In the post called On Repeat: How Patterns Kickstart Algebraic Reasoning, I shared 3 activities perfect for exploring repeating patterns with preschool and kindergarten kids:
By playing with repeating patterns, kids can look for, create, and analyze patterns and relationships and begin to apply their reasoning processes in increasingly abstract ways. But repeating patterns aren’t the only algebra going on in elementary school. We also explore growing patterns in our counting system--the coolest growing pattern of 'em all.
Growing patterns, sometimes called sequences, progress from step to step. With these patterns, we can not only identify the core but also look for a pattern that will help us anticipate or predict what the pattern will be at any point along the way.
We can still use letters to name growing patterns (for example AB, AAB, AAAB...) but also find real life patterns in the coolest growing pattern of 'em all—our counting system.
Hey, that AB, AAB, AAAB pattern appears all over our number system
like with 14, 114, 1114…. Pretty cool!
Connect Algebra to Counting
The patterns in our number system are essential for connecting algebra to counting. It’s not enough for kids to be able to count by 1s because that’s not always efficient. We want kids to be flexible counters and flexible thinkers.
Kids need opportunities to look for and analyze the patterns that appear in our counting system. That’ll help them build number sense, apply place value understanding, make magnitude comparisons, and see how numbers relate to each other.
One of the best ways for young kids to identify, explore, and explain patterns in our counting system is through exploration with an interactive Hundred Chart.
Hundred Pocket Chart--My Hero!
This picture shows my favorite type of hundred chart to display in classrooms from Prek to 3rd grade. I like it because it’s highly flexible for all sorts of explorations and very economical. I bought mine online for about $18. I don’t work for Learning Resources, but the one they sell is pretty good quality.
To have adequate wall space for a hundred pocket chart, you might have to shrink the space (and time) you’re currently allowing for your calendar. I know, you love your calendar. It's a beloved and comfy part of your daily routine. But it doesn't offer much conceptual math learning. It's base 7, afterall. Not that useful. If the picture below is your classroom wall, I apologize. It looks like the teacher catalog threw up and was nursed back to health by the laminating machine. It's making me very, very anxious. Too much of a good thing is just too much.
But I do love the pocket hundred chart you can just make out there on the right. I recently made the courageous choice to replace my beloved daily calendar routine with interactions with a pocket hundred chart. You can read about my uncomfortable but successful journey in the post Why I Swapped Calendar for a Hundred Chart.
I think you’ll get excited reading through the following Ten Powerful Ways to Interact with the Hundred Chart and be ready to make a shift in wall (and time) priorities in your classroom.
Ten Interactive Activities with a Pocket Hundred Chart
1. START SIMPLE
Since the cards are (re)moveable, you don’t have to use all 100 numbers in the set. For preK, use the chart to practice the number sequence. Fill in only the first 20 numbers or even 10. Mix up the cards and have children “fix the chart.”
Do lots of discussion but keep it brief.
2. HIGHLIGHT THE MULTIPLES
With a chart built to 50 or 100, have kids use the red colored numbers to show the multiples of 10, or the multiples of 3 in green (that makes a cool design on the board), and so on. What diagonal patterns do they notice in addition to the patterns that appear in columns or rows?
3. TEEN TROUBLE
Lots of young kids struggle with teen numbers. Kids leave some numbers out, mix some up, or say some twice. I have a theory about this. When a child can't yet pronounce the /th/ sound "feerteen" sounds an awful lot like "feerteen." (That's 13 and 14 for those who don't speak preschool-ese.) The teens are tricky to say and to conceptualize. Hundred chart to the rescue! Build the chart just to 20. Flip the teens numbers over to red-colored cards to make them stand out.
Do lots of discussion with questions such as, "What number is ONE LARGER than 17?" "What number comes BEFORE 15?" Support this experience by having children make sets of fewer than 20 objects (buttons, counters, flat marbles) in a center then having the children show you how many objects there are by pointing to the correct number on the hundreds chart. Talk about the teen numbers as "ten and some more" to help kids begin to connect counting to place value.
4. NAUGHTY SPRITES
When children are out of the classroom, remove one or more of the numbers. Tell students that a sprite/fairy came into the classroom and hid some of the numbers. Have the children tell what numbers are missing, find where they are hidden in the classroom, and place them in the correct pocket on the chart.
For fun, you might hide numbers that are meaningful to the kids--like hiding the number of the days you've been in school or the number of kids in the class.
5. MIXED UP SPRITES
When children are out of the classroom, mix up the numbers on the chart. This can be done randomly or with intention of highlighting a specific counting pattern. Tell students that a sprite came into the classroom and mixed up the numbers on the chart. If you’re hoping kids will discover a specific counting pattern, have those numbers available only in red.
Have the children tell how they know where the numbers belong.
Observe: Do they always have to count by 1s starting at 1? How else could they know where to put a number? Ask lots of questions about the rows and columns, ones and tens.
6. PERSONAL NUMBERS
Ask a child to flip over a number then tell why that number is special. For example, a student might flip over 6 and say, "Six is the number of kittens my cat just had." Another child might flip over the number 48 and say, "48 is a number in my address." You can be pretty certain at least a few of your kiddos will turn over a number that's their age. I wonder if any will turn over a number and say, "It's the number of hours of Fortnite I played last week." (If it's my sons, that's probably why the number 90 is highlighted in blue in this photo. Yikes!)
7. FINISH IT
Ask young kids to complete a row. Later, you can ask them to complete a column. That can be tough. Challenge them to do it without counting by 1s starting at 1. How could they be more efficient? What patterns could help them? Can they put the cards in the correct place without going from smallest to largest down the column? That's even tougher but really places a strong focus on the patterns in the 10s and 1s places.
8. MYSTERY NUMBER
Build the chart to 100. Play Mystery Number. For example: Start at 77. Go down one, go to the right one, go up two. Where did you land? 68!
After a while, kids should be able to identify the Mystery Number without referring to the hundreds chart. They can visualize the moves that add or subtract 10s or 1s. That's powerful, flexible thinking that connects to place value reasoning!
In the video shown here, Hundred Chart Arrow Problems, you see an activity that's a spin on Mystery Number that's great for older kids connecting place value to algebra. Read the full instructions for Hundred Chart Arrow Problems in the video description.
9. MORE OR LESS
Say a number and have kids tell what is 1 more or 1 less, 2 more or 2 less, or 10 more or 10 less. If desired, have children work with a partner and use unifix cubes or base ten blocks to build the numbers. Observe: How efficiently can they add or take away? Discuss: What are they thinking about as they solve? There will be many "right" ways to find an answer--counting on, thinking in 10s and 1s, looking at the row above or below, using manipulatives and counting in groups.
10. CENTER TIME
Make the chart one of your permanent math centers so that children can interact with the materials independently. Include challenge cards with prompts such as “Create a diagonal pattern using red cards. What do you notice? Do you think there is another diagonal pattern? Make it too.”
Concluding Pep Talk
I hope you’re ready to shrink down calendar to allow for more TIME and WALL SPACE for meaningful math discussions about our amazing number system—the coolest growing pattern around. Get yourself a hundred pocket chart and get going. Even if you've been using calendar all year, it's never too late to change up your routine for something that gives more mathematical bang for your buck.
Let me know what you think of these ideas, add your own suggestions in the comment section, or send me a Tweet. I'd love to hear how you are using a pocket hundred chart to build math-positive mindsets.
If you like these ideas, hit subscribe. And find many more tips in my book Math-Positive Mindsets: Growing a Child's Mind without Losing Yours.