“This was the best money I have ever spent on a teaching tool.” ~ a teacher in Wisconsin
Students will fill in the blanks to find multiply-then-add expressions that equal exactly 22.
Students fill in blanks in an equation using each digit from zero to nine only once to find true solutions.
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).
Students multiply letters to create names and find classmates with the same encoded values.
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.
Students identify letters that cannot be used in their words and search for the longest words encoding to 720.
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.
Students identify that each number is a perfect square minus one, following a specific pattern for calculations.
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.
Students calculate the number of blue lines at step 12 by multiplying the step number by seven and adding one.
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.
Students calculate the number of blue squares at step twelve by multiplying thirteen times four to find the total.
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.
Students calculate the number of blue squares by multiplying the step number by five and then adding four.
Students will use the patterns they find in the first few steps to predict a step much further along.
Students predict how many blue sides there will be at step 5.
I reveal the solution (it’s 48) and ask students to predict step 12.
Students calculate the number of blue sides in step 12 by multiplying the step number by 9 and adding 3.
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.
Students calculate the number of blue squares in step 12 by multiplying the step number by 6 and adding 2.
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!
Students multiply the step number by the next number to find the total of even squares at that step.
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.
Students discover how to use exponents to simplify repeated multiplication by illustrating the process of calculating powers of two.
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.
Students identify the pattern of X’s by multiplying the number of O’s by 3 and adding 1 for any 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.
Students count the number of squares in each step and record their findings on paper.
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 calculate the sum of the 50th and 49th perfect squares to find how many squares exist at this step.
Students will make mathematical predictions about an infinitely repeating sequence of triangles.
Students count the blue triangles in each step and look for patterns before making a prediction about their quantity.
Students break each blue triangle into three smaller triangles to find the total number of triangles in step four.
After revealing that step 6 has 243 triangles, we will try to predict all the way up to step 20!
Students identify a pattern in multiplying triangles to calculate the total at various steps using exponents for efficiency.
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 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.
Students identify patterns in placing parentheses that significantly change the value of expressions for their guidebook project.
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.
Students multiply a number by a factor and then divide by the same factor to return to the original number.
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 uncover patterns with exponents and make predictions about the powers of 0 and 1.
Students identify two patterns about exponents.
Students identify the pattern of multiplying or dividing by the base as the exponent increases or decreases.
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.
Students factor 365 in an attempt to create a better system of months and weeks than our current calendar.
Students create three different ways to group three hundred sixty-five days into months with an even number of days each.
Students divide 365 days into months and create a special intercalary month for leftover days to maintain a full year.
Students group the days of their month into even weeks with five days each to create a structured calendar.
Students create names for their months and days of the week to finalize their new calendar system.
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 guess how many times their dollar doubles to reach one million dollars without doing any calculations.
Students set up a table with two columns to track the number of dollars over several days of doubling.
Students learn to use exponents to simplify repeated multiplication when calculating the amount after doubling for several days.
Students calculate how tripling money each day reaches one million dollars using exponents instead of lengthy tables for answers.
Students calculate how many days it takes to reach one million dollars by doubling ten dollars or tripling one dollar.
Students ask questions about multiplying amounts of money and investigate how different multipliers affect the total over time.