Wayne RESA

Unit PlannerBig Ideas Math 8

Wayne Resa - Math / Grade 8 / Mathematics / Big Ideas Math 8 / Week 11 - Week 14
2 Curriculum Developers
Unit Abstract

In this unit, Eighth Grade Students will . . .

  • Use similar triangles to explain why the slope is the same between any two points on a line.
  • Graph proportional relationships, interpreting the unit rate as the slope.
  • Compare proportional relationships represented in different ways.
  • Derive y = mx and y = mx + b.
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Expectations/Standards
MI: Mathematics
MI: Grade 8
Expressions & Equations
8.EE.B. Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.EE.B.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Functions
8.F.B. Use functions to model relationships between quantities.
8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
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Practice Standards
  • SMP1 - Make sense of problems and persevere in solving them
  • SMP2 - Reason abstractly and quantitatively
  • SMP3 - Construct viable arguments and critique the reasoning of others
  • SMP4 - Model with Mathematics
  • SMP5 - Use appropriate tools strategically
  • SMP6 - Attend to precision
  • SMP7 - Look for and make use of structure
  • SMP8 - Look for and express regularity in reasoning
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Concepts from Previous Units

Sixth Grade

  • Make tables of equivalent ratios and plot the pairs of values in a coordinate plane.
  • Write an equation in two variables and analyze the relationship between the independent and dependent variables using graphs and tables.

Seventh Grade

  • Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions.
  • Represent proportional relationships with equations.
Connections to Upcoming Units

Ninth Grade

  • Identify linear functions using graph, tables, and equations
  • Find the slope of a line and use it to write a linear equation in slope-intercept form
  • Solve real-life problems using function notation, linear equations, slopes, and y-intercepts
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Key Terms / Vocabulary

Teacher Edition Vocabulary: linear equation, solution of a linear equation, solution points, slope( rise/run), x-intercept, y-interecept, slope-intercept form, standard form, point slope form, negative slope, positive slope, undefined slope, zero slope

Other Vocabulary: deposit, balance, acre, vertical line segment, horizontal line segment, right triangle, rate of change, steepness, change in y (vertical change), change in x (horizontal change), direct variation, proportional, constant of proportionality, mileage, point of intersection, combinations, models,


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Lesson Plan Sequence
The following lesson plan sequence is obtained from Big Ideas Learning (2015). Each lesson is aligned with a learning objective to inform the teachers on what students should be able to do at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day.
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Language Support
The use of sentence stems as a language support are beneficial to all students, including English Language Learners. The use of sentence stems encourages the learning of mathematics in a language rich environment which has an impact on other learning as well. The sentence stems are a beginning place for supporting students' use of academic language and encourage discussion and writing as students learn content.
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