# What is pre-algebra?

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What does a child study in their "pre-algebra" year?

Tara

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The ones I have seen cover all the fundamentals so that the student has a good foundation (which is essential before heading into algebra). Then it has covered integers and some of the less complicated algebra concepts.

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Aren't Fractions and Decimals also integral parts of Pre-Algebra?

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The ones I have seen cover all the fundamentals

And what would one consider "all the fundamentals"?

Tara

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And what would one consider "all the fundamentals"?

Tara

At least all four operations, fractions and decimals.

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Aren't Fractions and Decimals also integral parts of Pre-Algebra?

Definitely!

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I was just reading the NCTM standards for middle grades (6-8) today, and thinking about what makes a student "algebra ready" as well as numerically fluent enough for high school maths. :)

The NCTM standards list expectations for middle school math content within the following ten strands:

• Number and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability
• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation

Students in the middle grades move from working with whole numbers and primarily addition and subtraction activities in the elementary grades, to working with rational numbers and integers, and primarily multiplication and division activities. Before algebra, students move beyond simple problem solving with ratios, proportions, and percentages, to broader, more complex concepts of proportional relationships, including functions and linear relationships. Middle grades students need to be able to reason proportionally and apply this reasoning to a variety of situations. Middle grades students are expected to master algebra skills and concepts and to incorporate algebraic thinking throughout their lessons. PreAlgebra looks more like "Algebra 1 lite" than arithmetic. Middle school math standards expect that students have the ability to represent and analyze relationships symbolically and, as with proportional reasoning, can apply algebraic thinking to a variety of situations.

The reasoning abilities of middle grades students should be fostered at all times. Middle grades math teachers can help improve their students' reasoning abilities and address middle school math standards by conducting lessons that provide them ample opportunity to question, examine, conjecture, and experiment. Additionally, teachers should expect their students to explain their thinking and reasoning throughout every math activity. Middle school math teachers should try to incorporate the use of conjectures and proving or disproving these conjectures in almost every lesson. Middle grades students need many opportunities to explore various ways to represent mathematical information. Students should be comfortable using symbolic (formulas, equations, expressions), tabular, and graphical representations. Middle grades students should also be able to use coordinate graphs to represent and to analyze a variety of relationships. I believe that PreAlgebra is the perfect time to teach a student to graph on graph paper, so that they can quickly move to the graphing calculator as a tool in Algebra. They should gain experience using variables to represent numerical relationships and to show the interdependence of quantities. As with conjectures, try to incorporate the use of symbolic and graphical representations in as many lessons as possible.Middle grades students need to be adept at identifying, describing, extending, and representing patterns. They should be exposed to a wide variety of patterns. The types of patterns that students are exposed to in the middle grades needs to increase in complexity and variety. Students should start to spend more time exploring, analyzing, and representing functions and linear and non-linear relations. If you can bring out those types of relations in weather patterns, stock market reports, rabbit populations, or any other data set you can analyze in your own backyard, even better.

PreAlgebra is a very important time in a student's course of study. But it's not necessarily just one book, or one year. It's the two or three years prior to further study of linear and quadratic functions, inequalities, and probability distributions. The more the student reads, thinks and learns in *all* areas of life, with particular emphasis with number fluency, the better her algebra experience will be.

Lori

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What does a child study in their "pre-algebra" year?

Tara

Wondering what you're looking for here.

To me, pre-algebra is just making sure the student is ready for algebra. And sometimes it's kinda like keeping them in a holding pattern until they're mentally ready to delve into algebra full-time.

My son spent 7th grade doing Singapore 6A/B and I feel it fully prepared him for algebra in 8th. The things I was looking for:

- fractions are down solid, since they are big in algebra

- he's been introduced to an unknown variable

- he isn't showing any signs of needing more time on "basics" like math facts, translating in and out of percents/decimals/fractions, solving geometry problems, or ratios/rates/miles per hour type calculations

- he's ready to do more math problems each day

- he's ready to learn new things independently if need be

- he's able to solve problems where multiple things are going on at the same time

I personally decided to add one thing to his pre-algebra year (I added negative numbers to Singapore 6), but really I think it's okay if the "pre-algebra" year doesn't cover every single thing, as long as the maturity is there to handle new concepts.

Julie

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Wondering what you're looking for here.

I'm not looking for anything specific. I just see people talking about their kid's pre-algebra year and I didn't know what they meant by that (aside from the obvious, the year before they start algebra).

Tara

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Wondering what you're looking for here.

To me, pre-algebra is just making sure the student is ready for algebra. And sometimes it's kinda like keeping them in a holding pattern until they're mentally ready to delve into algebra full-time.

Julie

This is a lot of what pre-algebra is to me.

We are stalling. We will spend some time reviewing fractions, then spend a good deal of time working on simple equations and the logic of equations. I will also be going over more negative numbers as this has barely been touched on in previous curriculums.

In truth, mathmatically ds could go to algebra any time, but I don't think his brain and logic are ready. Pre-algebra is just taking a year to shore up the skills if they need it or stall for mental and emotional growth, thats where we are. It can serve different purposes for different kids and it can be skipped if the child is really ready to move on.

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I'm not looking for anything specific. I just see people talking about their kid's pre-algebra year and I didn't know what they meant by that (aside from the obvious, the year before they start algebra).

Tara

Well, it looks like you've got quite a few ideas on it, then! I agree that it's a pretty ambiguous title. Just think of it as another class called "Math."

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