My young mathematicians were obvious. They finished everything not only quickly but also correctly. I was a beginning teacher and had no idea what to do with them. So they waited. Luckily they were all very well behaved – and bored. There were sooo many different levels of math students in my classroom. I knew I had to give my strugglers extra time.
What should I do with these young mathematicians? The ones who learned and understood immediately. The ones who were possibly gifted mathematicians? The ones who finished all of their work before I could finish passing out assignments?
They will learn “anyway” I was told.
Just focus on your “needy kids”.
So, okay. I did.
Until “that parent”. That parent who really cared about her child’s learning. That parent who made me really think about what I was doing. What I was teaching. To ALL of my students.
There were so-o-o many needs. So-o-o many levels. I knew I was “losing” some of them. I had pushed those thoughts aside because of the complexity of having resources for so many different levels was daunting.
And so I began to create.
I needed materials that would:
- Enhance problem-solving and mathematical reasoning abilities
- Offer practice and maintenance of previously learned skills and concepts – even gifted students have “gaps” in learning
- Build literacy skills
- Nurture collaborative learning behaviors
Meeting the needs of all your students can be overwhelming. Who am I kidding? Meeting the needs of all your students IS overwhelming!
Students gifted in mathematical thinking and problem-solving need greater depth and breadth of topics and open-ended opportunities for solving more complex problems (Sheffield, 1994). True, of course. But in a classroom filled with diversity, meeting the needs of students who just seem to “get math” is . . . well . . . overwhelming!
Just let them pull out their library book and read when they finish their work. Right? WRONG!
To nurture and extend your young mathematicians, having fun, engaging and challenging math extensions at your fingertips is a must!
This is one of my very favorite activities to broaden student thinking. It takes some time to introduce and then practice before students are independent with it, but the thinking is excellent and so worth the time!
It involves replacing some numbers with letters-yes, it’s algebraic! These problems involve more complex thinking and will thrill your young mathematicians (and their parents)!
Start with simple equations that students already know. See the progression below.
- Begin with doubles. Write A + A = 4 on your whiteboard.
Ask students, “If A is a number, what number would it have to be? …2 of course. Because if I replace the letter A with the number 2, it will look like this 2 + 2 = 4″.
- “What does A equal in this problem: A + 7 = 10?”
- Continue with a few more until students get the idea. Be creative. If something you write doesn’t work, let your students help you figure out why. Use subtraction as well as addition.
- Now you can add in double-digit problems.
Make up a problem first. Any 2-digit problem will work. Just substitute letters for one of the addends, the subtrahend, or the minuend. At this point, always give the answer in numbers.
▶ Here is an example of what I do:
❶ I think of a 2-digit problem and write it down in my own journal, on a sticky, or somewhere that I can refer to – there are a lot of distractions when teaching! Did she just take something very small out of her hair?!!
❷ I think and record the problem for myself. Let’s use 72 – 10 = 62 as an example. Make it as simple or as challenging as you need to meet the needs of your students.
❸ For the students’ problem, I write:
72 – AB = 62
A =_____ B = _____
Each letter in your problem will represent a different digit. If you use AA or BB, that signifies that the number has two digits that are the same.
For example: 58 – 33 = 25
The students’ problem would be 58 – AA = 25 and A = 3.
Post a few of these problems for your young mathematicians to solve when they finish early, for morning work, or during any other “spare moments”.
Once you have students who can pose their own problems, have them write their problems on index cards and sign their names at the bottom of the card.
Place these in a center titled Alpha Numbers. If you do not use centers in your classroom, punch a hole in each index card, put a ring through it and hang the cards from a command hook. You now have many new activities for your early finishers. And, they were created by your students! Your early finisher “stash” will grow with no effort or time from you!! Fabulous!
Below is a resource using this idea. It will work for grades K-3 depending on how advanced your students’ level. It has pictures and examples for your students and 20 ready-to-go pages that include 57 challenges!
The two characters throughout the tasks add humor, engagement, and encourage your students to persevere with renewed effort and confidence as they work through the tasks. The page below is the story of the two characters from the complete resource that has 20 pages of early finisher challenges. Just click the picture to see the complete resource.
I hope you’ll try out the four pages in the free version below. They will get the thinking started.
There are 57 different challenges in the full 20-page resource. That’s 57 ways you’ll be ready to meet the needs of your young mathematicians!
Let me know how the tasks work for you. Share any tips or suggestions you have in the comments below. I’d love to hear your Young Mathematicians tips.
And as always,