151 Xs) I challenge students with a new formation of Xs and Os. (The secret: in this version, you start with 4 Xs and add 12 Xs at each step.)
Students will use the patterns they find in the first few steps to predict a step much further along.
Students begin by just counting and making a prediction for step 6 in the pattern.
After revealing the answer (it’s 48), students will make a prediction for step 12.
I reveal that step 12 has 168 squares and then challenge students to predict much larger steps. Answers – Step 49: 2,499 – Step 99: 9,999 – Step 999: 999,999
Students will use the patterns they find in the first three steps to predict the 50th step.
Students will look for patterns and predict how many squares there will be at step 10.
Next, they’ll predict how many squares there will be at step 50!
I reveal the answer (2,550) and propose the challenge of adding the first 50 odd numbers. (Psst, you can square 50).
Students will use the patterns they find in the first three steps to predict the 20th step.
Students will note patterns and look for how many slices there will be at step 6.
After checking the answer (it’s 64), we’ll extend the pattern and ask students to predict step 20.
I reveal the answer (1,048,576) and then propose a challenge! What if you split pieces three ways instead of two, tripling the pieces at each step?
Students will use the patterns they find in the first four steps to predict the 100th step.
Students will look for patterns and then predict how many seats there will be at step ten.
Next, they predict how many seats they’ll have at 100 desks!
I reveal the answer (402) and propose an extension involving non-rectangular desks.
Students will use the patterns they find in the first four steps to predict the 100th step.
First, students count the squares in each step, search for three patterns, and predict Step 5.
Next, they use their patterns to predict Step 10.
Finally, students try to predict Step 100.
We review the answer and I introduce two extensions: Triangular Numbers and Carl Friedrich Gauss.
Students will use the patterns they find in the first four steps to predict the 50th step.
First, students count the squares in steps 1 through 4. They’ll identify patterns and make a prediction about step 5.
We look at the patterns, unveil the truth about step 5, and students try to predict step 10.
We unveil the number of squares in step 10 and then challenge students to predict step 50!
Students see if their predictions were correct and I reveal a final pattern as well as the name of this sequence of numbers.
Students will make mathematical predictions about an infinitely repeating sequence of triangles.
First, students simply count up triangles in the first three steps (1, 3, and 9). Then they predict what the 4th step will be like.
We reveal that step 4 has 27 triangles. I ask students to predict step 6.
After revealing that step 6 has 243 triangles, we will try to predict all the way up to step 20!
I discuss the pattern of repeating 3s and show how exponents are the key to quickly finding any step. And students confirm that, yes, step 20 has over a billion triangles!
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 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 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 will analyze examples and non-examples to deduce the topic: shapes with 180º rotational symmetry
First, students get a set of shapes categorized in two groups.
Then they get a set of ungrouped shapes. Which columns will they go in?
Finally, I reveal the topic: 180º rotational symmetry
Students will analyze examples and non-examples to deduce the topic: regular and irregular polygons.
First, students get a set of items categorized in two groups.
Then they get a set of ungrouped items. Which columns will they go in?
Finally, I reveal the topic: regular vs irregular polygons.
Students will spot the number of parallel and perpendicular lines in shapes and then form groups of shapes.
First, students will identify the number of sets of parallel and perpendicular sides in various shapes.
Next, they create three or four groups based on their findings in step one.
Finally, students venture to the third dimension and look for parallel and perpendicular lines in a cube. For the final question: there are 18 sets of parallel lines in a cube and 24 sets of perpendicular lines. Although technically, we’d call them “edges” instead of lines.
Students will group letters by their type of reflective symmetry and then form symmetrical words and sentences.
First, students will find the lines of symmetry for the capital letters.
Next, they put them in categories based on their lines of symmetry.
Then, students will form words with symmetry.
Finally, they’ll create the longest sentences they can using only symmetrical words.
Students will analyze the shapes and determine the pattern: we’ve got trapezoids!
First, students guess the topic by looking at examples and non-examples, and then discuss their ideas with peers.
Next, students will decide which of three items are examples and which are non-examples of the given topic.
Finally, students identified and classified three shapes based on their parallel sides to distinguish between trapezoids and non-examples.
Students will inductively discover the rules of a triangle’s angles.
Students try to create the biggest possible angle inside of a triangle.
They look for triangles with one or more right angles.
Then they add up three angles, trying to find the largest and smallest sums possible.
Students try to create triangles with two and three congruent angles.
We close by posing the question: how are angles and sides related? (Larger/smaller angles mean longer/shorter sides. Same sized angles? Same size sides. )
Students analyze the similarities and differences of several quadrilaterals.
Students note that living things, as well as quadrilaterals, can be grouped in a variety of different sized categories. They consider how one quadrilateral is similar to and different from two others.
Students learn several criteria for grouping quadrilaterals (right angles, parallel sides, and congruent sides), then revisit their worksheet to increase their level of precision.
Students develop a hierarchy using the criteria from the previous video.
Students debate which is longer: a ray or a line.
I introduce students to lines, line segments, and rays. Finally, I pose the delicious question: “Which is the longest?”
Now we ponder: “Which has more points on it?”
Finally, students explore an idea such as: “What would a ray think about a line?” or “If a line wrote a poem to a line segment, what would it be like?” They can then create a mini-story, a comic, a play, or whatever you see fit!
Students will inductively determine the formula for the area of a triangle. Then we apply it to other, more complex shapes.
Using examples, students will attempt to deduce the formula for the area of a triangle.
We reveal the rule.
Students attempt to decompose more complex shapes into triangles.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will find and describe the most interesting shapes in this geometric image.
Students will try to find a path across this city which crosses each bridge exactly once.
First, students will cross five bridges exactly once.
Next, they’ll try to cross seven bridges one time each. ⚠️ Note: This is impossible.
They come up with three more layouts using seven bridges. At least one should work.
Students count how many bridges come out of the cities. They’re looking for patterns to determine whether a map will work.
Finally, they try four other maps and learn about Euler and the Seven Bridges of Königsberg!
Students will find several solutions for magic triangles of various sizes.
First, students find a solution that adds up to 9 for an order-3 magic triangle.
Next, they find a solution that equals 17 for an order-4 magic triangle.
They revisit the order-3 triangle and find the remaining three solutions.
Finally, your students will return to the order-4 triangle to find as many solutions as possible. (There are 18 unique solutions).
Students will search for patterns of prime numbers within a triangle made famous by Laurence Klauber.
Students build their own Klauber triangle.
Then they highlight all of the prime numbers, looking for patterns.
I reveal a giant triangle and then challenge them to create their own shape to look for prime patterns.
Students will generate an Ulam Spiral, highlight the primes, and note what patterns they see.
Students arrange the first 100 (or so) integers into a spiral.
They will highlight (or circle) only the primes in their spiral, looking for patterns.
Finally, they will either extend their spiral or try to create a new shape or spiral and look for patterns.
Students will search for patterns, patterns, and more patterns within the fascinating Pascal’s Triangle.
Students will look for one pattern in this triangle and then use that pattern to add another row.
After I build out the triangle a bit more, students will search for even more patterns.
I show one set of interesting patterns, reveal the triangle’s name, and then point students towards more resources.
Goldbach’s Conjecture states that, “Any even number can be written as the sum of two primes.” Is it true?
Students will see that any positive integer is also the sum of four or fewer perfect squares.
Students find another solution for 10.
They see how many solutions they can find for 50 – and look for patterns along the way.
They work with 99 and any other number they’d like to explore.
Students arrange integers into squares so that each row, column, and diagonal will add up to the same sum.
I introduce the idea of a magic square and then start students off with a 3×3 square that has 5 in the middle.
As an extra hint, I reveal that the sums must all equal 15.
Finally, I reveal the solution and challenge your students to try a 4×4 magic square!
How few colors do you need to color in any map so that no two neighboring regions are the same color?
First, students solve a map coloring problem by using the fewest colors while ensuring neighboring regions do not share the same color.
Next, students will determine the fewest number of colors needed to fill in a more complex map.
Finally, students are challenged to color a complex map using only four colors or to create a map needing more.
Students will try to explain why the first X odds add up to the same number as X2.
Students divide equilateral triangles over and over to create a Sierpinski Triangle.
Students learn to create their own Sierpinski Triangle by starting with an equilateral triangle.
Then, they create Sierpinski Carpets by starting with a square.
Finally, they experiment with three-dimensional versions, perhaps creating a Menger Sponge using Lego or in Minecraft.
Students will create a fractal known as The Koch Snowflake.
Students first create a Koch Curve – a simplified version of the Koch Snowflake.
They’ll take their curve from step 1 and extend it to become a snowflake.
Finally, students will create new versions of the Koch Snowflake by experimenting with different starting shapes.
Students will explore the unproven Waring’s Conjecture.
First, we demonstrate with 7 and 15. Students try with 27.
Then, students test with more odds. They try to develop a theory.
Students will determine if all perfect squares can be written as the sum of two primes.
Students will work with primes and perfect squares to investigate Legendre’s Conjecture.
Students will use the prime sieve to find primes up to 150.
Students will search for special primes and look for patterns along the way.
First, students search for twin primes: prime numbers with a difference of two.
Then, they look for cousin primes: prime numbers with a difference of four.
Finally, they look for prime quintuplets: five primes in which the difference between the largest and smallest is 12.
Students will experiment with sticky notes to find the area of a circle and, along the way, discover pi!
First, students will cut up post-it notes, trying to see how many they can fit inside of a circle.
Then, you can reveal that (if you had perfect precision) you could fit exactly π post-its into the circle.
Turn any number into a palindrome by following these steps…
Start with any number and get to 1 using just two rules. It seems to always work…
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!
Students will work with negative numbers and a grid to get their car around a track first.
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 develop a winning strategy for this simple math game.
Students learn the rules of the game.
Then, they develop a strategy guide.
Students will analyze graphs showing how three countries’ populations have aged over 70 years.
First, students notice changes in the age of the United States’ population from 1950 to 2020.
Next, they look at the US, Japan, and Afghanistan’s age graphs together, finding similarities and differences.
Finally, they consider what unique needs each population would have in 2020 and create a business idea to serve that need.
Students will compare the population of a country with that country’s total Olympic medal count and look for patterns.
Students pick 5 to 7 countries and look up the populations and counts.
Next, they calculate medals per million for each country.
Finally, they analyze their data and look for patterns. Would those patterns continue across other countries?
Students will create and analyze a graph showing countries’ winter and summer Olympic medals.
Students pick a handful of countries and then predict which ones will be stronger in winter or summer or about even.
Next, they find the summer and winter medal totals for each country.
Then, they create a graph and plot each country using the medal data as coordinates.
Finally, they check their predictions and then give each country an award based on their medal counts.
Students will analyze data about a movie series, create graphs, note trends, and make a recommendation: should we make another movie in this series?
Students select a series of 5-10 movies and look up their box office returns as well as critical ratings.
Next, they adjust each movie’s box office returns for inflation so that we can fairly compare the films.
Now, students will create a scatter plot to look for a relationship between the movies’ financial and critical success.
Students will note trends and outliers and then make a prediction about how well another movie in the series would do.
Next, students will make graphs showing the critical ratings and box office returns of the series over time.
Finally, they will make a recommendation: should we make another movie in this series?
Students will compare the costs of living, wages, and quality of life in three different cities and then decide which is right for them.
Students will learn about cost of living and pick a third city to investigate.
Then, they’ll get a job and look up wages in the different cities.
They’ll convert their information into monthly amounts.
Next, students will consider the “Quality of Life” in each of the cities.
They’ll analyze the “Cost vs Fun” of their cities by creating a scatter plot.
Finally, they’ll decide which city is best for them and develop a persuasive argument.
Students will investigate the intriguing question: does a donut or a salad have more sugar? Using an image from an article, they’ll determine if the photo is true or misleading, how they might add to it, and how they could create their own version.
Students rank how much they trust the donut image.
Then they check the math, using ratios to determine if the original image is accurate.
They choose three new food items to compare, looking up the sugar content, then creating donut ratios for each.
Finally, they redo the original image, choosing a new nutrient to use as the comparison.
Students will update their original belief of how much they trust the image.
Students will analyze advertisements about caffeine and create a public service announcement to communicate their findings.
Students will analyze their advertisements using this worksheet, identifying the audience for each ad, then deciding which ad was most misleading.
They’ll create a Public Service Announcement to promote a better understanding of caffeine.
Students, now armed with data about five caffeinated beverages, will survey a set of peers and/or adults to uncover misconceptions about caffeine.
Students conduct a survey, asking people to predict the amount of caffeine in each drink.
They find the average of their survey responses
Then graph the real data against the survey data.
Finally, students will identify misconceptions and infer what might cause those misconceptions.
Students will investigate the amount of caffeine in different drinks and analyze the data.
Optionally read this article from The Atlantic about caffeine and increased ER visits. Students will brainstorm questions about caffeine.
Students look up the caffeine content of five different drinks and calculate how many one could have before it became dangerous.
Analyze that data using any method you’d like. This is left open so that you can assign an appropriate task for your kids’ abilities: bar graphs, measures of central tendency, equivalence with ratios, etc.
Students will work with equivalence to find meals and activities that equal the calories in one popular meal from a restaurant.
First, students will pick a restaurant and then find how many calories are recommended per day.
Then they’ll create a common meal from that restaurant and calculate the calories in that meal compared to the recommended calories per day.
Now they’ll create several interesting equivalences, showing how the calories in their meal equal the calories in other meals or the calories spent on activities.
They use their information to design a parody ad.
Bonus: They are now hired by the restaurant to create an ad for a low-calorie meal.
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 find at least three ways to express the weight of the world’s heaviest pumpkin.
First, students will make a guess. How much does the heaviest pumpkin in the world weigh?
Then, they’ll convert that measurement into units of their choosing. I demonstrate with “Mr. Byrds.”
Students will find the information to calculate how many times we could fill up a jet plane using the fuel that would fit in an olympic-sized pool.
First, students will need to figure out how much water is in an olympic-sized pool, pick a plane, and determine much fuel that plane can hold.
I’ll reveal how many times I could fill up my jet plane.
Students will figure out much pasta they can cook using the water in an olympic-sized pool.
First, students will need to figure out how much water is in an olympic-sized pool and how much water you need for a pound of pasta.
I reveal my calculations – which may or may not be the same as what students arrived at. And that’s ok!
Students will find the information they need to calculate how many 2 liter bottles they could fill up using the water in an olympic-sized pool.
First, students will need to figure out how much water is in an olympic-sized pool.
I reveal my calculations – which may or may not be the same as what students arrived at. And that’s ok!
Students will balance various requirements in order to find the perfect gifts for their very special friends.
Students look for gifts that have a large volume while balancing a low price.
Next, they find gifts that are heavy, but don’t take up much space. And also are as cheap as possible.
For the third gift, students are looking for something long – maximizing one dimension while minimizing the other two. They’ll also want to save money.
Use this step whenever you’d like. Students can write a letter explaining their thought process behind the gift(s) they chose.
Students will convert between multiple measurements and calculate area per hour to estimate how long it will take to mow a large lawn.
Students begin by identifying what information they’ll need to know. Then they will try to find that info. We’re going for a rough estimate here, so they really only need to know the size of the Great Lawn, the speed they will walk, and the width of their mower.
Next, they convert all of their units into feet and square feet (feel free to adapt this however you’d like).
Now, they calculate how many square feet of grass they can mow in one hour and then determine how long it would take to mow the whole lawn.
As an extension, students can pick a new mower and a new speed and re-calculate their time. Alternate speeds could include: world’s fastest mile time, fastest land animal, student’s sprinting speed, backwards walking speed, etc.
Finally, they can pick a new lawn, determine the measurements, and decide how long that lawn would take to mow.
Students explore the big idea: Shapes can have the same perimeter, but very different areas.
Students create at least five different rectangles with 16m of perimeter.
They organize their information and look for a pattern between the shape’s dimensions and its area.
Students create three ways to use three of their different rectangles. I give an Alien Zoo example.
Students explore the properties of angles, search city maps for intersecting streets, and then design their own street intersection.
Explore how a lone angle creates a second angle. And the two angles always add up to 360º.
Explore how 2, 4, 6, or even 8 intersecting angles still add up to 360º.
Browse online city maps (Google Maps, Open Street Maps, etc) to find an interesting intersection of streets. Measure these angles and check that they also add up to 360º.
Create their own intersection of streets. They’ll label the street names, mark interesting sights, and measure each angle, ensuring that they add up to 360º.
Students will calculate the volume of laptops throughout history using the formula for the volume of a rectangular prism.
Find five laptops from across history (this Wikipedia page is a nice starting point) and jot down essential information..
Calculate the volume of their five laptops, estimating them as rectangular prisms.
Pick their two favorite laptops and sketch them using this triangular dot grid paper to create accurate, 3d scaled drawings.
Explore shapes with equivalent volumes. They will redistribute the volume of one of their laptops into a new, 3D shape. Same volume but different dimensions.
Finally, students will build two of their sketches: the laptop’s original dimensions and then a model of the reconfigured dimensions with an equivalent volume. Naturally, they can continue extending this idea by finding equivalent volumes of other items or building on the marketing of their “new laptop design.”
Students will calculate how much it would cost to fill up a car with liquids of their choosing.
Students compare the cost of various liquids with gasoline.
Then they choose a car and determine its fuel tank capacity.
Using my 2008 Kia Rondo, we calculate the price per fill up.
Students use price anchoring to create an advertisement comparing gas prices to another liquid.
Students will determine how the diameter and circumference of circles are related.
First, students make a guess about how many times they’d need to go across a circle in order to equal the distance around.
Next, they’ll measure across printouts of famous circles.
Then, using string, they’ll measure around.
Now, students will look for a relationship between the diameter and circumference.
We reveal that the relationship is π.
I explain a bit more about π.
Students will create purposefully misleading graphs to better learn how proper graphs should be created.
Technique 1: Showing Just a Moment
Technique 2: Bar Graphs with Bad Scales
Technique 3: Leaving Out Information
Technique 4: Asking the Wrong Group
Technique 5: Line Graphs with Bad Scales
Bonus: Getting Too Fancy
Now, your students will produce their own bad graphs.
Using Google Earth and authentic measurements, students will reach a reasonable estimate of how many students could fit on their playground.
Make guesses about how many people could fit on a four-square court.
Calculate the area of a four-square court as well as how much space a student takes up.
Calculate how many people really could fit on a four-square court and then test it with real kids.
Calculate how many students could fit onto the entire playground using Google Earth.
Extend the idea to calculate how many people could fit into other large spaces.
Students will determine which unit is most likely if an elephant weighs 176,000. Then… the real fun begins.
First, I tell students that my elephant weighs 176,000. They must determine the most likely units.
We learn that this is in ounces. Now, students have to find out how many corgis it would take to equal the weight of one elephant.
Now, students determine how many cars (they pick the make and model) it would take to equal the weight of one elephant.
Finally, students get to pick their own unit of measurement and compare it to the weight of an elephant.
Students will determine which unit is most likely if a movie is 0.017 long. Then… the real fun begins.
I tell students that I’ve just finished an epic movie that was 0.017 long. They have to determine which unit I’m using.
I offer some scaffolding help to get kids started on their unit conversions (not necessary for all students).
Then, we wonder how long this movie would be if measured in months?
Now, we determine the length of the movie when measured in days on Venus!
Finally, students can pick their own unit of time to measure the length of this long movie.
Students will convert between many US units of volume.
We have a bathtub filled with 640 of water. Which unit is most likely?
What if we filled that bathtub using juice boxes? How many would it take?
What if we filled an Olympic-sized pool using bathtubs?
Finally, students pick their own item to fill a bathtub with.
Students will convert between many units of time.
I announce that I’ve just turned 341,640 old and ask students to determine which units make the most sense.
I provide a little scaffolding, showing why months is a very unlikely unit.
Then, I ask students to determine how old I am in Saturn years.
After revealing my findings, I ask a final question: how many flies’ lifetimes old am I?
I reveal my answer and then open the door for students to use other unusual units of time to express my (or their!) age
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.