Correlation to the Standards

Topic in Algebra

1.0

a.  What is an integer……. And ……What other kinds of

      numbers are there?

1.     Elephants Child Story by Rudyard Kipling

            2.  Math on the Spot  (see teachers notes)

1.0

b. Order  and comparison of the set of integers

1.     Johnny’s Story (see teachers notes)

2.0

c. Addition with integers

          1. Race Cars (see teachers notes)

          2. Addition Table with Integers  (see teachers notes)

2.0

d. Subtraction with integers

1.     Postman Story  (see teachers notes)

1.1

e. Multiplication with Integers

         1.Building a Model for Multiplication –

             Using Base Ten Blocks – * PGS 6-22

         2.Developing Understanding and Skills –

            Display Multiplication and Horizontal Multiplication –

            * PGS 27-49

         3.Quadratic Expressions and Equations In Base Ten –

            * PGS 56-70

1.1

f. Division with integers

1.1

g. The Distributive property

1.     The Distributive Property and the Multiplication of   

     Mixed Numbers - * PGS 91-93

Correlation to the Standards

Topic in Algebra

1.1

h. Order of operations

1.1

i. Properties of real numbers

        1.Commutative Property of addition and multiplication

        2.Associative Property of addition and multiplication

        3.Additive Inverse of a sum

        4.Multiplicative Inverse of a product

2.0

j. Midpoint of two points

       1.Graphically

       2.Numerically

3.0

k. Absolute Value

2.0

l. Numerical Square Roots

     1. Geoboard Formulas – Squares – Bias Squares

            and Parallelograms (see teachers notes)

     2.  Ptyhagorean Theorem Practice ( see teachers notes)

Correlation to the Standards

Topic in Algebra

4.0

a. Real world situations using algebraic expressions

1.     Paper Clip Chains ** PGS 44-47

4.0

b. Evaluation of algebraic expressions

1.     Magic Math (see teachers notes)

4.0

c. Solving linear equations with one variable 

             1.one – step

                Rates – Mixing Measures (cm and in)

                ** PGS 177-179

              2.two – steps

5.0

d. Solving linear equations having multiple amounts of one variable

              1.one – step

              2.two – steps

6.0

e. Combining like terms to solve linear equations in the form:   

   aX + b = cX + d where a is an integer and b,c and x are

   real numbers

6.0

f. Solving linear equations involving fractional amounts of a variable

6.0

g. Combine processes to solve linear equations of the form

    aX + b = c where a,b,c,x and d are real numbers

Correlation to the Standards

Topic in Algebra

6.0

a. Model linear relationships in the real world

1.     Time Trials  - ** PGS 163-166

2.  Let’s Party (see teachers notes)

6.0

b. Investigate linear relationships in geometry

        1. What ‘s Symmetry!  (see teachers notes)

2. Easy As Pie  (see teachers notes)

3. Arranging Tables   (see teachers notes)

4. Hinged  (see teachers notes)

Building            5. Blocks  (see teachers notes)

6.0

c. Ratio and proportion

1.       Rectangle Ratios - ** PGS 77-82

6.0

d. Linear and arithmetic sequences

         1. That Figures – Set 1,2,3 and 4  (see teachers notes)

2. Roller Coaster Sums  (see teachers notes)

          3.  Stacking Cups - *** PGS 160-163

9.0

e. Transform linear expressions in X and Y ( cX + dY = e) to show X in terms of Y or Y in terms of X

1.     Give Me Five  (see teachers notes)

f. Compare vertical change (change in Y or dependent variable) to the horizontal change (change in x or independent variable) on a graph

1.     Bars and Graphs  (see teachers notes)

Correlation to the Standards

Topic in Algebra

g. Exploration of minimal numerical conditions needed to determine the specific graph and algebraic form of a linear function

1.     Functioning with Knots - *** PGS  131-137

         2. Rectangle Jamboree - *** PGS 178-180

h. Explore the role of the constant b in Y = ax + b, where a, b, x and y are real numbers

1.     U571 – How Deep Did They Go? Parts 1,2 and 3

(see teachers notes)

i. Fit linear functions / curves to given sets of points on a grid and fit algebraic forms to those linear curves in real world situations

       1.  Dropped (dropping balls) -  (see teachers notes)

2.     High Ball (see teachers notes)

3.     Have Gravity:  Must Travel -  (see teachers notes)

4.     The Ideal B.A.S.E. Jump -  (see teachers notes)

j. Given the expression for the general or ‘n-th” term of a  

   linear sequence and its numerical value form some “n”, find 

    the value of n.

       1.  Color Tiles Parts 1,2, and 3  -  (see teachers notes)

k. Locate points in disjoint regions formed by one or two

     given boundary points on a number line.

     1.  Triangles of Squares (see teachers notes)

6.0

l. Solve linear inequalities in one variable and graph the

     solution.

Correlation to the Standards

Topic in Algebra

a. Concept of exponents (positive, negative and zero)

b. Properties of exponents

c. Combining like terms, using linear and quadratic terms in one variable

d. Finding the product of a 2^nd degree polynomial

e. Graphing points (x, P(x)) where x is a measure of length for the 

        polynomial region having “area”: 

        P(x) = ax² + bx + c where x, a, b, and c are real numbers.

f. Factoring polynomials of second degree in one variable

g. Investigation of quadratic sequences of figurate numbers to     

    generate quadratic functions:  find and expression for the

   “n-th” term

Correlation to the Standards

Topic in Algebra

h. Explore quadratic functions and effects on their graphs when

    coefficients and constants are varied

i. Given the expression for the “n-th” term of a polynomial

   (quadratic) sequence and its numerical value for some N, find

    the value of N.

j. Solve quadratic equations in the form ax² + bx + c = 0,

    using the real number factor property:  MN = 0 which

    implies M = 0 or N= 0

k. Solve quadratic equations of the form:  (aX + b)² = c, where x,  

     a, b, and c are real numbers and c³0

l. Completing the square

Correlation to the Standards

Topic in Algebra

a. Transforming a linear inequality in two variables x and y:

    aX + bY > c or aX + < c, so that one variable is in terms 

    of the other

b. Locate points in disjoint regions formed by one or two

   given linear boundaries in a plane and compare them to

    points on the boundaries (two dimensional space)

c. Solve systems of linear inequalities in two variables by

    graphical methods

d. Solve systems of linear functions in two variables by

     graphical methods

e. Solve systems of linear functions in two variable by

    combining like sides of equations

f. Solve systems of linear functions in two variables by

   substitution methods

Correlation to the Standards

Topic in Algebra

g. Develop the concepts for the Pythagorean Theorem for right

    triangles and apply to real world situations

h. Investigate exponential functions in the form y = b^x, where b is

    a positive constant, and b, x, and y are real numbers

i. Investigate inverse variation using the form y =  k/x, where k is a positive integer and x and y are real numbers with x ¹ 0