Bar diagrams

PUFM 1.4 Subtraction

Posted on June 11, 2012September 26, 2015 by Denise Gaskins

Photo by Martin Thomas via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

When adding, we combine two addends to get a sum. For subtraction we are given the sum and one addend and must find the “missing addend”.

— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers

Notice that subtraction is not defined independently of addition. It must be taught along with addition, as an inverse (or mirror-image) operation. The basic question of subtraction is, “What would I have to add to this number, to get that number?”

Inverse operations are a very fundamental idea in mathematics. The inverse of any math operation is whatever will get you back to where you started. In order to fully understand a math operation, you must understand its inverse.

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The Problem with Manipulatives

Posted on March 2, 2011September 26, 2015 by Denise Gaskins

You may have seen this video making the edu-blog rounds:

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Hobbit Math: Elementary Problem Solving 5th Grade

Posted on June 7, 2010December 6, 2016 by Denise Gaskins

[Photo by OliBac. Visit OliBac’s photostream for more.]

The elementary grades 1-4 laid the foundations, the basics of arithmetic: addition, subtraction, multiplication, division, and fractions. In grade 5, students are expected to master most aspects of fraction math and begin working with the rest of the Math Monsters: decimals, ratios, and percents (all of which are specialized fractions).

Word problems grow ever more complex as well, and learning to explain (justify) multi-step solutions becomes a first step toward writing proofs.

This installment of my elementary problem solving series is based on the Singapore Primary Mathematics, Level 5A. For your reading pleasure, I have translated the problems into the world of J.R.R. Tolkien’s classic, The Hobbit.

[Note: No decimals or percents here. Those are in 5B, which will need an article of its own. But first I need to pick a book. I’m thinking maybe Naya Nuki…]

Printable Worksheet

In case you’d like to try your hand at the problems before reading my solutions, I’ve put together a printable worksheet:

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Best Articles about Solving Word Problems

Posted on May 24, 2010August 12, 2015 by Denise Gaskins

[Photo by scui3asteveo.]

~~I’m still working on that Best of Blog page.~~ [It’s done! :D] Here are the 20 best Let’s Play Math! blog articles about solving word problems (also known as story problems)…

Solving Word Problems

More recent posts tagged ‘Word problems’

Bar Diagrams Help Students Think

More recent posts tagged ‘Bar diagrams’

Narnia Math: Elementary Problem Solving 4th Grade

Posted on December 11, 2009August 12, 2015 by Denise Gaskins

[Photo by armigeress.]

In 4th grade, math problems take a large step up on the difficulty scale. Students are more mature and can read and follow more complex stories. Multi-step word problems become the new norm, and proportional relationships (like “three times as many”) show up frequently. As the year progresses, fractions grow to be a dominant theme.

As a math teacher, one of my top goals is that my students learn to solve word problems. Arithmetic is (relatively) easy, but many children struggle in applying it to “real world” situations.

In previous posts, I introduced the problem-solving tools of word algebra and bar diagrams, either of which can help students organize the information in a word problem and translate it into a mathematical calculation. The earlier posts in this series are:

In this installment, I will continue to demonstrate the problem-solving tool of bar diagrams through a series of ten 4th grade problems based on the Singapore Primary Math series, level 4A. For your reading pleasure, I have translated the problems into the universe of a family-favorite story by C. S. Lewis, The Lion, the Witch and the Wardrobe.

Update

I’ve put the word problems from my elementary problem solving series into printable worksheets:

Word Problems from Literature

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Elementary Problem Solving: Review

Posted on October 23, 2009September 26, 2015 by Denise Gaskins

[Bill Watterson identifies the trouble with math problems, through the eyes of Calvin and Hobbes.]

It’s time to revive and (hopefully!) finish my long-neglected series on solving word problems in elementary mathematics. I’ve been having fun making up the problems, so now I just have to write the posts. Coming up soon:

4th grade math in The Lion, the Witch and the Wardrobe.
5th grade math in The Hobbit.
6th grade math in… I haven’t decided yet. Any suggestions?

Since it has been more than two years since the last entry, however, I wanted to take a few minutes to recap our progress so far and to refer new readers back to the original posts: