Curriculum / Math / 10th Grade / Unit 1: Constructions, Proof, and Rigid Motion / Lesson 6
Math
Unit 1
10th Grade
Lesson 6 of 19
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Use principles of proof to justify each step in solving an equation.
The core standards covered in this lesson
A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
The foundational standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Given: $${2\left ( x+3 \right )-8=10}$$
Prove: $${x=6}$$
Given: $${a=3x+6}$$ and $${x=\frac{1}{3}b-2}$$
Prove: $${a=b}$$
Given: $${f(x)=(a-b)(a+b)}$$, $${g(x)=a^2-b^2}$$
Prove: $${f(x) = g(x)}$$ for all values where $${a\neq 0}$$, $${b\neq 0}$$ and $${a\neq b}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Given: $${j(x) = (a+b)^2}$$, $${h(x) = a^2 + 2ab + b^2}$$
Prove: $${j(x) = h(x)}$$
Lesson 5
Lesson 7
Topic A: Constructions of Basic Geometric Figures
Describe the precise definition and notation for foundational geometric figures.
G.CO.A.1
Construct an equilateral triangle with only a straight-edge and a compass. Copy a line segment.
G.CO.A.1 G.CO.D.12 G.CO.D.13
Construct, bisect, and copy an angle.
G.CO.A.1 G.CO.D.12
Construct a perpendicular bisector.
Construct the altitudes and perpendicular bisectors of sides of triangles.
G.CO.C.10 G.CO.D.12
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Topic B: Justification and Proof of Angle Measure
A.REI.A.1
Use angle relationships around a point to find missing measures. Prove angle relationships around a point using geometric statements and reasons.
G.CO.C.9
Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships
Describe and identify rigid motions.
G.CO.A.1 G.CO.A.2 G.CO.B.6
Describe rigid motions. Use algebraic rules to translate points and line segments and describe translations on the coordinate plane.
G.CO.A.2 G.CO.B.6
Translate points and line segments not on the coordinate plane using constructions. Describe properties of translations with respect to line segments and angles.
G.CO.A.2 G.CO.A.4 G.CO.A.5
Construct parallel lines. Prove the relationship between corresponding angles. Use this relationship to find missing measures directly and algebraically.
G.CO.A.1 G.CO.A.4 G.CO.C.9 G.CO.D.12
Prove angle relationships in parallel line diagrams.
G.CO.A.1 G.CO.C.9
Construct auxiliary parallel lines and use these in the development of proofs and identification of missing measures.
G.CO.C.9 G.CO.D.12
Topic D: Reflections and Rotations of Points, Line Segments, and Angles
Perform reflections on a coordinate plane across axes and other defined lines. Identify characteristics and an algebraic rule for the reflection.
G.CO.A.2 G.CO.A.4 G.CO.A.5 G.CO.B.6
Use construction and patty paper to reflect a figure not on the coordinate plane. Describe the properties of a reflection.
Perform rotations on a coordinate plane. Identify characteristics and algebraic rules for the rotation.
Use construction and patty paper to rotate a figure not on the coordinate plane. Describe the properties of a rotation.
G.CO.A.2 G.CO.A.5 G.CO.B.6
Describe a sequence of rigid motions that will map a point, line segment, or angle onto another figure.
G.CO.A.5 G.CO.B.6
Describe rigid motions, or sequences of rigid motions that have the same effect on a figure.
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