School City of Hobart
School City of Hobart Mathematics

Mathematics - Mathematics - Grade 8

Mathematics - Grade 8

In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives - operating computer equipment, planning timelines and schedules, reading and interpreting data, comparing prices, managing personal finances, and completing other problem-solving tasks. What they learn in mathematics and how they learn it will provide an excellent preparation for a challenging and ever-changing future.


Number Theory

    Number Sense
The learner will be able to know the properties of rational* and irrational* numbers expressed in a variety of forms. They understand and use exponents*, powers, and roots. * rational numbers: numbers that can be written as a ratio of two integers* (e.g., 1/2, 5/6, 23/9) * integers: ..., -3, -2, -1, 0, 1, 2, 3, ... * irrational numbers: numbers that cannot be written as a ratio of two integers *exponent: e.g., the exponent 4 in 3 4 tells you to write four 3s and compute 3 x 3 x 3 x 3 .
Strand Source
Number Sense IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.1
The learner will be able to read, write, compare, and solve problems using decimals in scientific notation*. Example: Write 0.00357 in scientific notation. * scientific notation: a shorthand way of writing numbers (e.g., 300,000 = 3 x 10 5, 0.0000005 = 5 x 10 -7) .
Strand Source
Number Sense IDOE
Assessment Resources
- Scientific Notation, McGraw-Hill, Form A, skill test [CTB].  
- Scientific Notation, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.2
The learner will be able to know that every rational number is either a terminating or repeating decimal and that every irrational number is a non-repeating decimal. Example: Recognize that 2.375 is a terminating decimal, 5.121212... is a repeating decimal, and that ~ = 3.14159265... is a non-repeating decimal. Name a rational number. Explain your reasoning. .
Strand Source
Number Sense IDOE
Assessment Resources
- Properties of Rational and Irrational Numbers, McGraw-Hill, Form A, skill test [CTB].  
- Properties of Rational and Irrational Numbers, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.3
The learner will be able to understand that computations with an irrational number and a rational number (other than zero) produce an irrational number. Example: Tell whether the product of 7 and ~ is rational or irrational. Explain how you know that your answer is correct. .
Strand Source
Number Sense IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.4
The learner will be able to understand and evaluate negative integer* exponents. Example: Write 2-3 as a fraction. * integers: ..., -3, -2, -1, 0, 1, 2, 3,.
Strand Source
Number Sense IDOE
Assessment Resources
- Negative Integer Exponents, McGraw-Hill, Form A, skill test [CTB].  
- Negative Integer Exponents, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.5
The learner will be able to use the laws of exponents for integer exponents. Example: Write 2 2 x 2 3 as 2 x 2 x ... and then as a single power of 2. Explain what you are doing. .
Strand Source
Number Sense IDOE
Instructional Resources
- Solving With Order, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Solving With Order.pdf
Assessment Resources
- Laws of Exponents for Integer Exponents, McGraw-Hill, Form A, skill test [CTB].  
- Laws of Exponents for Integer Exponents, McGraw-Hill, Form B, skill test [CTB].  
- Solving With Order, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Solving With Order.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.6
The learner will be able to use the inverse relationship between squaring and finding the square root of a perfect square integer. .
Strand Source
Number Sense IDOE
Assessment Resources
- Inverse Relationship Square Roots, McGraw-Hill, Form A, skill test [CTB].  
- Inverse Relationship Square Roots, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.1.7
The learner will be able to calculate and find approximations of square roots. Example: For an integer that is not a perfect square, find the two integers (one larger, one smaller) that are closest to its square root and explain your reasoning. .
Strand Source
Number Sense IDOE
Assessment Resources
- Approximations of Square Roots, McGraw-Hill, Form A, skill test [CTB].  
- Approximations of Square Roots, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Rational and Irrational Numbers

    Computation
The learner will be able to compute with rational numbers* expressed in a variety of forms. They solve problems involving ratios, proportions, and percentages. * rational numbers: numbers that can be written as a ratio of two integers (e.g., 1/2, 5/6 , 23/9).
Strand Source
Problem Solving IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.2.1
The learner will be able to add, subtract, multiply, and divide rational numbers (integers*, fractions, and terminating decimals) in multi-step problems. Example: -3.4 + 2.8 x 5.75 = ?, 1 4/5 + -3/8 x 2 2/9 = ?, 81.04 x 17.4 - 2.79 = ? * integers: ..., -3, -2, -1, 0, 1, 2, 3, ... .
Strand Source
Problem Solving IDOE
Instructional Resources
- Basic Counting Principle, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Basic Counting Principle.pdf
Assessment Resources
- Four Operations to Solve Problems, McGraw-Hill, Form A, skill test [CTB].  
- Four Operations to Solve Problems, McGraw-Hill, Form B, skill test [CTB].  
- Basic Counting Principle, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Basic Counting Principle.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.2.2
The learner will be able to solve problems by computing simple and compound interest. Example: You leave $100 in each of three bank accounts paying 5% interest per year. One account pays simple interest, one pays interest compounded annually, and the third pays interest compounded quarterly. Use a spreadsheet to find the amount of money in each account after one year, two years, three years, ten years, and twenty years. Compare the results in the three accounts and explain how compounding affects the balance in each account. .
Strand Source
Problem Solving IDOE
Assessment Resources
- Simple and Compound Interest, McGraw-Hill, Form A, skill test [CTB].  
- Simple and Compound Interest, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.2.3
The learner will be able to use estimation techniques to decide whether answers to computations on a calculator are reasonable. Example: Your friend says that 15% of $25 is $375. Without solving, explain why you think the answer is wrong. .
Strand Source
Problem Solving IDOE
Assessment Resources
- Estimation to Check Calculator Results, McGraw-Hill, Form A, skill test [CTB].  
- Estimation to Check Calculator Results, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.2.4
The learner will be able to use mental arithmetic to compute with common fractions, decimals, powers, and percents. Example: Find 20% of $50 without using pencil and paper. .
Strand Source
Problem Solving IDOE
Assessment Resources
- Mental Math Fraction Decimal Power Percent, McGraw-Hill, Form A, skill test [CTB].  
- Mental Math Fraction Decimal Power Percent, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Algebraic Concepts

    Algebra and Functions
The learner will be able to solve simple linear equations and inequalities. They interpret and evaluate expressions involving integer* powers. They graph and interpret functions. They understand the concepts of slope* and rate. *integers: ... -3, -2, -1, 0, 1, 2, 3,.
Strand Source
Algebraic Concepts IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.1
The learner will be able to write and solve linear equations and inequalities in one variable, interpret the solution or solutions in their context, and verify the reasonableness of the results. Example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be least $100. Write an inequality for the number of sales you need to make, solve it, and check that your answer is reasonable. .
Strand Source
Linear Equations IDOE
Instructional Resources
- Equations & Inequalities, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8equation_inequality.pdf
Assessment Resources
- Write Solve Linear Equations Inequalities, McGraw-Hill, Form A, skill test [CTB].  
- Write Solve Linear Equations Inequalities, McGraw-Hill, Form B, skill test [CTB].  
- Equations & Inequalities, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8equation_inequality.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.2
The learner will be able to solve systems of two linear equations using the substitution method and identify approximate solutions graphically. Example: Solve the system. 2x + 3y = 6 y = 0 .
Strand Source
Linear Equations IDOE
Instructional Resources
- Equations & Inequalities, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8equation_inequality.pdf
Assessment Resources
- Two Linear Equations Using Substitution, McGraw-Hill, Form A, skill test [CTB].  
- Two Linear Equations Using Substitution, McGraw-Hill, Form B, skill test [CTB].  
- Equations & Inequalities, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8equation_inequality.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.3
The learner will be able to interpret positive integer powers as repeated multiplication and negative integer powers as repeated division or multiplication by the multiplicative inverse. Example: Use a spreadsheet to explore the relationship between positive and negative integer powers by making a table of values of powers of 3, from 3 -5 to 3 5. .
Strand Source
Exponents IDOE
Instructional Resources
- Solving With Order, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Solving With Order.pdf
Assessment Resources
- Positive and Negative Integer Powers, McGraw-Hill, Form A, skill test [CTB].  
- Positive and Negative Integer Powers, McGraw-Hill, Form B, skill test [CTB].  
- Solving With Order, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Solving With Order.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.4
The learner will be able to use the correct order of operations to find the values of algebraic expressions involving powers. Example: Use a scientific calculator to find the value of 3(2x + 5)2 when x = -35. .
Strand Source
Order of Operations IDOE
Instructional Resources
- Solving With Order, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Solving With Order.pdf
Assessment Resources
- Order of Operations Value of Expressions, McGraw-Hill, Form A, skill test [CTB].  
- Order of Operations Value of Expressions, McGraw-Hill, Form B, skill test [CTB].  
- Solving With Order, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Solving With Order.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Functions

    8.3.5
The learner will be able to identify and graph linear functions and identify lines with positive and negative slope. Example: Draw the graphs of y = 2x - 1, y = 3x - 1, y = -2x - 1, y = -3x - 1. Find the slope of each graph. What do you notice? .
Strand Source
Graphing Functions IDOE
Assessment Resources
- ID and Graph Linear Functions, McGraw-Hill, Form A, skill test [CTB].  
- ID and Graph Linear Functions, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.6
The learner will be able to find the slope of a linear function given the equation and write the equation of a line given the slope and any point on the line. Example: Write an equation of the line with slope 2 and y-intercept -4. .
Strand Source
Functions IDOE
Assessment Resources
- Final Slope of Linear Function Write Functions, McGraw-Hill, Form A, skill test [CTB].  
- Final Slope of Linear Function Write Functions, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.7
The learner will be able to demonstrate an understanding of rate as a measure of one quantity with respect to another quantity. Example: A car moving at a constant speed travels 90 km in 2 hours, 135 km in 3 hours, 180 km in 4 hours, etc. Draw a graph of distance as a function of time and find the slope of the graph. Explain what the slope tells you about the movement of the car. .
Strand Source
Functions IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.8
The learner will be able to demonstrate an understanding of the relationships among tables, equations, verbal expressions, and graphs of linear functions. Example: Write an equation that represents the verbal description: "the perimeter of a square is four times the side length." Construct a table of values for this relationship and draw its graph. .
Strand Source
Algebraic Functions IDOE
Assessment Resources
- Relationships Among Tables Equations ETC, McGraw-Hill, Form A, skill test [CTB].  
- Relationships Among Tables Equations ETC, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.9
The learner will be able to represent simple quadratic functions using verbal descriptions, tables, graphs, and formulas and translate among these representations. Example: Draw the graph of y = x 2, y = 2x 2, and y = 3x 2. Describe their similarities and differences. .
Strand Source
Absolute Value/Quadratic Functions IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.3.10
The learner will be able to graph functions of the form y = nx 2 and y = nx 3 and describe the similarities and differences in the graphs. Example: Draw the graphs of y = 2x 2 and y = 2x 3. Explain which graph shows faster growth. .
Strand Source
Graphing Functions IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Geometry

    Geometry
The learner will be able to deepen their understanding of plane and solid geometric shapes and properties by constructing shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems.
Strand Source
Figures: Identify IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.4.1
The learner will be able to identify and describe basic properties of geometric shapes: altitudes*, diagonals, angle and perpendicular bisectors*, central angles*, radii, diameters, and chords*. Example: Describe a central angle of a circle in words and draw a diagram. *altitude: line segment from vertex of triangle to meet the line containing the opposite side in a right angle * perpendicular bisector: line (or ray or line segment) at right angles to given line segment and dividing it in half *central angle: angle formed by joining two points on a circle to the center *chord: line segment joining two points on a circle .
Strand Source
Figures: Attributes IDOE
Instructional Resources
- Simple Constructions, web link [Textbook].  http://www.hobart.k12.in.us/cs/script.pl?submit=Pr-XvMCoAMgAAHB25HU Transpariencies: http://www.hobart.k12.in.us/district/l_math/8CopyingAngle.ppt http://www.hobart.k12.in.us/district/l_math/8BisectingSegment.ppt http://www.hobart.k12.in.us/district/l_math/8BisectingAngle.ppt http://www.hobart.k12.in.us/district/l_math/8copysegment.ppt
- Fun with Circle Graphs, web link [Lesson Plan].  http://www.hobart.k12.in.us/CS/script.pl?submit=fVEjRH8AAAEAAGN8F9oAAAAP
Assessment Resources
- Properties of Geometric Shapes, McGraw-Hill, Form A, skill test [CTB].  
- Properties of Geometric Shapes, McGraw-Hill, Form B, skill test [CTB].  
- Fun with Circle Graphs, web link [Lesson Plan].   http://www.hobart.k12.in.us/CS/script.pl?submit=fVEjRH8AAAEAAGN8F9oAAAAP
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.4.2
The learner will be able to perform simple constructions, such as bisectors of segments and angles, copies of segments and angles, and perpendicular segments. Describe and justify the constructions. Example: Explain the procedures used to construct the three angle bisectors of a triangle. .
Strand Source
Constructions IDOE
Instructional Resources
- Simple Constructions, web link [Textbook].  http://www.hobart.k12.in.us/cs/script.pl?submit=Pr-XvMCoAMgAAHB25HU Transpariencies: http://www.hobart.k12.in.us/district/l_math/8CopyingAngle.ppt http://www.hobart.k12.in.us/district/l_math/8BisectingSegment.ppt http://www.hobart.k12.in.us/district/l_math/8BisectingAngle.ppt http://www.hobart.k12.in.us/district/l_math/8copysegment.ppt
Assessment Resources
- Simple Construction, McGraw-Hill, Form A, skill test [CTB].  
- Simple Construction, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.4.3
The learner will be able to identify properties of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more figures intersect in a plane or in space. Example: Find two lines in your classroom that are not parallel, yet do not meet. .
Strand Source
Three-Dimensional Solids IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.4.4
The learner will be able to draw the translation (slide), rotation (turn), reflection (flip), and dilation (stretches and shrinks) of shapes. Example: Draw a rectangle and slide it 3 inches horizontally across your page. Then rotate it clockwise through 90º about the bottom left vertex. Draw the new rectangle in a different color. .
Strand Source
Translations IDOE
Assessment Resources
- Transformations, McGraw-Hill, Form A, skill test [CTB].  
- Transformations, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.4.5
The learner will be able to use the Pythagorean Theorem and its converse to solve problems in two and three dimensions. Example: Measure the dimensions of a shoe box and calculate the length of a diagonal from the top right to the bottom left of the box. Measure with a string to evaluate your solution. .
Strand Source
Geometric Proofs/Theorems IDOE
Assessment Resources
- Pythagorean Theorem, McGraw-Hill, Form A, skill test [CTB].  
- Pythagorean Theorem, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Measurement

    Measurement
The learner will be able to convert between units of measure and use rates and scale factors to solve problems. They compute the perimeter, area, and volume of geometric objects. They investigate how perimeter, area, and volume are affected by changes of scale.
Strand Source
Measurement Concepts IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.5.1
The learner will be able to convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system. Example: The area of a hall is 40 square yards. What is the area in square feet? .
Strand Source
Converting IDOE
Assessment Resources
- Attributes within Systems, McGraw-Hill, Form A, skill test [CTB].  
- Attributes within Systems, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.5.2
The learner will be able to solve simple problems involving rates and derived measurements for attributes such as velocity and density. Example: A car travels at 60 mph for 20 minutes. How far does it travel? What units are appropriate for distance? Explain your answer. .
Strand Source
Problem Solving IDOE
Assessment Resources
- Problems Involving Rate Velocity and Density, McGraw-Hill, Form A, skill test [CTB].  
- Problems Involving Rate Velocity and Density, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.5.3
The learner will be able to solve problems involving scale factors, area, and volume using ratio and proportion. Example: Calculate the volume and surface area of cubes with side 1 cm, 2 cm, 3 cm, etc. Make a table of your results and describe any patterns in the table. .
Strand Source
Problem Solving IDOE
Assessment Resources
- Ratio and Proportions to Solve Problems, McGraw-Hill, Form A, skill test [CTB].  
- Ratio and Proportions to Solve Problems, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.5.4
The learner will be able to use formulas for finding the perimeter and area of basic two-dimensional shapes and the surface area and volume of basic three-dimensional shapes, including rectangles, parallelograms*, trapezoids*, triangles, circles, prisms*, cylinders, spheres, cones, and pyramids. Example: Find the total surface area of a right triangular prism 14 feet high and with a base that measures 8 feet by 6 feet. *parallelogram: a four-sided figure with both pairs of opposite sides parallel *trapezoid: a four-sided figure with one pair of opposite sides parallel *prism: solid shape with fixed cross-section (right prism is a solid shape with two parallel faces that are polygons and other faces that are rectangles) .
Strand Source
Perimeter/Area/Volume IDOE
Assessment Resources
- Perimeter Area Volume Geometric Shapes, McGraw-Hill, Form A, skill test [CTB].  
- Perimeter Area Volume Geometric Shapes, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.5.5
The learner will be able to estimate and compute the area and volume of irregular two- and three-dimensional shapes by breaking the shapes down into more basic geometric objects. Example: Find the volume of a dog house that has a rectangular space that is 3 ft by 2 ft by 5 ft and has a triangular roof that is 1.5 ft higher than the walls of the house. .
Strand Source
Area IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Data Interpretation

    Data Analysis and Probability
The learner will be able to collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events.
Strand Source
Data Collection and Classification IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Probability/Statistics

    8.6.1
The learner will be able to identify claims based on statistical data and, in simple cases, evaluate the reasonableness of the claims. Design a study to investigate the claim. Example: A study shows that teenagers who use a certain brand of toothpaste have fewer cavities than those using other brands. Describe how you can test this claim in your school. .
Strand Source
Data Analysis IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.6.2
The learner will be able to identify different methods of selecting samples, analyzing the strengths and weaknesses of each method, and the possible bias in a sample or display. Example: Describe possible bias in the following survey: A local television station has a daily call-in poll. Viewers of the morning and noon newscasts are asked to call one telephone number to answer "yes" and a different telephone number to answer "no." The results are reported on the six-o'clock newscast. .
Strand Source
Sampling IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.6.3
The learner will be able to understand the meaning of, and be able to identify or compute the minimum value, the lower quartile*, the median*, the upper quartile*, the interquartile range, and the maximum value of a data set. Example: Arrange a set of test scores in increasing order and find the lowest and highest scores, the median, and the upper and lower quartiles. *lower quartile: the value that separates the lowest one-fourth of the values from the rest of the values *median: the value that divides a set of data written in order of size into two equal parts *upper quartile: the value that separates the highest one-fourth of the values from the rest of the values .
Strand Source
Data Analysis IDOE
Instructional Resources
- Box & Whisker Plots, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Box_Whisker Plots.pdf
Assessment Resources
- Upper Lower Quartile Median, McGraw-Hill, Form A, skill test [CTB].  
- Upper Lower Quartile Median, McGraw-Hill, Form B, skill test [CTB].  
- Box & Whisker Plots, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Box_Whisker Plots.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Data Interpretation

    8.6.4
The learner will be able to analyze, interpret, and display single- and two-variable data in appropriate bar, line, and circle graphs; stem-and-leaf plots*; and box-and-whisker plots* and explain which types of display are appropriate for various data sets. Example: The box-and-whisker plots below show winning times (hours: minutes) for the Indianapolis 500 race in selected years: 2:40 2:50 3:00 3:10 3:20 3:30 3:40 3:50 4:00 1981-1995 1966-1980* 1951-1965 *Except 1967, 1973, 1975, and 1976. In the years from 1951-1965, the slowest time was 3 h 57 min. Explain how the slowest time changed through the years 1951-1995. How did winning times change during that period? How did the median times change in the same period? *stem-and-leaf plot: e.g., this one shows 62, 63, 67, 71, 75, 75, 76, etc. Stem Leaf 6 2 3 7 7 1 5 5 6 8 9 8 0 1 1 2 3 5 5 7 8 8 9 1 2 2 3 3 4 *box-and-whisker plot: diagram showing median, quartiles, and range (see diagram on previous page) .
Strand Source
Analyzing/Evaluating Graphical Forms IDOE
Instructional Resources
- Fun with Circle Graphs, web link [Lesson Plan].  http://www.hobart.k12.in.us/CS/script.pl?submit=fVEjRH8AAAEAAGN8F9oAAAAP
- Box & Whisker Plots, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Box_Whisker Plots.pdf
Assessment Resources
- Analyze and Interpret Data, McGraw-Hill, Form A, skill test [CTB].  
- Analyze and Interpret Data, McGraw-Hill, Form B, skill test [CTB].  
- Fun with Circle Graphs, web link [Lesson Plan].   http://www.hobart.k12.in.us/CS/script.pl?submit=fVEjRH8AAAEAAGN8F9oAAAAP
- Box & Whisker Plots, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Box_Whisker Plots.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.6.5
The learner will be able to represent two-variable data with a scatterplot* on the coordinate plane and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data and write the equation of that line. Example: Survey some of the students at each grade level in your school, asking them how much time they spend on homework. Plot the grade level and time of each student as a point (grade, time) on a scatter diagram. Describe and justify any relationship between grade and time spent on homework. *scatterplot: a coordinate graph showing ordered pairs of data .
Strand Source
Scatterplots IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Probability/Statistics

    8.6.6
The learner will be able to understand and recognize equally likely events. Example: When you roll a number cube, what is the probability that the number on the top face will be a 6? Explain your answer. .
Strand Source
Probability IDOE
Assessment Resources
- Probability of Equally Likely Events, McGraw-Hill, Form A, skill test [CTB].  
- Probability of Equally Likely Events, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.6.7
The learner will be able to find the number of possible arrangements of several objects by using the Basic Counting Principle. Example: You are planning to place four pictures in a line on a shelf. Find the number of ways you can arrange the four pictures. .
Strand Source
Combinations IDOE
Instructional Resources
- Basic Counting Principle, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Basic Counting Principle.pdf
Assessment Resources
- Possible Arrangements of Objects, McGraw-Hill, Form A, skill test [CTB].  
- Possible Arrangements of Objects, McGraw-Hill, Form B, skill test [CTB].  
- Basic Counting Principle, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Basic Counting Principle.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

Problem Solving

    Problem Solving
The learner will be able to make decisions about how to approach problems and communicate their ideas.
Strand Source
Analyzing Problems IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.1
The learner will be able to analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. Example: Solve the problem: "For computers, binary numbers are great because they are simple to work with and they use just two values of voltage, magnetism, or other signal. This makes hardware easier to design and more noise resistant. Binary numbers let you represent any amount you want using just two digits: 0 and 1. The number you get when you count ten objects is written 1010. In expanded notation, this is 1 x 2 3 + 0 x 2 2 + 1 x 2 1 + 0 x 2 0. Write the number for thirteen in the binary (base 2) system." Decide to make an organized list. .
Strand Source
Analyzing Problems IDOE
Instructional Resources
- Basic Counting Principle, IDOE Curriculum Frameworks, web link [Lesson Plan].  http://www.hobart.k12.in.us/district/l_math/8Basic Counting Principle.pdf
Assessment Resources
- Approach Info Sequencing Patterns, McGraw-Hill, Form A, skill test [CTB].  
- Approach Info Sequencing Patterns, McGraw-Hill, Form B, skill test [CTB].  
- Basic Counting Principle, IDOE Curriculum Frameworks, web link [Lesson Plan].   http://www.hobart.k12.in.us/district/l_math/8Basic Counting Principle.pdf
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.2
The learner will be able to make and justify mathematical conjectures based on a general description of a mathematical question or problem. Example: In the first example, if you have only two symbols, 0 and 1, then one object: 1, two objects: 10, three objects: 11, four objects: 100. Predict the symbol for five objects. .
Strand Source
Analyzing Problems IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.3
The learner will be able to decide when and how to divide a problem into simpler parts. Example: In the first example, write expanded notation for the number five in base 2; begin with the fact that 5 = 4 + 1. .
Strand Source
Analyzing Problems IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.4
The learner will be able to apply strategies and results from simpler problems to solve more complex problems. Example: In the first example, write the first five numbers in base 2 notation and look for a pattern. .
Strand Source
Strategies IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.5
The learner will be able to make and test conjectures by using inductive reasoning. Example: In the first example, predict the base 2 notation for six objects, then use expanded notation to test your prediction. .
Strand Source
Strategies IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.6
The learner will be able to express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work. Example: In the first example, explain how you will find the base two notation for thirteen objects. .
Strand Source
Solution IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.7
The learner will be able to recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. Example: Measure the length and width of a basketball court. Use the Pythagorean Theorem to calculate the length of a diagonal. How accurately should you give your answer? .
Strand Source
Evaluating Solutions IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.8
The learner will be able to select and apply appropriate methods for estimating results of rational-number computations. Example: Use a calculator to find the cube of 15. Check your answer by finding the cubes of 10 and 20. .
Strand Source
Strategies IDOE
Assessment Resources
- Estimating Results, McGraw-Hill, Form A, skill test [CTB].  
- Estimating Results, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.9
The learner will be able to use graphing to estimate solutions and check the estimates with analytic approaches. Example: Use a graphing calculator to draw the straight line x + y = 10. Use this to estimate solutions of the inequality x + y > 10 by testing points on each side of the line. .
Strand Source
Strategies IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.10
The learner will be able to make precise calculations and check the validity of the results in the context of the problem. Example: In the first example, list the first thirteen numbers in base 2 notation. Use patterns or expanded notation to confirm your list. .
Strand Source
Strategies IDOE
Assessment Resources
- Precise Calculations for Solutions, McGraw-Hill, Form A, skill test [CTB].  
- Precise Calculations for Solutions, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.11
The learner will be able to decide whether a solution is reasonable in the context of the original situation. Example: In the basketball court example, does the accuracy of your answer depend on your initial measuring? .
Strand Source
Evaluating Solutions IDOE
Assessment Resources
- Reasonableness of Solutions, McGraw-Hill, Form A, skill test [CTB].  
- Reasonableness of Solutions, McGraw-Hill, Form B, skill test [CTB].  
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  
    8.7.12
The learner will be able to note the method of finding the solution and show a conceptual understanding of the method by solving similar problems. Example: In the first example, use your list of base 2 numbers to add numbers in base 2. Explain exactly how your addition process works. .
Strand Source
Evaluating Solutions IDOE
Unit Assessment Resources
- NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
- ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
  

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