The materials reviewed for the Carnegie Learning High School Math Solution Traditional series partially meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. Although the materials explicitly identify the Grade 6-8 readiness standards being built upon in some lessons in The Coherence Maps, the connections between those standards from Grades 6-8 and high school standards are not clear.

The following are examples where the materials do not explicitly identify Grades 6-8 standards:

The Getting Ready states how the lessons in the module build upon students prior experiences and what they will be learning. However, the materials do not explicitly identify Grades 6-8 standards. In Algebra I, Module 1, Getting Ready, the materials state, “You will investigate a variety of function families, recognizing their key characteristics. You will build on your work with numeric patterns to explore sequences as functions. You will expand your knowledge of lines of best fit to determine whether it is appropriate to use a linear model and differentiation between correlation and causation. The lessons in this module build on your prior experiences with functions, numeric patterns, and writing linear equations.”
The “In This Review” are questions that present a formative assessment opportunity, building from the Getting Ready, that reactivates students’ prior knowledge. Although the Lesson “In This Review” questions draw from students' experiences in Grades 6-8, the questions do not explicitly identify content from Grades 6-8. In Geometry, Module 3, Topic 2, Lesson 4, an Lesson Opener Review has students answer questions based on a triangle NPS. “Consider $\triangle NPS$ . 1. Calculate the value of $\sin P$ . 2. Calculate $m\angle P$ . 3. Calculate $m\angle N$ .” The Teacher Implementation Guide states, “In this Review. Students practice with the sine ratio. They will use this skill in ACTIVITY 1 The Cosine Ratio.”
The Teacher Implementation Guide states, that a Teacher can “Tap into your students’ prior learning by reading the narrative statement”. Narrative Statements can be found at the beginning of each lesson. In Algebra II, Module 4, Topic 1, Lesson 1, the materials state, “You have learned about many different types of functions. What functions can you define using points on the circle as the domain?” The Narrative Statement does not explicitly identify content from Grades 6-8.

The Teacher Implementation Guide includes a Standards Overview located in the Front Matter for each course. The Standards Overview shows which standards are covered in the lesson and the standards covered in spaced practice. Some of the spaced practice standards identified are from Grades 6-8, however it is not mentioned in the materials how these standards support the progression of the high school standards. Some spaced practice standards are addressed in the spaced review part of the mixed practice section. The materials provide an “Aligned Standards” box to identify which standard(s) are aligned to each question. Examples include but are not limited to:

In Algebra I, Module 1, Topic 3, Mixed Practice, Spaced Review, Question 1 is aligned to 8.EE.6 and has students calculate the slope of a line represented in a table. Question 2 is aligned to 8.EE.6 and has students determine whether the slope of an equation is positive, negative, zero, or undefined. Question 3 is aligned to 8.EE.7 and has students solve two-sided equations. Question 4 is aligned to 8.SP.1 and has students create a scatter plot given a data set, draw a line of best fit, and then write the equation for the line.
In Geometry, Module 1, Topic 2, Mixed Practice, Spaced Review, Question 3 is aligned to 8.F.1 and has students determine whether a mapping represents a function. Question 6 is aligned to 8.G.7 and has students determine the value of a diagonal of a rectangular prism.
In Algebra II, Module 2, Topic 3, Mixed Practice, Spaced Review, Question 2 is aligned to 8.G.7 and has students verify that a triangular piece of metal with the given side lengths is a right triangle, and if they can use Euclid’s formula to generate the given side lengths.

The Topic Overview includes, “What is the entry point for students?” in the “Connection to Prior Learning” section, although the connection to prior learning is explicitly stated, how it connects to the current topic is not always stated. Additionally, any Grades 6-8 content referenced in this section of the topic overview is not explicitly connected to specific standards. Examples from the Topic Overview include but are not limited to:

In Algebra I, Module 2, Topic 2, Topic Overview, the materials state, “In grade 7, students solved two-step inequalities and graphed the solutions on a number line.” Students build from this knowledge in this topic when they solve more complex inequalities in one variable and compound inequalities.
In Geometry, Module 1, Topic 3, Topic Overview, the materials state, “In middle school, students constructed triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, or no triangle. Through hands-on exploration, they developed an intuition regarding the minimum criteria for determining whether triangles are congruent.” Students build from this knowledge in this topic when they use triangle congruence theorems to prove congruent triangles.

The materials include a family guide with “Where have we been? Where are we going?” for each topic. These sections identify connections between middle school content and courses and lessons in the series, however, any Grade 6-8 content referenced in this section of the family guide is not explicitly connected to specific standards. Examples from the Family Guide include but are not limited to:

In Algebra I, Module 2 ,Topic 3, Family Guide, the materials state, “Where have we been? Students know that every point on the graph of an equation represents a value that makes the equation true…Students have written and solved systems of linear equations.” “Where are we going? Knowing how to solve systems of linear equations prepares students to solve systems that include nonlinear equations…”
In Geometry, Module 3, Topic 1, Family Guide, the materials state, “Where have we been? Students have developed an understanding of proportional reasoning by exploring multiplicative relationships and having used scale factors to solve problems. They have learned that two figures are similar; they can map one onto the other by a sequence of transformations.” “Where are we going? Understanding similarity further develops proportional reasoning. It provides the opportunity for students to connect spatial and numeric reasoning and lays the groundwork for understanding trigonometric ratios, which students will explore in the next topic.”
In Algebra II, Module 2, Topic 1, Family Guide, the materials state, “Where have we been? Students have factored expressions since elementary school. They have factored degree-2 polynomial equations in order to isolate key characteristics of the functions represented by those equations.” “Where are we going? … Students will use what they learned in this topic to help them build real-world polynomial models in the next topic.”

Downloadable Resources

2022

Carnegie Learning High School Math Solution Traditional

Publisher

Carnegie Learning

Subject

Math

Grades

HS

Report Release

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07/20/2022

Review Tool Version

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v1.5

Alignment

Usability

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Summary of Alignment & Usability: Carnegie Learning High School Math Solution Traditional | Math

Math High School

Math High School

High School

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Usability

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