8th Grade - Gateway 1
Back to 8th Grade Overview
Note on review tool versions
See the series overview page to confirm the review tool version used to create this report.
- Our current review tool version is 2.0. Learn more
- Reports conducted using earlier review tools (v1.0 and v1.5) contain valuable insights but may not fully align with our current instructional priorities. Read our guide to using earlier reports and review tools
Loading navigation...
Focus & Coherence
Gateway 1 - Meets Expectations | 85% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 6 / 8 |
The instructional materials reviewed for Grade 8 meet the requirements for Gateway 1. The materials devote the majority of class time to the major work for Grade 8. The materials are coherent and consistent with the CCSSM. There are explicit connections between major clusters. The supporting work is used to enhance the major clusters. The materials have some lessons and assessment items that go beyond the Grade 8 standards. Since the materials reviewed for Grade 8 meet the expectations for alignment to the CCSSM in the areas of focus and coherence, they were reviewed for rigor and the MPs.
Criterion 1.1: Focus
The instructional materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level. There are questions on four unit tests that are testing CCSSM from grades above Grade 8. Even though the materials assess topics that are in future grades, omission of these 8 assessment problems does not compromise the integrity of assessing the Grade 8 standards.
Indicator 1a
The instructional materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level. There are eight questions throughout the units that assess topics that are in future grades and could be omitted.
- On the Looking for Pythagoras unit test, question 7 is on using a 30-60-90 triangle, which is HSG.SRT.C.6. Teachers can skip Investigation 5, which is the one connected to the high school concept.
- On the Growing, Growing, Growing unit test, questions 1, 2, 4 and 8 are high school exponential functions HSF.LE.A.1. This entire unit should be moved from Grade 8 with the exception of Investigation 5 which does cover major work of Grade 8.
- On the Say It With Symbols unit test, question 5 is high school exponential and quadratic functions HSF.LE.A.1. Teachers can skip Investigation 4, which is the one connected to the high school concept.
- On the It's in the System unit test, questions 4 and 6 have system of inequalities and graphing inequalities which are high school HSA.REI.B.3 and HSA.REI.C.5. Teachers can skip Investigations 3.3 and 4, which are the ones connected to the high school concept.
- Two units are clearly identified as Algebra: Frogs, Fleas, and Painted Cubes and Function Junction, so are not being evaluated.
Skipping these eight assessment problems does not compromise the integrity of the Grade 8 standards. The major work of Grade 8 is still assessed appropriately.
*Evidence updated 10/27/15
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials reviewed for Grade 8 meet the expectations for the majority of class time being devoted to major work. Grade 8 has more than 65% of the work on the major clusters of 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, and 8.G.A. The units Thinking With Mathematical Models; Looking for Pythagoras; Growing, Growing, Growing; and Butterflies, Pinwheels, and Wallpaper had the majority of the lessons on major work. The only concern is that the units also contained work that is a high school standard and this could distract from the major work. A notation to teachers on where the distinctions are would be helpful to keep the focus on the major work.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Grade 8 meet the expectations for spending the majority of class time on the major clusters for Grade 8. Grade 8 has more than 65% of the work on the major clusters of 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, and 8.G.A.
- The units Thinking With Mathematical Models; Looking for Pythagoras; Growing, Growing, Growing; and Butterflies, Pinwheels, and Wallpaper had the majority of the lessons on major work.
- The concern is that the units also contained work that is high school CCSSM and this could distract from the major work. A notation to teachers on where the distinctions are would be helpful to keep the focus on the major work. One example of this is in Growing, Growing, Growing. The work with exponential equations is a high school standard, but used as a counter example to solidify linear work could be helpful. Without more guidance, teachers and students could spend a lot of time working on lessons that are actually high school concepts. Another example is that in Say it With Symbols there are lessons on quadratic, exponential and linear functions. The focus of Grade 8 is supposed to be linear functions and the work on quadratic and exponential functions could take time away from the work on linear functions.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 8 partially meet the expectations for coherence. There are areas where the materials have strong connections and areas that could be stronger. The Grade 8 materials could be completed within the timeline of 170-190 days. The connections between standards to build understanding are strong. There are some off grade level topics that could be identified to help teachers and students know that these are topics that are beyond the CCSSM necessary for that grade. Each investigation within each unit lists the CCSSM that are taught. The mathematical highlights for each unit stress the clusters from CCSSM. All investigations in the student books contain the standards included in that lesson. Every investigation includes activities that connect two or more clusters in a domain, or two or more domains. There is no unit or investigation that only focuses on one aspect of the CCSSM. Connections are evident in all grade levels and in all units. This is a very strong aspect of Connected Mathematics 3.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Grade 8 partially meet the expectations for the supporting content enhancing the major work. There are areas where the materials have strong connections and areas that could be stronger.
- In Thinking With Mathematical Models, the use of scatterplots to tie into linear equations enhances the major work of 8.EE.B.
- In Looking for Pythagoras, there is an attempt to connect working with irrational numbers and 8.G.B.
- There are connections made with linear equations and high school content standards in many of the units.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed for Grade 8 meet the expectations for being able to be taught in one school year.
- The Grade 8 materials could be completed within the timeline of 170-190 days.
- This includes all lessons, mathematical reflections, Looking Back and Looking Ahead and all assessments.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The materials reviewed for the Grade 8 partially meet the expectations for being consistent with the progressions in the standards. The connections between standards to build understanding are strong. There are some off grade level topics that could be identified to help teachers and students know that these are topics that are beyond the CCSSM necessary for that grade.
All three grade levels have major work on equations, EE.A and EE.B:
- Grade 6: Reason about and solve one-variable equations and inequalities can be found in several units (e.g., Let's Be Rational, Variables and Patterns) using informal methods of solving.
- Grade 7: Solve real-world and mathematical problems using numerical and algebraic expressions and equations is primarily in Moving Straight Ahead where they start using symbolic equations and properties of equality.
- Grade 8: Analyze and solve linear equations and pairs of simultaneous linear equations is found in It's in the System, where various methods of solving systems are explored.
All three grade levels have major work on ratio and proportional reasoning, 6.RP and 7.RP:
- Grade 6: Comparing Bits and Pieces begins work with ratios/rates and proportions then continues the major work of Grade 6 ratio and proportion into Variables and Patterns.
- Grade 7: Stretching and Shrinking works with ratios using scale factors and Comparing and Scaling continues the work by solving proportions using many strategies learned from Grade 6 and Grade 7.
- Grade 8: Butterflies, Pinwheels and Wallpaper use the concepts of proportional reasoning in transformational geometry work.
All three grades have major work on the number system (6.NS.A, 6.NS.B, 6.NS.C to 7.NS.A to 8.NS.A):
- Prime Time begins the work of 6.NS.B.4 when it asks students to find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
- This leads to finding the least common multiple in order to find common denominators for fractions in Comparing Bits and Pieces, Let's be Rational and Decimal Ops in Grade 6 and extends to ratios in Comparing and Scaling in Grade 7. This continues into Accentuate the Negative in Grade 7 with performing arithmetic operations with integers and rational numbers (7.NS.A).
- Comparing Bits and Pieces begins developing the ideas of positive and negative numbers on a number lines and absolute value (6.NS.C). This leads to 7.NS.A in Accentuate the Negative with operations on rational numbers. The also leads into 8.NS.A on approximating rational numbers (although not major work of Grade 8).
- Let's Be Rational begins 6.NS.A with students dividing fractions. This continues in Grade 7 with 7.NS.A in Accentuate the Negative.
There is limited support for differentiation of instruction.
- There is guidance for the teacher in the book titled A Guide to Connected Mathematics 3 that discusses differentiation. This gives best practices from research to be used while working on the problem with all students.
- Differentiation is embedded within the instructional model for Connected Mathematics 3 that all kids get the problem launched and summarized the same way and that the differentiation comes during the explore phase of the problem.
- There were specific strategies and guidance for English language learners.
- To help make differentiation more explicit, strategies need to be discussed in the teacher's unit planning pages and it needs to be tied into the specific problems so the teachers have guidance.
- The guide has general best practices but what to use with specific parts of a unit would make it more accessible for teachers and students.
There are many places where the materials relate grade level concepts to explicitly to prior knowledge from earlier grades. These can be found in the student editions in the problems and in the teacher editions in charts and in a narrative called Mathematics Background.
- Let's Be Rational in Grade 6: Page 3, "These situations require addition, subtraction, multiplication, and division of fractions, including mixed numbers. You will decided which operation makes sense in each situation;" "You may already know shortcuts for working with fractions..."
- Comparing and Scaling in Grade 7: Problem 2.3 references work in unit rates in the prior Grade 6 unit Comparing Bits and Pieces.
- Accentuate the Negative in Grade 7: Problem 4.2 references work with the distributive property in Grade 6.
- Accentuate the Negative in Grade 7: Page 3, "Most of the numbers you have worked with in math class have been greater than or equal to zero. However, ...;" "You will also learn more about the properties of operations on numbers." Page 4, "You will extend your knowledge of negative numbers." Page 8, "You have worked with whole numbers, fractions, and decimals in earlier units." Page 58, "You have already examined patterns in ..."
- Thinking With Mathematical Models in Grade 8: Page 3, "In earlier Connected Mathematics units, you explored relationships between two variables. You learned how to find linear relationships from tables and graphs and then write their equations. Using the equations, you solved problems."
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
The materials reviewed for Grade 8 meet the expectations for coherence. Each investigation within each unit lists the CCSSM that are taught. The mathematical highlights for each unit stress the clusters from CCSSM. All investigations in the student books contain the standards included in that lesson. Every investigation includes activities that connect two or more clusters in a domain, or two or more domains.
An example of this is in Butterflies, Pinwheels, and Wallpaper. Two of the highlights are identify congruent and similar triangles and quadrilaterals efficiently; and use properties of congruent and similar triangles to solve problems about shapes and measurements.
There are many links between major clusters in this curriculum.
- In It's in the System, investigation 1, students analyze and solve pairs of simultaneous linear equations (8.EE.C) and define, evaluate and compare functions (8.F.A).
- In Thinking With Mathematical Models, investigation 2, students graph proportional relationships, interpreting the unit rate as the slope of the graph (8.EE.B) and understand that a function is a rule that assigns to each input exactly one output. The graph of a function is a set of ordered pairs consisting of an input and the corresponding output (8.F.A).
- In Growing, Growing, Growing, investigation 1, students compare properties of two functions each represented in a different way (8.F.A) and use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large quantities (8.EE.A).
- Due to the nature of the problems being "investigations," there are very few instances where materials do not connect two or more clusters in a domain and almost all connect two or more domains. One example of this connection is in Thinking with Mathematical Models, investigation 2, Linear Models and Equations includes Expressions and Equations, Functions, and Statistics and Probability (8EE.B.5, 8.EE.C, 8.F.B.4, 8.F.A, 8.SP.A.1-8.SP.A.3).
- In Looking for Pythagoras understanding real numbers connects to 8.G.A, 8.G.B and 8.EE.A.
- In Butterflies, Pinwheels, and Wallpaper in lesson 1.1, 8.G.A.1, 8.G.A.1.A, 8.G.A.1.B, 8.G.A.1.C are all connected.
- There is no unit or investigation that only focuses on one aspect of the CCSSM. Connections are evident in all grade levels and in all units. This is a very strong aspect of Connected Mathematics 3.