The Value of Guess and Check The Value of Guess and Check, Mathematics Teaching in the Middle School, March 2010, p Providing students a structure for employing the guess-and-check method for solving word problems leads to an understanding of quantitative relationships and builds a bridge to algebra. P 393

Connection NCTM Algebra Standard says that middle grades should enable students to “represent and analyze mathematical situations and structures using algebraic symbols. Guess and check is a powerful problem- solving strategy that can connect a conceptual understanding of word problems with a symbolic representation. P 398

Let’s Begin Coby is building a rectangular playpen for his dog, Max. He has 48 feet of fencing and plans to make the length of the pen 6 feet longer than the width. What will be the dimensions of Max’s playpen? Guess and check

Structuring Guess and Check Arrange “guesses” and accompanying work in a table. Begin – What information is given? – What am I trying to find? – What do I need to know before I can do anything? What am I going to guess to start with? Once a guess is made other columns are built.

The Table Guess Width LengthPerimeter48 Check 12182(12+18) =60To high

New Questions What is the relationship between the quantities in the word problem? Now that I have made a guess, what do I know? How can I use the results from my previous guess to make a better guess? How do I know if my next guess should be greater or less than my previous guess?

The Table-Another Guess Guess Width LengthPerimeter48 Check 12182(12+18) =60To high

Guess and check builds a bridge between finding a concrete solution to the problem and creating a more abstract equation to represent the problem.

The Table-Another Guess and a General Case Guess Width LengthPerimeter48 Check 12182(12+18) =60To high

Getting Started What information is given? What am I trying to find? What do I need to know before I can do anything else? Create a table Check the solution – Adjust the next guess by the final outcome.

Try this one using a table A farmer has 12 animals, all chickens and horses. If the animals have a total of 34 legs, how many chickens are there?

A Possible Table Guess # of Chickens # of horses # of chicken legs # of horse legs Total # of legs Guess (34)

Looking Back Emphasis is on sense making over merely applying rote computational strategies. Guess and check gets students over the hurdle of not knowing what the problem says, what it means or how to get started. Using a “key word” approach promotes a “plug and chug” solution with limited understanding of underlying relations within the problem. – Bob has three times as many books as Mary. – Is it 3B = M or 3M = B

Remember Arrange guesses Keep track of guess and other numbers in a table Use the results from previous guess to make a better next guess Guess and check is as much about developing mathematical reasoning and problem solving as it is about finding a correct solution.

Guess and Check Builds a bridge between finding a concrete solution to the problem and creating a more abstract equation to represent the problem. Is a powerful problem-solving strategy that connects a conceptual understanding of world problems with a symbolic representation. Is simply one technique in the toolbox Is one strategy, the most important part is to know when to employ the tool and when not to employ the tool.

Take Time To Engage in a frequent analysis of quantitative relationships so as to describe and represent embedded relationships. Emphasize sense making over merely applying rote computation strategies

Another Problem Katie is thinking of three numbers. The greatest is three times as large as the least, or smallest number. The middle number is 5 more than the smallest number. The sum of the three numbers is 65. What are the three numbers?

Least #Middle #Greatest #SumCheck

Some birds are on two branches of a tree. If a bird goes down a branch the numbers are the same, if the bird goes up a level there are twice as many on the top as bottom.