| A MIND-STRETCHING SET OF CHALLENGES THAT REQUIRES ZERO PREP! |
How many tasks can be inspired by a simple two-digit number? When I began playing around with this idea, my brain exploded. This is just the kind of task we want for our students, right? mind-blowing and brain-stretching? And the best part? The challenge sets below require no prep at all and are about as high ceiling / low floor as you can get since students have the opportunity to come up with their own creative tasks in addition to doing the ones provided.
MORE OPEN-ENDED than OPEN-ENDED?
From the time I created S.C.A.M.P.E.R. with Numbers for younger students, I’ve been wondering about how creative constraints with numbers might be used with older students. What if students had the freedom to go with their strengths and play with numbers, not only through intriguing mathematical tasks, but across the disciplines.
After playing around with a few ideas, I’ve come up with many open-ended tasks and created quantitative and verbal reasoning tasks that can be applied to any number with two or more digits. The “Out of Our Math Minds” tasks specifically promote fluency and originality. Presenting this as an ongoing challenge and interactive bulletin board will encourage and celebrate creative thinking.
HOW IT WORKS:
Begin by telling students the “target number.” It’s best to start with an even two-digit number such as 24. Share the tasks with your students and allow them some time to do a few, then leave a display up for a set time period, perhaps a week or two. I’ve provided this TEACHER GUIDE that explains a few options and includes cards for most of the tasks.
Your students will initially go with their strengths. Your mathematically-gifted students will likely choose from the quantitative tasks, while those more verbally-inclined will be drawn to those tasks. You may want to challenge them to submit one of each kind of task in order to stretch their thinking. Celebrate students who try to come up with their own ideas. Even better- let them display what they’ve done and have the other students try to figure out what they’ve done!
HOW MANY OPEN-ENDED TASKS CAN WE CREATE WITH ONE NUMBER?
Quantitative Tasks
- Make the number using only the digits in the number. So, if the number is 24, you must make 24 using only the digits 2 and 4. One solution would be (4 x 4) + (2 x 4) = 24. Another would be 4(2 + 4) = 24. How many equations can you write?
- Make the number with a constraint (see “How Did We Get Here?” in Ian Byrd’s article).
- Add another digit in the number to create a 3-digit number. Make the number using only its digits. How many equations can you write? So, if 24 becomes 242, and you can use only single digits, you could write this equation: 4 x (4 + 2) x (2 + 4 + 4) + 2 = 242.
- Write equations using the digits of the number in all forms (fraction, decimals, exponents). One example 2(2.4 + 2.4 + 4.2) = 24 – (2 + 4). Another example: (2/4 + 2/4 + 4/2) x 4 x 2.
- Find out the number of steps required to make palindromes using the digits. For example, 24 can be made in one step, but we could use the digits to test any number that can be made from the digits: 42, 224, 442, 242, etc. Over time, students will pick up on patterns.
- Create your own mathematical task!
Verbal Tasks
- Write a poem or story, 24 words long.
- Write the number as a MAD GAB (Too win tea for).
- List words that can be made from the letters of the number written as a word.
- Create a list of LETTER-EQUATION puzzles such as these using the digits. For example: 24 = H in a D; 24 = The N of E in 2C. (Answers to these at the end of the post)
- Create a lipogrammatic poem, omitting the letters in the alphabet represented by the digits in the number. With the number 24, the second letter B and the fourth letter D would not appear in the poem at all. Find other kinds of constrained writing HERE.
- Write a sentence 24 different ways, as explained in “How Do I Write This? Let Me Count the Ways?”
- Create your own task that relates the number to something with letters or words!
Nonverbal Tasks (optional)
- Create a number drawing using only the digits and numbers that can be made from the digits (see photo). Note: In the sample pages found here, you can see other examples of this kind of illustration. In this book Brain Stretchers, these are also puzzles and the challenge is to determine the total of the numbers in the picture. Unique challenge! Print it out and display it for the five minutes before recess!
- Create a tessellation with the number of shapes.
- Draw something that illustrates the number without using words or numbers.
- Create your own task that involves illustrating or performing.
Many of you will adapt this to suit your needs because that’s what great teachers do! An interactive ongoing display of responses to only math tasks would still be a mind-blowing display! If you do this with your students, share about it and, even better, share any creative responses you get from students. You can leave a comment below or sharing in our Facebook group.
Answers to Letter Equation Puzzles: 24 = Hours in a Day/ 24 = the Number of Eggs in 2 Cartons.
RELATED ARTICLES:
5 Simple Ways to Add Creativity in Mathematics by Pronita Mehrotra
Grow Creativity! An ISTE Featured Article by Candace Hackett Shively