8th Grade Mathematics Curriculum 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...

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Transcript of 8th Grade Mathematics Curriculum 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...

  • 8th Grade Mathematics Curriculum Course Summary: In Grade 8, instructional time will focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling and association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Scope and Sequence:

    Time Frame Unit

    34 Days Number Sense, Expressions, and Equations

    68 Days Functions and Linear Relationships

    27 Days Transformations and Transversals

    35 Days Exponential Functions, Pythagorean Theorem, and Volume

  • Board Approved: July 23, 2015 2 | Page Revised: April, 2016 MLS Alignment: April, 2017

    Curriculum Revision Tracking

    Changes made in April, 2016:

    ● Unit 1: o Pacing was adjusted from 32 to 34 days o Sequence of Topics 6, 14, and 15 was changed.

  • Board Approved: July 23, 2015 3 | Page Revised: April, 2016 MLS Alignment: April, 2017

    Unit 1: Number Sense, Expressions and Equations Subject: Mathematics Grade: 8th Grade Name of Unit: Number Sense, Expressions, and Equations Length of Unit: 34 days Overview of Unit: Students will understand that there are numbers which are not rational and approximate them by rational numbers. Students will also analyze and solve linear equations. Priority Standards for unit:

    • MA.8.NS.A.1: Explore the real number system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or

    repeats. c. Convert decimals which repeat into fractions and fractions into repeating

    decimals. d. Generate equivalent representations of rational numbers.

    Supporting Standards for unit:

    ● MA.8.NS.A.2: Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

    ● MA.8.EEI.C.1: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many solutions

    or no solutions. b. Solve linear equations and inequalities with rational number coefficients,

    including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

    ● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.

    ● ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.

    ● ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.

    ● ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.

  • Board Approved: July 23, 2015 4 | Page Revised: April, 2016 MLS Alignment: April, 2017

    Standard Unwrapped Concepts (Students

    need to know)

    Unwrapped Skills (Students need to

    be able to do)

    Bloom’s Taxonomy

    Levels Webb's DOK

    MA.8.NS.A.1 differences between rational and

    irrational numbers. Know Remember 1

    MA.8.NS.A.1

    all rational numbers have a decimal expansion that terminates

    or repeats. Understand Understand 2

    MA.8.NS.A.1

    decimals which repeat into fractions and fractions into

    repeating decimals Convert Apply 2

    MA.8.NS.A.1 equivalent representations of

    rational numbers Generate Create 2 Essential Questions:

    1. In earlier courses you studied rational numbers. What other types of numbers are there? 2. In earlier courses you studied rational numbers. Why do you need them? 3. Why do you write equations?

    Enduring Understanding/Big Ideas:

    1. There are rational and irrational numbers in the real number system. 2. Know the differences between them can help you understand if a fraction can be made

    from the number, or whether or not a decimal and be derived from a fraction or square roots.

    3. Complex questions can be solved using the structure of an equation and the process of inverse operations to isolate variables.

    Unit Vocabulary:

    Academic Cross-Curricular Words Content/Domain Specific

    Ratios

    Percents

    Topic 1 Irrational Numbers

    Perfect Square Real Number

    Repeating Decimal Square Root

    Terminating Decimal

    Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)

  • Board Approved: July 23, 2015 5 | Page Revised: April, 2016 MLS Alignment: April, 2017

    digits Topic 1: Rational & Irrational Numbers

    Standard Topic & Section Suggested # of Days

    Notes

    MA.8.NS.A.1 1.1: Expressing Rational Numbers and Decimal Expansion

    1

    MA.8.NS.A.1 1.2: Exploring Rational Numbers 1

    MA.8.NS.A.1 1.3: Approximating Rational Numbers

    1

    MA.8.NS.A.2 1.4: Comparing and Ordering Rational and Irrational Numbers

    1

    MA.8.NS.A.1 MA.8.NS.A.2

    1.5: Problem Solving 1

    Review Day 1.5 Review, Look Over and Test within a three day period (suggested) Test 1.5

  • Board Approved: July 23, 2015 6 | Page Revised: April, 2016 MLS Alignment: April, 2017

    digits Topic 2: Linear Equations in One Variable

    Standard Topic & Section Suggested # of Days

    Notes

    Add/Subtract/Multiply/Divide Integers

    2 Supplement Algebra 2.5 and 2.6

    as needed

    Intervention Clusters 10, 11 and 12.1 “Fractions”

    Approx. 4 as needed

    Use Intervention Lessons, Journal Entries and Intervention

    HW assignments as needed

    Supplement Distributive Property

    1 Supplement May need to create own practice

    Supplement Simplifying Expressions (Combining Like Terms)

    1 Supplement May need to create own practice

    Intervention Cluster 25 “Expressions and Equations”

    Approx. 4 as needed

    Use Intervention Lessons, Journal Entries and Intervention

    HW assignments as needed

    MA.7.EEI.B.1 2.1: Solving Two-Step Equations 1 Algebra 3.1 - 3.4

    MA.7.EEI.B.1 2.2: Solving Equations with Variables on Both Sides

    1 Algebra 3.1 - 3.4

    MA.7.EEI.B.2 2.3: Solving Equations Using the Distributive Property

    1 Algebra 3.1 - 3.4

    REVIEW Solving Equations 1

    Quiz Solving Equations 1

    MA.7.EEI.B.2 2.4: Solutions - One, None, or Infinitely Many

    1

    MA.7.EEI.B.2 2.5: Problem Solving 1

    Review Topic 2 1.5

    Test Topic 2 1.5

  • Board Approved: July 23, 2015 7 | Page Revised: April, 2016 MLS Alignment: April, 2017

    Unit 2: Functions and Linear Relationships Subject: Mathematics Grade: 8th Grade Name of Unit: Functions and Linear Relationships Length of Unit: 68 Days Overview of Unit: Students will understand the concepts related to identifying, creating, manipulating and solving functions and systems of equations. Students will also understand the concepts of using and creating systems of categorical data. Priority Standards for unit:

    ● 8.EEI.B.1: Graph proportional relationships. a. Interpret the unit rate as the slope of the graph. b. Compare two different proportional relationships.

    For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

    ● 8.EEI.B.2: Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.

    a. Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane.

    b. 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.

    ● 8.EEI.C.1: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many

    solutions or no solutions. b. Solve linear equations and inequalities with rational number coefficients,

    including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

    ● 8.EEI.C.2: Analyze and solve systems of linear equations. a. Graph systems of linear equations and recognize the intersection as the

    solution to the system. b. Explain why solution(s) to a system of two linear equations in two variables

    correspond to point(s) of intersection of the graphs. c. Explain why systems of linear equations can have one solution, no solution or

    infini