Tuesday, February 8, 2011

Everyday Math Unit 6

In fourth and Fifth Grade Everyday Mathematics, your child worked with addition and subtraction of positive and negative numbers. In this unit, students use multiplication patterns to help them establish the rules for multiplying and dividing with positive and negatieve numbers. They also develop and use an algorithm for the division of fractions.

In the rest of the unit, your child will explore beginning algebra concepts. First, the class reviews how to determine whether a number sentence is true or false. This involves understanding what to do with numbers that are grouped within parentheses and knowing in what order to calculate if the groupings of numbers are not made explicit by parentheses.

Students then solve simple equations by trial and error to reinforce what it means to solve an equation-to replace a variable with a number that will make the number sentence true.

Next, they solve pan-balance problems, first introduced in Fifth Grade, to develop a more systematic approach to solving equations.

Students learn that each step in the solution of a pan-balance problem can be represented by an equation, thus leading to the solution of the original equation. You might ask your child to demonstrate how pan-balance problems work.

Finally, your child will learn how to solve inequalities-number sentences comparing two quantities that are not equal. You can see examples of these problems on our practice test for unit 6. You can also practice all of these skills in Mr. Hartwell's ultimate hotlist.

The lessons of Unit 6 bridge the gap between arithmetic and algebra. The unit's first objective is to present how the meaning and the relationships of the four operations are presented across the set of rational numbers. The second objective of the unit is to review and extend previous work with equations and inequalities. Unit 6 has four main areas of focus:

* To review multiplication of fractions and mixed numbers.
* To introduce an algorithm for division of fractions.
* To perform basic operations with positive and negative numbers.
* To review and model equation-solving techniques.

Important Vocabulary
cover-up method
An informal method for finding the solution of an open sentence by covering up a part of the sentence containing a variable.

Division of Fractions Property A property of dividing that says division by a fraction is the same as multiplication by the reciprocal of the fraction. Another name for this property is the "invert and multiply rule."

equivalent equations Equations with the same solution. For example, 2+x=4 and 6+x=8 are equivalent equations with solution 2.

inequality A number senteence with a relation symbol other than =.

integer A number in the set {...,-4, -3, -2, -1, 1, 2, 3, 4, 4, ...}. A whole number or its opposite, where 0 is its own opposite.

Multiplication Property of -1 A property of multiplication that says multiplying any number by -1 gives the opposite of the number. For example, -1*5=-5 and -1*-3=-(-3)=3. Some calculators apply this property with a [+/-] key that toggles between a positive and negative value in the display.

order of operations Rules that tell the order in which operations in an expression should be carried out. The conventional order of operation is:
1. Do the operations inside groupinig symbols. Work from the innermose set of grouping symbols outward. Inside grouping symbols, follow Rules 2-4.
2. Calculate all the expressions with exponents.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Order of operations can be rememberd by the acronym P.E.M.D.A.S. P(parentheses) E(exponents) M(multiplication) D(division) A(addition) S(subtraction).

reciprocals Two numbers whose product is 1.

trial-and-error method A method for finding the solution of an equation by trying a sequence of test numbers.

In this unit, students will also begin Hands On Equations. This is a great way to learn algebra in a concrete way! The flipchart that we use in class can be found here. Make sure you download the program to view it first.

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