Pattern Challenges (2nd through 5th grade)

What in the world is a Math Stackers Pattern Challenge?

Picture this…a group of four of your kiddos have just observed and discussed a given pattern of stacked Math Stackers. The timer is set for 1 minute…they wait with anxious excitement to begin their challenge….then, the initial charge comes….”GO!”

They scramble to collect the blocks that are needed to correctly build and continue the pattern. As the seconds pass, they begin to strategize for maximum height, “We need to get it higher, two of us get the blocks and the other two stack them!” Thirty seconds left and the engineering instincts in each kid kicks in…”Oh no, it’s gonna fall!!! Carefully stack it a little more to the right to balance it!” Ten seconds left, “We need to double check the pattern!” TIMES UP!

The group of enthusiastic builders back away slightly from their patterned creation and now it’s time for the good stuff…the power of math thinking as you ask,”What will be the 17th Math Stacker in your pattern?” And the wheels begin spinning.

Let’s start from the beginning with an example and how to structure this in your classroom.

What you need:

A class set of Math Stackers (Elementary or Combo Set)

How to set up:

Pick a pattern that is on your kids’ level. Either start the pattern by building with Math Stackers or have a picture of a pattern of Math Stackers ready to go that you created previously. (If using an image for them to analyze, this allows them to have more blocks to use during the challenge.)

Let’s start with the pattern pictured to the right.

Step 1:

Your kiddos are given 20 seconds (or so) to discuss what patterns exist in the stack, meaning: what repeated sets do you see.

(At this time, they will not actually add onto the pattern, just discuss their observations.)

For this example, they would identify that the blocks 2, 4 and 3 are stacked and then it begins to repeat with another 2, then 4. The next Math Stacker should be a 3-block to complete the 2nd full set of the pattern. Then the three blocks will be repeated over and over again until the minute time limit is up.

Step 2:

Set the timer for 1 minute and start the challenge!

During this time, they stack the correct pattern as high as they can without knocking it over. If they do knock it over, they must keep building onto whatever is left of their stack :). When time is up, they back away. (I have an additional rule that their stack must stand for 5 seconds without any group member holding up any part of it. But this of course, is a classroom-by-classroom call. I just like the way it adds the engineering aspect to the challenge and gets them to eventually make the judgement call that if they add another block it may make the tower tumble.)

At this time a picture of the group’s tower may be taken and throughout the week, an added competition between all of the small groups in the class can be created to see which group can build the tallest, correct tower.

Step 3:

Discuss and check the pattern. Your group communicates the pattern(s) that exist and then checks to see that they have continued the pattern correctly. If any part of the pattern is incorrect, they may find it at this time and fix it.

Step 4:

Math thinking time! This is where you get to ask all sorts of nitty gritty math questions. Your questions will of course depend on your grade level and students’ current understanding.

The following is a question that I ask with this level of pattern and I’ve included different types of responses that students typically give. (I’ll put the responses in order of strategic thinking.)

Question: What will be the 17th Math Stacker?

Responses:

a. The 4-block! I counted on my fingers “2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4”.

b. The 4-block! We had 13 blocks stacked in our whole pattern (as an example) and the top block was a 2-block. I added 4 more blocks to it and ended with a 4-block.

c. The 4-block! If our pattern is 3 different blocks repeating, I can count by 3s to 15, which will be a 3-block. Then I need 2 more to get to 17, which would be the 2-block and then finally the 4-block.

d. The 4-block! If our pattern is 3 different blocks repeating, I can multiply 3 to get as close to 17 as possible…3 x 6 = 18. The 18th block will be a 3-block, but I need the 17th block so it will be the block before the 3-block….and that is the 4-block. (This can also be explained 3 x 5 = 15…is the 3-block… + 2 more blocks = 4-block.)

I love having the kids share their reasoning no matter what strategy they use to solve. As they share, they will experience different types of strategic thinking and get ideas about how to think about future patterns!

(See a video of this challenge in action.)

What next? Amp the math thinking up!

After your kiddos have done a few challenges at the same level and it is clear that they are ready for more…give it to them! :)

How? Manipulate the thinking by incorporating different, simultaneous patterns. I do this by altering the blocks position in the pattern. Below are two more patterns, each one increasing in math thinking. Your students will have all sorts of ways to respond to the math thinking questions, similar to the different strategies expressed in the first pattern. They may use their fingers, build out the pattern with the Math Stackers (they can lay the pattern on the ground if it is not possible to stack that high), use skip counting, etc. Below I am going to include the responses I get that show higher level, strategic math thinking. This thinking evolves over time, after many pattern challenges, and will become more common as students share their different strategies..and it is amazing!

LEVEL 2

Question 1: What is happening in this pattern?

Response: There are 3 numbers that are repeating…9, 8, 6. But the blocks are positioned different. The first block is horizontal, the second is vertical, the third is horizontal, the fourth is vertical, the fifth is horizontal….so there is another pattern going on: the position of the blocks is horizontal, vertical, horizontal, vertical….

Question 2: What position in the pattern (1st, 2nd, 3rd, 4th, etc…) will the 9-block be exactly like it is in the 1st position?

(I actually have them knock their build stack down so they can’t just look at it and count.)

Response: Since the numbers are repeating every 3 blocks and the positions are repeating every 2 blocks, it will take six stacked blocks before every number has been stacked in both positions. After this, the pattern repeats as it is in the first block. So the 9-block will be stacked exactly like it is in the 1st position again in the 7th position.

Question 3: What will be the 29th Math Stacker and its position in the pattern?

Response: If after every six blocks the pattern repeats, then I know I can multiply 6 to get as close to 29 as possible… 6 x 5 = 30. The 30th block in the pattern will be a 6-block standing vertical, so the 29th block will be the block before the 30th, so it is the 8-block stacked horizontally!

LEVEL 3

Question 1: What is happening in this pattern?

Response: There are 4 numbers that are repeating…9, 7, 3, 6. There are also 3 different positions: laid to the left, right, then vertical.

Question 2: What position in the pattern (1st, 2nd, 3rd, 4th, etc…) will the 3-block be exactly like it is in the 3rd position?

Response: Since the numbers are repeating every 4 blocks and the positions are repeating every 3 blocks, it will take twelve stacked blocks before every number has been stacked in all three positions (4 x 3 = 12). The 12th block would be the fourth number, 6, positioned in the 3rd position, vertical. After this, the pattern repeats as it is in the first block. But the 3-block stacked vertical is the 3rd block in the original pattern, so it won’t be until the 15th position before it is stacked vertical again, 4 x 3 = 12, 12 + 3 = 15.

Question 3: What will be the 38th Math Stacker and its position in the pattern?

Response: If after every twelve blocks stacked the pattern repeats, then I know I can multiply 12 to get as close to 38 as possible… 12 x 3 = 36. The 36th block in the pattern will be a 6-block standing vertical, so the 38th block will be two more blocks stacked like in the 1st and 2nd positions, so it is the 7-block stacked to the right!

Once again, this thinking evolves over time, through consistency and the sharing of ideas. With this type of math thinking, your kiddos are actually strategically using multiplication in the form commonly referred to as “least common multiple” to analyze their pattern. They are connecting operations and reasoning, and these connections are always our goal as educators!

Now it’s your turn. Try out a Math Stackers Pattern Challenge and build math thinkers in your classroom!

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Happy Math Stacking!