SAU #35 Grade 8 Mathematics
Strand: Numbers, Numeration, Operations, and Number Theory
Broad Goals
Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system. Students will understand the meanings of and relationships between number operations and their properties. Compute accurately and efficiently and make reasonable estimates.

 

Strand: Geometry and Measurement

Broad Goals

Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

Develop spatial reasoning and visualization techniques and skills.

Students will use geometric transformations to analyze situations and solve problems.

Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

 

Strand: Data Analysis, Statistics, and Probability

Broad Goal

Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

 

Strand: Functions, Relations, and Algebra
Broad Goals
Students will recognize and describe patterns. Students will represent, analyze, and model mathematical situations and structures. Students will analyze change in various contexts.

Numbers, Numeration, Operations, and Number Theory

Broad Goal #1: Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
1.1.1 Use visual models to compare and order decimals.

1.1.2 Given a decimal number out to the thousandths place create a model to demonstrate understanding of place value.

1.1.3 Understand and demonstrate that each place value is a tenth of the previous.

1.1.4 Recognize and use exponential, scientific, and calculator notation.

1.1.5 Translate between fraction, decimal, and percent as ways to express the same number.

1.1.6 Read, write, order, and use rational numbers.

1.1.7 Use visual models to help demonstrate the meaning of percents and their fraction and decimal equivalents.

1.1.8 Explain the meaning of percents and apply them in problem situations.

1.1.9 Develop the concept of an irrational number.

1.1.10 Write the decimal for any common fraction.

1.1.11 Write the common fraction for any terminating decimal.

1.1.12 Explore the patterns for repeating decimals.

1.1.13 Evaluate expressions with a base of ten and negative exponents.

    

 

 

 

 

 

 

 

 

 

1/4 = .25 = 25%

 

 


A number whole decimal representation neither repeats nor terminates.

 

 


The thirds and the sixths


10-3 = 1/103= 1/1000 = .001

 

 Decimal Squares

 

 

 

 

 

 

 

 

 

Decimal Squares

Numbers, Numeration, Operations, and Number Theory

Broad Goal #2: Students will understand the meanings of and relationships between number operations and their properties.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
1.2.1 Develop operation sense with rational numbers.

 

1.2.2 Use and identify the distributive, associative, and commutative properties and the identity properties for addition and multiplication with rational numbers.

1.2.3 Understand and apply the concept of absolute value when working with integers.

   Multiplying by a fraction less than one results in a small number and vice versa. Decimal Maze Activity – Marie Snyder

Numbers, Numeration, Operations, and Number Theory

Broad Goal #3: Compute accurately and efficiently and make reasonable estimates.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
1.3.1 Refine the procedures of operations on decimals using manipulatives, emphasizing estimation strategies.

1.3.2 Refine and apply algorithms to perform the four basic operations on rational numbers.

1.3.3 Develop and use different strategies to estimate the results of rational number computations and judge the reasonableness of the results.

1.3.4 Apply the order of operations when simplifying expressions with rational numbers and various symbols of inclusion and powers and roots.

1.3.5 Solve problems using percents.

1.3.6 Approximate decimals for irrational.

    

 

 


48 x 78 is a little less than 40 because 48 is just under half and 78 is almost 80.

 

 

 


The square root of thirty is between five and six.

  

 

Geometry and Measurement

Broad Goal #1: Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
2.1.1 Use coordinate geometry to represent and examine geometric shapes and relationships.

2.1.2 Investigate properties of two- and three- dimensional geometric shapes through hands-on experience.

2.1.3 Deduce relationships among congruent figures and similar figures.

2.1.4 Build a three-dimensional shape from a two-dimensional sketch.

 

 		  Parallel lines have equal slopes.


Using manipulatives, projects, and sketches.

 

 

Prism, pyramid, sphere, rectangular solid.

  

Geometry and Measurement

Broad Goal #2: Develop spatial reasoning and visualization techniques and skills.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
2.2.1 Identify and construct three-dimensional objects from two-dimensional perspectives and draw two-dimensional sketches, preserving significant features from three-dimensional objects.

2.2.2 Use manipulatives and technology to model situations geometrically and to solve problems in mathematics and other curricular areas.

 

 

 		     

Geometry and Measurement

Broad Goal #3: Students will use geometric transformations to analyze situations and solve problems.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
2.3.1 Apply the effects of reflections, translations, and rotations in the study of congruence.

2.3.2 Apply the effects of dilations in the study of similarity.

      

Geometry and Measurement

Broad Goal #4: Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
2.4.1 Convert between like units of square measure and like units of cubic measure.

 

2.4.2 Use unit analysis to convert measurements, to determine appropriate units, and to solve problems.

2.4.3 Choose appropriate techniques and tools to measure quantities in order to achieve any given degree of precision, accuracy, and error (or tolerance) of measure.

2.4.4 Make scale drawings and use the concept of scale to solve problems such as with maps and diagrams.

2.4.5 Verify the Pythagorean Theorem by drawing and measuring squares on the sides of right triangles.

2.4.6 Understand and apply the Pythagorean Theorem to real-world situations.

   9 square feet = 1 square yard; 1000 cubic millimeters = 1 cubic centimeter.

58 ft/sec = how many miles per hour?

  

Geometry and Measurement

Broad Goal #5: Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
2.5.1 Express the sine, cosine, and tangent ratios for triangles.

2.5.2 Use the sine, cosine, and tangent ratios to solve problems.

2.5.3 Solve simple problems involving rates such as speed and density.

      

Data Analysis, Statistics, and Probability

Broad Goal #1: Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
3.1.1 Select, create, and use appropriate representations to analyze data and make predictions.

3.1.2 Make and defend conjectures about possible relationships between two characteristics of a sample on the basis of a scatterplot.

3.1.3 Approximate lines of fit for appropriate scatterplots.

3.1.4 Use an appropriate measure of central tendency in problem situations.

3.1.5 Design and use sampling techniques.

3.1.6 Given a set of data, choose an appropriate display.

3.1.7 Using counting principles to determine the number of outcomes for a given situation, deciding whether order matters.

   Tables, histograms, stem and leaf plots, box and whisker plots

 

 

 



Mean, median, or mode

  

Functions, Relations, and Algebra

Broad Goal #1: Students will recognize and describe patterns.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
4.1.1 Recognize, describe, analyze, extend, generalize, and create a variety of patterns using models, tables, graphs, and simple rules.

4.1.2 Generalize the nth term in numeric (i.e. 5, 7, 9, 11…) and geometric patterns (i.e. 1, 5, 25, 125…) and in patterns involving geometric figures (i.e. using pattern blocks or toothpicks).

      

Functions, Relations, and Algebra

Broad Goal #2: Students will represent, analyze, and model mathematical situations and structures.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
4.2.1 Graph a linear equation in two variables paying particular attention to the meaning of intercepts and slope.

4.2.2 Simplify algebraic expressions using the standard order of operations concretely and symbolically.

4.2.3 Solve a single-variable equation symbolically, or by using a graph or table.

4.2.4 Solve single-variable inequalities

4.2.5 Solve problems that require the use of inequalities in one variable.

 

4.2.6 Demonstrate an understanding of linear functions using tables, graphs, and verbal descriptions.

4.2.7 Translate among representations of linear relationships including symbolic equations, tables, and graphs.

 

 		   

 

 



3x + 5 = 11.5

 


12 > -2x Use real-world context and graphic approach.

 

 


Given a table of ordered pairs, write the equation: X 0 1 2 3 4
Y 5 7 9 11 13

A phone plan with a flat rate of $6 with a phone rate of $.10/min would be 0 min. = $6, 1 min. = $6.10, 2 min = $6.20, y = 6 + .10x

  

Functions, Relations, and Algebra

Broad Goal #3: Students will analyze change in various contexts.

8th Grade
Student Outcomes Alignment Examples Resources/Activities
4.3.1 Describe how a change in one quantity results in a change in another within functional relationship.

4.3.2 Quantify and interpret rates of change in discrete (cost per unit) and in continuous (distance per unit of time) settings.

4.3.3 Given a graph, table, or equation identify whether the relationship is linear and if so identify the constant rate of change.

4.3.4 Given a graph, table, or equation identify whether the relationship is exponential and if so identify the growth factor.

4.3.5 Solve problems involving linear and exponential growth in contextual situations using tables and graphs.

4.3.6 Use proportional reasoning strategies to solve problems.

   How a change in one length or width effects perimeter, area and volume.

 

 

 

 

 

 

 

 


Equivalent fractions, cross products and looking at factors.