To become problem solvers and not just answer-getters, our young mathematicians need to SLOW DOWN and consider “the whole picture” and the underlying structure. Let’s inspire REASONING instead of RUSHING! With:
- ENGAGING Numberless story problems
- RELEVANT Student created word problems
- DAILY discussions about math in their world
- High interest RICH math tasks and 3 Act problems
- Number Talks & Solution SHARING
- Error ANALYSIS
- “UNSOLVABLE” problems [check out Robert Kaplinsky’s Shepherd problem if you aren’t familiar with it. Show & discuss it with your students]
PHOTO INSPIRED PROBLEM SOLVING
Get 100 PHOTOS to Inspire Reasoning about MATH!
Grab my go-to Google Slides Problem Solving Photos resource. There are over 100 fun photos with open-ended questions, to use as is, or tailor to your needs.
Ask a first grader how many runners have finished? Ask a sixth grader what percentage of runners are still running if 4/5 of them finished? Level up your boring textbook questions with the same beautiful photo!
Allow time for kids WONDER about math in the real world before throwing questions at them right away! Add the “animate text” feature to delay a question. What a fabulous way to have daily discussions about math!
For this post, I would like to focus on ways to move the thinking forward during independent time, since that is where “word problems” fall flat as problem solving pancakes -THUD!
Consider low floor – high ceiling activities your students can do independently & frequently while you work with other groups. Consider something easy to facilitate,. that will actually move student thinking forward even when you aren’t there to ask the good questions!
“Get the learners to ask the questions! Kids who can write math problems… can solve them.“
-TOO MANY NCTM PUBLISHED AUTHORS AND EXPERTS TO POSSIBLY LIST HERE. 🙂
THIS HAS BEEN AN NCTM BEST PRACTICE FOR DECADES!
PREVIEW These Student Created Word Problem Activities
Challenge your students to carefully consider subtraction situations versus addition situations; and eventually multiplication and division scenarios too. This could be the highlight of math class with this incredibly engaging and meaningful activity!
Grab 3 plastic cups or brown paper bags. Print and cut out the cards and separate them into their bags. Have kids choose a number pair, an operation and a topic. Then they write their own word problem. Sounds easy, right?
I thought so. I had to pick my jaw up off the floor when students selected a number pair like 21 and 7 with the multiplication card and proceeded to compose a division story. While. Holding. The word. Multiplication. In. Their. Hands.
Everything about the numbers 21 and 7 screamed division to them.
This is why it is ESSENTIAL to provide as many opportunities to consider possible paths to a solution. This is why I have so many great links to numberless lessons on my links page. Have you seen Robert Kaplinsky’s Shepard Problem video? YOU MUST. The link is there as well. Please consider using numberless problems… and this Word Problem Generator with your students.
This is a fabulous activity to do throughout the year. There are so many combinations that it never gets old! (My students have started making their own topic cards and adding them to the center…. sometimes during lunch! Now THAT is buy-in!)
This should start as young as 1st and 2nd Grade!, but you might find they are NOT off and running writing their own problems! If you teach first or second grade My First Math Story offers a scaffolded approach. There are fill in the blank mad libs style problems for addition and subtraction. There are LOTS of options, but many of your students will be ready to move quickly to the story writing stage. For those who need more emerging level experiences, there are plenty.
It is self- differentiated because students CHOOSE THEIR OWN NUMBERS! OH!! And speaking of choosing your own numbers…
PREVIEW THESE NUMBERLESS WORD PROBLEMS
For more DIFFERENTIATED PROBLEM SOLVING, go numberless! It intrigues (okay, so it technically forces) students to consider the context (all they have is context) Check out Brian Bushart’s fabulous blog to learn more!
I have added my own twist on numberless word problems, with numberless task cards to sort by the operation required. These are designed to keep your students reasoning through problems INDEPENDENTLY while you work with small groups.
Learners will compare addition situations to subtraction contexts. Or they can compare multiplication to addition… and division. It is SO IMPORTANT to focus on the ENTIRE CONTEXT and not key words.
After sorting, they can use their own numbers to solve! Personally, I also have students critique each others’ sorts before they solve. I do this with them the first time. (Available for grades 1-5, including fractions!)
Engaging, relevant problems will ALWAYS yield more effort from students. Naturally occurring questions, particularly those posed verbally are some of the best rich tasks for students to solve! (if you’re sneaky, you can take a problem from your book and twist it into a real problem about your own class trip, cafeteria or talent show)
Photo or Video openers will always blow a textbook question out of the water. These photo slides are great warm-ups that you can use whole group, small group, or independently via Google Classroom. They are also an effective way to build math vocabulary. When you want an open pathway… you can say “answer” but if you want them to consider division contexts, ask for the quotient.
Finally…. please don’t forget about calculators! They free up the brain for reasoning. ‘Nuff said. Let the kids use them now and then. They’re happy. You’re happy. Everybody’s happy. Calculators are like the Nutella of math class!
What do we do now? Quite simply, we do MORE problem solving. Consider some of the ideas I have shared to gain buy-in and sharpen reasoning skills. I have found these strategies to be the “best supporting “Best Supporting Players” across grade levels since they focus our energy on reasoning about the context. Plus they are fun.
What other ways do you elicit buy in for problem solving? Do you already use 3 Act Tasks in your math classroom? Do you evaluate problems already solved by others? What do you feel gives you the most bang for your educational buck?
My Own Problem Solving Timeline
1980: When I was a kid we had word problems, but even if we guessed at both of them we could still get A’s in math! Until we attempted to move beyond computation and we fell apart saying we “weren’t math people.”
1990: There were more word problems, but we figured out how to ignore the words and do something with the numbers. (Usually the last thing we learned how to do. Hey, it worked more often than not!)
2000: I started teaching and realized that kids are being held to MUCH higher standards (with MUCH shorter attention spans.) I learned that kids put way more effort into tasks that seemed legitimate or just plain fun! I began having my students write problems about topics that interested them.
2010: These kids have the attention span of fleas and our curriculum seems to move that quickly too! I must adapt and give them relevant topics and visuals and of course, manipulatives. But we have to clean up quickly. It’s time to assess again! Wait, didn’t we take a test yesterday?
2020: OMG DID I SRSLY SAY THAT ALMST 10 YRS AGO NOW? Math curriculums are more rigorous than ever, and kids rarely have the stamina to type all the letters in a word! And those flea-sized attention spans of the last decade??? Oh how I long for those now! GAME ON, TEACHERS!