# Algebraic Problem Solving

An employer recruits experienced and fresh workmen for his firm under the condition that he cannot employ more then 9 people.If 5 freshmen are recruited, how many experienced men have to be recruited ?

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At this stage, patterns and algebra problems often involve working backwards, using a process of elimination, trial and error and using inverse operations.

These strategies need to be explicitly taught to students.

Well, it's going to be w plus w plus 2w plus 2w. The perimeter of this garden is going to be equal to w plus 2w plus w plus 2w, which is equal to what?

But they also tell us that the actual numerical value of the perimeter is 60 feet. So this perimeter 6w must be equal to 60 if we assume that we're dealing with feet. We can divide both sides of this equation by 6 so that we have just a w on the left-hand side.

The problems below provide students with opportunities to explore these problem solving strategies and share their strategies with others.

For further information please see Newman’s error analysis Use Newman’s prompts as a whole class to model how to start thinking about solving the problem.So let's draw this garden here, Tina's garden. So if this is the width, then this is also going to be the width. And they tell us that the length of the garden is twice the width. In this GED Math: Quantitative, Arithmetic & Algebraic Problem Solving study guide are dozens of entertaining math video lessons developed by professional educators to ensure you have a quality understanding of number sense, decimals, fractions, data, functions, polynomials, geometry and more. This course is designed to prepare you for the GED Math exam, covering all of the topics outlined in the official test materials provided by the GED Testing Service.Our professional instructors created this comprehensive course to help you master these objectives.When you reach questions 3 and 4 that deal with how to work the problem out, ask students what problem solving approach they might take. Discuss with the students how they could use the process of elimination to assist in solving this problem.Use Newman’s prompts (PDF 41.18KB) as a whole class to model how to start thinking about solving the problem.The latter is symmetric; is ruled by “the logic of iff”; is syntactic, insofar concrete meaning have evaporated; its epistemological style is anti-arithmetic.But procedural thinking allows pupils to do concrete experiments and get feedbacks from the problematic-situation; and this, in the long run, is useful in order to jump to relational polarity, where more formal algebraic manipulations can be done.The mathematical language required needs to be modelled by the teacher and students need to be provided with opportunities to talk through their thinking.Students need experiences in both solving problems and posing their own problems.

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