Numberless Word Problems

Posted on by Denise Gaskins

As I mentioned yesterday, my new book includes links to online resources to help you play with word problems. So this week, I’m sharing a few of my favorites.

Visit the Kickstarter

Today we examine a time-tested method to help kids reason about math: Leave out the numbers.

First up, there’s Brian Bushart’s numberless problem bank for young students. Then we’ll look at Farrar Williams’s modern revision of a math teaching classic with problems for upper-elementary and middle school students.

Have fun thinking math with your kids!

Word Problem Bank

Word problems are commonplace in mathematics classrooms, and yet they regularly confound students and lead to frustrated teachers saying things like:

  • “They just add all the numbers! It doesn’t matter what the problem says.”
  • “They don’t stop to think! They just start computing as soon as they’re done reading the problem.”

Brian Bushart offers a collection of ready-to-go slide presentations that walk through the steps of making a word problem make sense.

Visit the Site

Math With No Numbers

Discover Farrar Williams’s book Numberless Math Problems: A Modern Update of S.Y. Gillian’s Classic Problems Without Figures, available in ebook or paperback.

Williams writes: “In order to answer the question, they’ll have to explain it, because the problem doesn’t give you anything to calculate with. The only way to answer is by explaining your process. See how sneaky a numberless problem is? It makes students really think about the process of solving the problem.”

Find Out More

“When students face a word problem, they often revert to pulling all the numbers out and “doing something” to them. They want to add, subtract, multiply, or divide them, without really considering which operation is the right one to perform or why.

    “When you don’t have numbers, it sidesteps that problem.

      “For students who freeze up when they see the numbers, this can be a really good way to get them to think about their process with math.”

      —Farrar Williams, Math With No Numbers

      CREDITS: Feature photo (top) by saeed karimi via Unsplash.com.

      Problem Solving with James Tanton

      Posted on by Denise Gaskins

      At the back of my new Word Problems from Literature book, I’ve included an appendix with links to recommended online resources.

      Check in on the Kickstarter

      So I thought this week, I’d share some of my favorites with you. First up: Problem Solving Tips from James Tanton.

      You may know Tanton from the popular Exploding Dots and other activities at the Global Math Project website. But he’s been busy for decades sharing the delight and the beauty of the subject. He currently serves as the Mathematician-at-Large for the Mathematical Association of America.

      Read on to discover several of Tanton’s best problem-solving tips for middle school and older students.

      Have fun exploring math with your kids!

      How to Think like a School Math Genius

      In this 4-video series, Tanton presents five key principles for brilliant mathematical thinking, along with loads and loads of examples to explain what he means by each of them. A call for parents and teachers to be mindful of the life thinking we should foster, encourage, promote, embrace and reward — even in a math class!

      Watch the Videos

      Two Key — but Ignored —Steps to Solving Any Math Problem

      How many degrees in a Martian circle?
      Every challenge or problem we encounter in mathematics (or life!) elicits a human response. The dryness of textbooks and worksheets in the school world might suggest otherwise, but connecting with one’s emotions is fundamental and vital for success — and of course, joy — in doing mathematics.

      Read the Article

      MAA AMC Curriculum Inspirations

      Essays and videos showing how to approach math puzzles in a way that a) is relevant and connected to the curriculum, and b) revels in deep, joyous, mulling and flailing, reflection, intellectual play and extension, insight, and grand mathematical delight.

      Scroll down and start with the Ten Problem-Solving Strategies.

      Download the Puzzles

      Think Puzzles and Think Cool Math

      Here are some essays illustrating astounding tidbits of mathematical delight. And here are some purely visual puzzles to surprise.

      Explore and Enjoy

      “The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

        “There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

          “Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

          —James Tanton

          CREDITS: Feature photo (top) by Ian Stauffer via Unsplash.com.

          Why Word Problems?

          Posted on by Denise Gaskins

          Wow! My Word Problems from Literature Kickstarter is just barreling along. I love seeing how many people are interested in a playful approach to teaching math.

          Check It Out

          But you might wonder: Why do I care so much about word problems?

          In many textbooks, word problems are an afterthought tacked on to the end of a math lesson.

          For me, it’s just the opposite. Word problems are the key part of a lesson, because that’s where children come face-to-face with the meanings of math concepts.

          The Key to Learning Math

          If we want our children to learn real math, we need to offer them plenty of problems to solve. A child may work through several pages of number calculations by rote, following memorized steps, but a good problem demands more thought.

          A story problem puts flesh on the abstract bones of arithmetic. Word problems encourage children to ponder what it means for one thing to be bigger than another, or smaller, or faster, or slower, or made up of several parts.

          Word Problems from Literature will feed your child’s mathematical imagination with story problems inspired by classic books, from 2nd-grade stories based on Mr. Popper’s Penguins to prealgebra stumpers inspired by The Lord of the Rings.

          And when you finish my puzzles, I’ll show you how to create your own word problems from literature, using your children’s favorite story worlds.

          The Trouble with Word Problems

          Most young children solve math problems by the flash-of-insight method: They hear the problem, and they know by instinct how to solve it.

          This is fine for simple problems like “Four kittens played with a yarn ball. Two more kittens came to join the fun. Then how many kittens were playing with the yarn ball?”

          When problems grow more difficult, however, that flash of insight becomes less reliable, so we find our children fidgeting with their paper or staring out the window. They complain, “I don’t know what to do. It’s too hard.”

          Too often, the frustrated child concludes, “I’m just not good at math.”

          But the truth is that nobody is good at math, if you define “good at math” to mean they can see the answer instantly. Here’s a more useful definition: You’re good at math if you have problem-solving tools and know how to use them.

          And that is something everyone can learn.

          Word Problems from Literature and the Word Problems Student Workbook will show you how. Order your copies today!

          Visit the Kickstarter

           
          * * *

          This blog is reader-supported.

          If you’d like to help fund the blog on an on-going basis, then please head to my Patreon page.

          If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

          Which I am going to say right now. Thank you!

          “Why Word Problems?” copyright © 2022 by Denise Gaskins. Photos copyright © TarasMalyarevich, ArturVerkhovetskiy, Wavebreakmedia / Depositphotos.

          Sample My New Playful Word Problems Book

          Posted on by Denise Gaskins

          I’m so excited to announce that on August 9th, I’m launching my newest playful math book, Word Problems from Literature (2nd Edition).

          And the prelaunch page is now live! You can sign up to get an email from Kickstarter as soon as the campaign launches.

          Visit the Prelaunch Page
          (free Kickstarter account required)

          This is one of my all-time favorite books, and I’ve had so much fun with this new edition — adding stories, writing make-your-own-problem prompts, sneaking a few teaching tips into the worked-out solutions, creating an almost-magical guide to helping kids reason their way through math problems.

          I’ve put together a free 14-page printable (pdf) “Word Problems Sampler” to give you a taste of things to come, including three ready-to-use student workbook pages.

          Check it out:

          Download the Sample Pages

          Help Your Kids Learn Math the Creative Way

          • Are you a parent trying to help your child learn math?
          • Or a teacher looking for creative ideas for your classroom?
          • Or a homeschooling parent hoping to enrich your student’s understanding?

          Then you’ll love Word Problems from Literature and the Word Problems Student Workbook because they prepare your children for school success, providing the tools they need to solve tough math problems.

          Feed your child’s mathematical imagination with puzzles inspired by classic books, from 2nd-grade stories based on Mr. Popper’s Penguins to prealgebra stumpers inspired by The Lord of the Rings.

          Hit the button to visit the prelaunch page and sign up for notifications:

          Get Notified

          6th Grade Minimalist Math Curriculum

          Posted on by Denise Gaskins

          For details on using a Minimalist Math Curriculum, see my earlier post How To Make Time for Exploration.

          If you’re teaching or homeschooling students in 6th grade, here’s the new minimalist curriculum link:

          As I mentioned in my earlier post, a minimalist curriculum can be a great way to free up time for playing math games and exploring enrichment activities (like these).

          How To Make Time for Exploration

          Posted on by Denise Gaskins

          Perhaps the most common objection I hear to using math games and enrichment activities is, “I don’t have the time. I can’t even get through our regular math book!”

          Well, here’s one possible solution: Use a “Minimalist Math” outline to guide your instruction, turning your regular textbook into a backup resource, teaching only the topics your children don’t already know, leaving more time free for exploration and playful discovery.

          Minimalist Math: Getting Down to Basics

          Michelle at ResearchParent.com condensed the elementary math curriculum down to 360 problems per year, just 10 per week.

          Take just a few puzzles each day, and talk math with your kids:

          • What do they notice in the problem?
          • Does it remind them of anything?
          • How might they try to figure it out?
          • Does it make them wonder about numbers, shapes, or patterns?

          Use colorful markers on a whiteboard for low-stress exploration. If your children can solve a problem and explain their reasoning, you don’t need to study that topic. When they get stuck, follow the Notice-Wonder-Create method described in this blog post series.

          If you’re both stymied, that’s when you pull out your regular textbook (or look the topic up online).

          Practice with Games

          Of course, children still need plenty of practice to master the math facts and solidify their knowledge.

          Since you’re not spending as much time on lessons and homework, you can plan on playing lots of math games. Games are a fun, low-stress way to firm up math skills.

          Check out My Best (Free) Math Games for All Ages, and follow the Math Game Monday posts on my blog.

          Read Library Books

          To enrich your child’s mind with the great ideas of mathematics and whet their appetite for learning, nothing beats a “living” math book.

          A living book is one that brings our minds into direct contact with the great ideas of life.

          Check out my Math with Living Books lists to get started, and ask your librarian for more suggestions.

          For Older Students

          Michelle’s Minimalist Math Curriculum goes through 6th grade (so far). But you could use the Corbettmaths 5-a-Day problems in the same way for older students.

          And for enrichment activities to fill up your free math time, I can’t think of a better resource for all ages than the NrichMaths website.

          “When I first started homeschooling, math became the most overwhelming, unpleasant part of our day. As someone who loves math, I didn’t want to continue on a path that was leading to such bad attitudes.

          “My Minimalist Math Curriculum covers the same breadth of topics as a traditional curriculum without all the repetition. You are welcome to use what I created in whatever way serves your family.”

          — Michelle, Research Parent
          Mathematics Activities for Kids

           
          * * *

          This blog is reader-supported.

          If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

          If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

          Which I am going to say right now. Thank you!

          “How To Make Time for Exploration” copyright © 2022 by Denise Gaskins. Image at the top of the post copyright © Aron Visuals, Andrew Ebrahim, and Melissa Askew via Unsplash.com.

          Playful Math Carnival #154: The Math Journaling Edition

          Posted on by Denise Gaskins

          Welcome to the 154th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

          Bookmark this post, so you can take your time browsing.

          There’s so much playful math to enjoy!

          By tradition, we start the carnival with a puzzle/activity in honor of our 154th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

          Try This Puzzle/Activity

          Since 154 is a nonagonal number, I think you might enjoy visiting some of my old “Adventures of Alexandria Jones” posts about figurate numbers:

          And then try this math journaling prompt: Build or draw your own nonagonal numbers — numbers built from 9-sided polygons.

          How many nonagonal numbers can you find? What do you notice? Does it make you wonder?

          Click here for all the mathy goodness!

          How To Respond to Your Child’s Math Writing

          Posted on by Denise Gaskins

          In previous posts, I encouraged parents, homeschoolers, and teachers to explore the world of math and introduced one of my favorite learning tools, the math journal. Then I shared several of my favorite types of journaling prompts to get your kids started writing about math.

          Math journal prompts offer a wide range of options for students to explore. Most of the prompts do not have a “right” or “wrong” answer. Our goal is to root around in some small corner of the world of math, to lift a stone and peek underneath it, just to see what we can find.

          The idea that being good at math means finding the right answers is a huge myth. Of course, many problems in math do have a single right answer. But even for those problems, the answer is not the real math of the problem.

          Math is all about thinking.

          It’s like taking a road trip. You may have a destination, but there are many paths you could take to get there. Different students may take different paths — they may think about the problem in different ways.

          It’s this reasoning that is the real math, and the right answer is just a side effect of reasoning well.

          Continue reading How To Respond to Your Child’s Math Writing

          5 Ways To Enrich Your Student’s Experience of Math

          Posted on by Denise Gaskins

          In previous posts, I encouraged parents, homeschoolers, and teachers to explore the world of math and introduced one of my favorite learning tools, the math journal.

          But you may be wondering, what can my students do with their journal? How do I find good math prompts?

          Here are five different ways your children can explore math through writing, classified by the type of reasoning involved.

          #1: Game Prompts

          Ask your children to play a number or strategy game and then write about it.

          Game prompts break through the idea that math is dull and boring. They help students develop a positive attitude toward math while practicing their number skills or strategic thinking.

          Continue reading 5 Ways To Enrich Your Student’s Experience of Math

          What Is a Math Journal?

          Posted on by Denise Gaskins

          In my previous post, I encouraged parents, homeschoolers, and teachers to think of math as a nature walk through an infinite world of wonder.

          A math journal is a record of your child’s journey through this world of mathematics.

          In a math journal, children explore their own concepts about numbers, shapes, and patterns through drawing or writing in response to a question. Journaling teaches them to see with mathematical eyes — not just to remember what we adults tell them, but to create their own math.

          Journaling brings math back into the liberal arts. It makes abstract ideas accessible and stretches children’s understanding, building math fluency and creating a solid foundation for future learning.

          Continue reading What Is a Math Journal?