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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!