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In 8th grade, students analyze, create and represent linear and simple non-linear functions in multiple ways to make connections between them, including mathematical concepts related to bivariate data and Pythagorean Theorem, and “real-world” situations like those arising from two & three dimensional space.
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Learning Progression 1
Identify, Solve, Write, and Produce Examples of Linear Equations in One Variable with Rational Coefficients with One Solution, Infinitely Many Solutions, or No Solution while Solving Mathematical & Real-world Problems
Learning Intention 1: I am learning to understand equations conceptually through the use of context and continuing tables in order to solve them algebraically. (1.1 Example 3 solving by substitution)
Learning Intention 1: I am learning to understand equations conceptually through the use of context and continuing tables in order to solve them algebraically. (1.1 Example 3 solving by substitution)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
1a. I can select a value to substitute into a linear equaton.
1b. I can adjust my next selection based on the results of the last selection.
1c. I can identify when a value yields a solution to the equation.
1d. I can communicate the meaning of the solution in the context of the problem, if any.
Learning Intention 2: I am learning to understand equations conceptually through the use of algebra tiles & other manipulatives in order to solve them algebraically. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Learning Intention 2: I am learning to understand equations conceptually through the use of algebra tiles & other manipulatives in order to solve them algebraically. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
2a. I can model an equation with CONCRETE algebra tiles or another manipulative, including drawing the goal of one positive algebra tile.
2b. I can distribute when necessary to draw the complete equation with pictures of algebra tiles.
2c. I can simplify each equivalent expression, if possible.
2d. I can collect variables on one side and constants on the other side using properties of equality.
2e. I can make the coefficient of the variable one using properties of equality.
2f. I can DRAW the CONCRETE representation and connect the CONCRETE tile to the DRAWN representation of it.
2g. I can write the SYMBOLIC representation and connect the CONCRETE tile to the symbolic representation of it.
Learning Intention 3: I am learning to understand equations conceptually through the use of algebra tiles & other manipulatives in order to solve them algebraically. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Learning Intention 3: I am learning to understand equations conceptually through the use of algebra tiles & other manipulatives in order to solve them algebraically. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
3a. I can model an equation with DRAWINGS of algebra tiles or another manipulative, including drawing the goal of one positive algebra tile.
3b. I can distribute when necessary to draw the complete equation with pictures of algebra tiles.
3c. I can simplify each equivalent expression, if possible.
3d. I can collect variables on one side and constants on the other side using properties of equality.
3e. I can make the coefficient of the variable one.
3f. I can write the SYMBOLIC representation and connect the DRAWN tile to the symbolic representation of it.
Learning Intention 4: I am learning to understand equations conceptually through the use of algebra tiles & other manipulatives in order to solve them algebraically. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Learning Intention 4: I am learning to understand equations conceptually through the use of algebra tiles & other manipulatives in order to solve them algebraically. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
4a. I can model an equation with SYMBOLIC representations of algebra tiles or another manipulative, including writing the goal of one positive coefficient of the variable.
4b. I can distribute when necessary to draw the complete equation with pictures of algebra tiles.
4c. I can simplify each equivalent expression, if possible.
4d. I can collect variables on one side and constants on the other side using properties of equality.
4e. I can make the coefficient of the variable one.
Learning Intention 5: I am learning to translate word problems leading to linear equations through the use of context & tape diagrams. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Learning Intention 5: I am learning to translate word problems leading to linear equations through the use of context & tape diagrams. (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
5a. I can construct a tape diagram incrementally as I read or after I read a word problem.
5b. I can identify equality in the problem and use it to separate one half of the tape diagram from the other.
5c. I can write an equation using each half of the tape diagram.
Learning Intention 6: I am learning to write linear equations in one variable with integer coefficients (level 1) including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (Activity 1.3 except d, 1.3 Activities 2 & 1.3 Exercise 5)
Learning Intention 6: I am learning to write linear equations in one variable with integer coefficients (level 1) including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (Activity 1.3 except d, 1.3 Activities 2 & 1.3 Exercise 5)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
6a. I can translate a word problem with integers.
6b. I can translate a word problem with the need to use the distributive property.
6c. I can translate a word problem with multiple terms.
Learning Intention 7: I am learning to solve linear equations in one variable with integer coefficients (level 1) including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (1.1 Examples 1 & 2; 1.2 Examples 1, 2 & 3; 1.3 Example 1)
Learning Intention 7: I am learning to solve linear equations in one variable with integer coefficients (level 1) including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (1.1 Examples 1 & 2; 1.2 Examples 1, 2 & 3; 1.3 Example 1)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
7a. I can distribute when necessary. (Procedural, level 3)
7b. I can simplify each equivalent expression, if possible. (Procedural, level 3)
7c. I can collect variables on one side and constants on the other side using properties of equality. (Procedural, level 1)
7d. I can make the coefficient of the variable one using properties of equality. (Procedural, level 1)
7e. I can communicate the meaning of the solution in the context of the problem, if any. (Conceptual, level 1)
Learning Intention 8: I am learning to write & solve examples of linear equations in one variable with rational coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (1.1 Example 4 & 1.2 Example 4; 1.3 Activities 1d & 3; 1.3 Exercise 6)
Learning Intention 8: I am learning to write & solve examples of linear equations in one variable with rational coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (1.1 Example 4 & 1.2 Example 4; 1.3 Activities 1d & 3; 1.3 Exercise 6)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
8a. I can translate a word problem with rationals. (Conceptual, level 3)
8b. I can distribute rationals when necessary. (Procedural, level 3)
8c. I can simplify rationals in each equivalent expression, if possible. (Procedural, level 3)
8d. I can collect variables on one side and constants on the other side using properties of equality. (Procedural, level 3)
8e. I can make a rational coefficient of the variable one using properties of equality. (Procedural, level 3)
8f. I can communicate the meaning of the solution in the context of the problem, if any. (Conceptual, level 3)
Learning Intention 9: I am learning to solve & produce examples of linear equations in one variable with rational coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Learning Intention 9: I am learning to solve & produce examples of linear equations in one variable with rational coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms (level 3). (Select problems from 1.3 Exercises, 1.2 Exercises & 1.1 Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
Given an equation,
9a. I can distribute rationals when necessary. (Procedural, level 3)
9b. I can simplify rationals in each equivalent expression, if possible. (Procedural, level 3)
9c. I can collect variables on one side and constants on the other side using properties of equality. (Procedural, level 3)
9d. I can make a rational coefficient of the variable one using properties of equality. (Procedural, level 3)
9e. I can create a contextual word problem that fits the given equation. (Application, level 4)
Learning Intention 10: I am learning to show a linear equation's number of solutions. (1.3 Examples)
Learning Intention 10: I am learning to show a linear equation's number of solutions. (1.3 Examples)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
10a. I can show that a linear equation in one variable has one solution by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a results. (Conceptual, level 3)
10b. I can show that a linear equation in one variable has no solution by successively transforming the given equation into simpler forms until an equivalent equation of the form a = b results (where a and b are different numbers). (Conceptual, level 3)
10c. I can show that a linear equation in one variable has infinitely many solutions by successively transforming the given equation into simpler forms until an equivalent equation of the form a = a results (where a and b are different numbers). (Conceptual, level 3)
Learning Intention 11: I am learning to identify a linear equation's number of solutions. (select problems from 1.3 Exercises 18-35)
Learning Intention 11: I am learning to identify a linear equation's number of solutions. (select problems from 1.3 Exercises 18-35)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
11a. I can identify examples of linear equations in one variable with one solution. (Procedural, level 2)
11b. I can identify examples of linear equations in one variable with infinitely many solutions. (Procedural, level 2)
11c. I can identify examples of linear equations in one variable with no solutions. (Procedural, level 2)
Learning Intention 12: I am learning to write a linear equation's number of solutions. (1.3 Exercise #31)
Learning Intention 12: I am learning to write a linear equation's number of solutions. (1.3 Exercise #31)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
12a. I can write examples of linear equations in one variable with one solution. (Application, level 2)
12b. I can write examples of linear equations in one variable with infinitely many solutions. (Application, level 2)
12c. I can write examples of linear equations in one variable with no solutions. (Application, level 2)
Learning Progression 2 (application and depth, time permitting)
Use Geometry Theorems, Properties, and Relationships to Solve Mathematical & Real-world Problems
Learning Intention 13 (application & depth): I am learning to create equations from congruent angles. (Chapter 3 What you Learned Before)
Learning Intention 13 (application & depth): I am learning to create equations from congruent angles. (Chapter 3 What you Learned Before)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
13a. I can identify two congruent angles.
13b. I can choose angle measures for each side of the equation.
13c. I can solve the resulting equation.
Learning Intention 14 (application & depth): I am learning about angle relationships inside and outside of triangles. (3.2 Activity 1, 3 & 4; 1.1 Activity 1 & Activity 2)
Learning Intention 14 (application & depth): I am learning about angle relationships inside and outside of triangles. (3.2 Activity 1, 3 & 4; 1.1 Activity 1 & Activity 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
14a. Using a line and a visual representation, I can show the relationship between the interior angles of a triangle.
14b. Using a line and a visual representation, I can show the relationship between the exterior angles of a triangle.
Learning Intention 15 (application & depth): I am learning to solve problems involving triangles. (3.2 Examples, 1.1 Activity 3 & 1.2 Activities 1 & 2)
Learning Intention 15 (application & depth): I am learning to solve problems involving triangles. (3.2 Examples, 1.1 Activity 3 & 1.2 Activities 1 & 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
15a. I can use the relationship of interior and/or exterior angles to write equations.
15b. I can solve the resulting equation.
Learning Intention 16 (application & depth): I am learning to extend my knowledge of angle relationships to include polygons. (3.3 Activities 1 & 2, 1.2 Activity 2 extended to the angle sum of the square)
Learning Intention 16 (application & depth): I am learning to extend my knowledge of angle relationships to include polygons. (3.3 Activities 1 & 2, 1.2 Activity 2 extended to the angle sum of the square)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
16a. Using lines and a visual representation, I can show the relationship between the interior angles of a polygon.
16b. Using lines and a visual representation, I can show the relationship between the exterior angles of a polygon.
Learning Intention 17 (application & depth): I am learning to solve problems involving polygons. (3.3 Examples)
Learning Intention 17 (application & depth): I am learning to solve problems involving polygons. (3.3 Examples)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
17a. I can use the relationship of interior and/or exterior angles to write equations.
17b. I can solve the resulting equation.
Learning Intention 18 (one or two days): I am learning about parallel lines cut by a transversal and angle relationships. (3.1 Activities 1-3; 3.1 Examples 1-3)
Learning Intention 18 (one or two days): I am learning about parallel lines cut by a transversal and angle relationships. (3.1 Activities 1-3; 3.1 Examples 1-3)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
18a. I can define the term: parallel lines.
18b. I can define the term: transversal.
18c. I can define the term: corresponding angle.
18d. I can identify corresponding angle relationships in parallel lines cut by a transversal.
18e. I can use the relationship of corresponding angles to write equations.
18f. I can solve the resulting equation.
Reengagement of seventh grade:
18g. I remember the definition of vertical angles and can identify them in parallel lines cut by a transversal.
18h. I can define the term: complementary angles
18i. I remember the definition of supplementary angles and can identify them in parallel lines cut by a transversal.
18j. I remember the definition of adjacent angles and can identify them in parallel lines cut by a transversal.
Learning Intention 19 (one or two days): I am learning about parallel lines cut by a transversal and other angle relationships. (3.1 Example 4; 3.2 Activity 2)
Learning Intention 19 (one or two days): I am learning about parallel lines cut by a transversal and other angle relationships. (3.1 Example 4; 3.2 Activity 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
19a. I can define the term, interior angles, as it relates to parallel lines cut by a transversal.
19b. I can define the term, exterior angles, as it relates to parallel lines cut by a transversal.
19c. I can define the term, alternate angles, as it relates to parallel lines cut by a transversal.
19d. I can define the term, consecutive angles, as it relates to parallel lines cut by a transversal.
19e. I can define the term: alternate interior angle.
19f. I can define the term: alternate exterior angle.
19g. I can define the term: consecutive / same side interior angle.
19h. I can define the term: consecutive / same side interior angle.
19i. I can define the term: same side exterior angle.
19j. I can identify corresponding angle relationships in parallel lines cut by a transversal.
19k. I can use angle relationships to write equations.
19l. I can solve the resulting equation.
Learning Intention 20 (one or two days): I am learning to use angle pair relationships to solve problems in parallel lines. (3.1 Exercises)
Learning Intention 20 (one or two days): I am learning to use angle pair relationships to solve problems in parallel lines. (3.1 Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
20a. I can use angle relationships to write equations in real-world problems involving parallel lines.
20b. I can use angle relationships to write equations in mathematical problems involving parallel lines.
20c. I can solve the resulting equation.
Learning Progression 3 (depth time permitting)
Construct Statements about Solving Two Equations at the Same Time to Determine the Unknowns using a Table and Algebra
Learning Intention 21 (optional depth day- solving systems): I am learning to connect parallel lines cut by a transversal to the number of solutions to a linear system. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.4 Key Idea - Applied to Parallel Lines Cut by a Transversal, Transition to Systems, Graphing Systems is saved for Unit 5 depth)
Learning Intention 21 (optional depth day- solving systems): I am learning to connect parallel lines cut by a transversal to the number of solutions to a linear system. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.4 Key Idea - Applied to Parallel Lines Cut by a Transversal, Transition to Systems, Graphing Systems is saved for Unit 5 depth)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
21a. I can see & visually solve the system of one of the two parallel lines cut by the transversal. (Conceptual, level 3)
21b. I can see & visually solve the system of the two parallel lines without the transversal. (Conceptual, level 3)
21c. I can draw a line that is collinear to either one of the two parallel lines or the transversal. (Conceptual, level 3)
21d. I can apply my knowledge to recognize the number of solutions to any linear system. (Conceptual, level 3)
Learning Intention 22 (optional depth day- solving systems): I am learning to solve two equations at the same time using a table. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.1 Activity 1 & 2)
Learning Intention 22 (optional depth day- solving systems): I am learning to solve two equations at the same time using a table. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.1 Activity 1 & 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
22a. I can select ordered pairs to substitute into a linear system.
22b. I can adjust my next ordered pair selection based on the results of the last selection.
22c. I can identify when an ordered pair selection yields a solution to a single equation.
22d. I can identify when an ordered pair selection yields a solution to a both equations.
22e. I can communicate the meaning of the solution in the context of the problem.
Learning Intention 23 (optional depth day- solving systems): I am learning to solve two equations at the same time using substitution. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.2 Lesson)
Learning Intention 23 (optional depth day- solving systems): I am learning to solve two equations at the same time using substitution. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.2 Lesson)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
23a. I can write a tape diagram for each equation in a linear system. (Conceptual, level 2)
23b. I can use the tape diagrams to write two equations. (Conceptual, level 1)
23c. I can identify where the equality is between two tape diagrams and use it to make a single tape diagram, with one unknown, out of the two tape diagrams. (Conceptual, level 3)
23d. I can use the new tape diagram to write a single equation. (Conceptual, level 3)
23e. I can connect the visual substitution to its algebraic counterpart. (Conceptual, level 3)
23f. I can solve the linear system by substitution. (Procedural, level 3)
Learning Intention 24 (optional depth day- solving systems): I am learning to understand how to solve two equations at the same time using elimination. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Activities 1-3 using Algebra Tiles)
Learning Intention 24 (optional depth day- solving systems): I am learning to understand how to solve two equations at the same time using elimination. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Activities 1-3 using Algebra Tiles)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
24a. I can model an equation with algebra tiles or another manipulative. (Conceptual, level 3)
24b. I can work with partner with a related equation. (social criterion)
24c. We can create zero pairs by combining our equations. (Conceptual, level 3)
24d. We can adjust one or both of our equations using properties of equality to create a zero pair. (Conceptual, level 3)
Learning Intention 25 (optional depth day- solving systems): I am learning to solve two equations at the same time using elimination. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Lesson)
Learning Intention 25 (optional depth day- solving systems): I am learning to solve two equations at the same time using elimination. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Lesson)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
25a. I can use algebra tiles or other manipulatives to understand the need and the process of elimination. (Conceptual, level 3)
25b. I can solve a system by addition. (Procedural, level 3)
25c. I can solve a system by subtraction. (Procedural, level 3)
25d. I can use properties of equality to change one of the linear equations before solving it. (Procedural, level 3)
25e. I can use properties of equality to change both of the linear equations before solving it. (Procedural, level 3)
Learning Intention 26 (optional depth day- solving systems): I am learning to solve real-world problems leading to two linear equations in two variables. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Example 3; 5.2 Example 2)
Learning Intention 26 (optional depth day- solving systems): I am learning to solve real-world problems leading to two linear equations in two variables. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Example 3; 5.2 Example 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
26a. I can use tape diagrams and/or manipualtives to understand the construction of a linear system problem and to translate it into symbols. (Conceptual, level 4)
26b. I can solve a linear system. (Conceptual, level 4)
26c. I can interpret the solution(s) or lack of solution in the context of the problem. (Conceptual, level 4)
Learning Intention 27 (optional depth day- solving systems): I am learning to solve mathematical problems leading to two linear equations in two variables. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Select Exercises, 5.2 Select Exercises)
Learning Intention 27 (optional depth day- solving systems): I am learning to solve mathematical problems leading to two linear equations in two variables. Graphing is saved for Math 8 Unit 5. Systems should be taught to mastery if there is time at the end of the school year. (5.3 Select Exercises, 5.2 Select Exercises)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
27a. I can solve a linear system. (Procedural, level 4)
Learning Intention 28 (optional depth day- solving systems): I am learning to analyze problems leading to two linear equations in two variables in multiple representations. (Level 4 not in Text)
Learning Intention 28 (optional depth day- solving systems): I am learning to analyze problems leading to two linear equations in two variables in multiple representations. (Level 4 not in Text)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
28a. I understand the different representations of a linear system. (Conceptual, level 4)
28b. I can solve a linear system with each equation represented differently. (Procedural, level 4)
28c. I can analyze the system and its solution(s) or lack of solution in context. (Application, level 4)
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