5th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Does Not Meet Expectations | 35% |
|---|---|
Criterion 1.1: Focus | 2 / 6 |
Criterion 1.2: Coherence | 3 / 8 |
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, do not meet expectations for focus and coherence. For focus, the materials do not assess grade-level content, and they partially provide all students with extensive work with grade-level problems to meet the full intent of grade-level standards. The materials do not meet expectations for coherence and consistency with the CCSSM, as they do not address the major clusters of the grade and do not have content from prior and future grades connected to grade-level work. The materials do have supporting content connected to major work and partially make connections between clusters and domains.
Criterion 1.1: Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, do not meet expectations for focus as they do not assess grade-level content and partially provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1a
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, do not meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum has a Grade 5 Tests and Cumulative Reviews section which includes an End-of-Chapter test for each chapter, a Cumulative Review for every chapter after Chapter 1 and one End-of-the-Year test. The assessments include items that addresses and explicitly assess topics from the following: (i) Probability, including chance, likely outcomes, and/or probability models, (ii) Statistical distributions, including center, variation, clumping, outliers, mean, median, mode, range, and/or quartiles; and statistical association or trends, including two-way tables, bivariate measurement data, scatter plots, trend line, line of best fit, and/or correlation, and (iii) Similarity, transformations, and/or congruence.
Note: The user guide identifies the tests as optional; however, the publisher orientation session identified these assessments as a required component for school use. Therefore, the tests are included in this review.
Examples of assessments or assessment items that address (i) probability; (ii) statistical distributions; (iii) similarity, transformations, and/or congruence include, but are not limited to:
Tests and Cumulative Reviews, Chapter 5 Test, Question 4, “The chart shows Alice’s science test scores for five different tests… b) Calculate the average” (6.SP.3)
Indicator 1b
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide limited opportunities for all students to engage with extensive work with grade-level-problems for standards including but not limited to: 5.NBT.1, 5.NBT.6, and 5.NF.5a . The materials provide limited opportunities for all students to meet the full intent with grade-level-problems for the following standard: 5.NF.5b . Some off-grade-level work negatively impacts students’ work with grade-level content.
The materials are divided into two Worktexts, 5-A and 5-B. Each Worktext is divided into chapters. Each chapter is divided into lessons that contain content instruction, mental math problems, puzzle corners, and practice problems, in addition to chapter reviews and a chapter test.
Examples of extensive work with grade-level problems to meet the full intent of some grade-level standards include:
Worktext 5-A, Chapter 1: The Four Operations, The Multiplication Algorithm, Question 2, students use the standard algorithm to solve multiplication problems of multi-digit by one whole number. “Multiply 5- and 6-digit numbers. a. 17552 x 7 b. 27805 x 3 c. 144123 x 5 “ In More Multiplication, Questions 1 and 2, students use the standard algorithm to solve multiplication problems of multi-digit by multi-digit numbers. Question 1, “Multiply. Remember: you will need to place two zeros in the third line. b. 409 x 228 c. 246 x 137” Question 2, “Practice 4-digit by 2-digit and 5-digit by 2-digit multiplications. d. 20516 x 37 e. 31447 x 29” Students engage in extensive work with grade-level problems to meet the full intent of 5.NBT.5 (Fluidly multiply multi-digit whole numbers using the standard algorithm.)
Worktext 5-A, Chapter 4: Decimals, Part 1, Comparing Decimals, Question 2, “Write these numbers in order, from the smallest to the greatest. The number line above can help. ___<___<___<___<___<___<___<___<___” The numbers the students are given are the following: 5.01, 5.3, 5.03, 4.8, 5.24, 4.92, 5.1, 5.15 and 5.19. Question 3, “Compare the numbers and write <, =, or >. You can use the place value charts to help. a 0.6 ___ 0.006 b. 0.03 ___ 0.3” Question 4, “Compare the numbers and write <, =, or >. c. 5.007 ___ 5.4 d. 3.004 ___ 3.400” Students engage in extensive work with grade-level problems to meet the full intent of 5.NBT.3 (Read, write, and compare decimals to the thousandths.)
Worktext 5-B, Chapter 9: Geometry, Volume, Question 1, “Find the Volume of these figures in cubic units. “V” means volume. a. V = ______ cubic units, b V = ______ cubic units” For part “a” a picture of six cubic are provided arranged side by side in rows of three and for part “b” a picture of a rectangular prism is provided made out of cubes two layers of 2x4 cubes” Students are provided the information before the problem that, “This little cube is 1 cubic unit.” Question 2, “Find the total volume of each figure when the edge length of the little cube is given. Remember to include the unit! c. The edge of each cube is 1cm. V = ______ d. The edge of each cube is 1 m. V = ______” Students are given pictures of cubic units in various configurations. Question 3, “Find the volume of these rectangular prisms by finding the amount of cubic units in the bottom layer and multiplying that by the height (how many layers there are). b. Cubes in the bottom layer ______ Height ______ Volume ______” Students are given a picture of rectangular prisms that has a length of 2, width of six, and height of four. Students engage in extensive work with grade-level problems to meet the full intent of 5.MD.4 (Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.)
The materials provide limited opportunities for all students to engage in extensive work with grade-level-problems for standards including, but not limited to:
Students do not have the opportunity to engage in extensive work with 5.NBT.1 (Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left). In Worktext 5-A, Chapter 4: Decimals, Part 1, More Decimals: Thousandths, Question 3, “Fill in, following the model. Note: the phrase “copies of” corresponds to multiplication, and “makes” corresponds to the equal sign. b. ____copies of \frac{1}{100} makes one tenth. ____ x = … f. ____copies of \frac{1}{1000} makes one whole. ____ x = ” Students are not provided extensive work with recognizing that in a multi-digit number, a digit in one place is 1/10 of what it represents in the place to its left.
Students do not have the opportunity to engage in extensive work with 5.NF.5a (Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication). In Worktext 5-B, Chapter 8: Fractions: Multiply and Divide, Multiplication as Scaling/Resizing Decimals, Question 3, “ Will the resulting stick be longer or shorter than the original —- or equally long? You do not have to calculate anything. Compare. a. \frac{9}{8} x —- is longer/shorther than —- … d. \frac{99}{100} x —- is longer/shorter than —-.” Students are not provided extensive work with comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
The materials does not provide for all students the opportunity to engage in the full intent of the following standard:
Students are not provided the opportunity to engage with the full intent of 5.NF.5b (Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1). Throughout the materials students are not provided the opportunity to explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number or explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
The materials include some off-grade-level content that negatively impacts students’ work with the grade-level standards. An example includes, but is not limited to:
Worktext 5-A, Chapter 1: The Four Operations, Review: Addition and Subtraction, Question 1, “Write one addition equation and one subtraction equation to match each bar model. Then solve for x. a. Addition: Subtraction: x = ______” A bar model is shown one part is labeled x the other is labeled 1,057. Below the bar the total is labeled 2,370. Students are asked to solve equations with variables, which does not align to a fifth grade standard.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, do not meet expectations for coherence. The materials partially include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade and do have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The majority of the materials, when implemented as designed, do not address the major clusters of the grade, and the materials do not include content from future grades that is identified and related to grade-level work and do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
Indicator 1c
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, do not meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The materials do not devote at least 65$$\%$$ of instructional time to the major clusters of the grade:
The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 4 out of 9, approximately 44$$\%$$.
The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 66.5 out of 128, approximately 52$$\%$$.
The total number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) 78 out of 157, approximately 50$$\%$$.
A day-level analysis is most representative of the instructional materials as the lessons typically cover multiple days that focus on major work of the grade. As a result, approximately 50$$\%$$ of the instructional materials focus on major work of the grade.
Indicator 1d
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed to connect supporting standards/clusters to the grade’s major standards/clusters. The materials include a Common Core Alignment Document that does not provide guidance for connections between supporting and major work of the grade.
Examples of connections between supporting and major work include:
Worktext 5-A, Chapter 1: The Four Operations, Review: Addition and Subtraction, connects the supporting work of 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them), to the major work of 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm). For example, Question 9, “Write a single expression, numbers and operations for each problem, not just the answer! c. The price of a phone that costs $$\$128$$ is lowered (discounted) by $$\$31$$. George bought five of them. What was the total cost?” Students write and then solve expressions.
Worktext 5-A, Chapter 3: Problem Solving, Problem Solving with Bar Models 1, connects the supporting work of 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them) to the major work of 5.NBT.6 (Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models). For example, Question 2, “Solve. Draw a bar model. Write a single equation that records all the calculations to solve the problem. a. The price of a train ride is $$\$12$$. It went up by \frac{1}{6}. What is the new price? Equation: ___________.” Students create a bar model that helps them to write an equation to solve a problem.
Worktext 5-B, Chapter 7: Fractions: Add and Subtract, Line Plots and More Measuring, connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit. Use operations on fractions for this grade to solve problems involving information presented in line plots.) to the major work of 5.NF.2 (Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.). For example, Question 3, ”c. If Jake puts the three longest cockroaches end-to-end, how long a ‘train’ do they make?” Students use addition of fractions to solve questions about a line plot they create on the lengths of cockroaches.
A supporting work is not connected to the major work of the grade, but the separation is mathematically reasonable. For example:
5.MD.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real world problems.
Indicator 1e
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, partially meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Materials contain multiple connections of supporting work to supporting work throughout, however, some connections of major work to major work are entirely absent from the grade-level materials. Included within the materials is a Common Core Alignment document, however, the document does not provide explicit guidance for connections between or among domains and clusters.
There are some connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:
Worktext 5-A, Chapter 2: Large Numbers and the Calculator, Multiplying Numbers by Powers of Ten, connects the major work of 5.NBT.A (Understand the place value system.) to the major work of 5.NBT.B (Perform operations with multi-digit numbers and with decimals to hundredths.). For example, Question 4, “Explain how the power of ten, number of zeros, and the digits shifting relate in these types of multiplication. Use 104 x 758 for an example.” Students use their understanding of the place value system to perform operations with multi-digit numbers and explain the placement of the decimal point.
Worktext 5-A, Chapter 5: Graphing, Number Patterns in the Coordinate Grid, connects the supporting work of 5.OA.B (Analyze patterns and relationships.) to the supporting work of 5.G.A (Graph points on the coordinate plane to solve real-world and mathematical problems.). For example, Question 1, “a. Fill in the x and y values according to the given rules. The rule for x-values: start at 0, and add 1 each time. The rule for y-values: start at 0, and add 2 each time. b. Plot the points formed by the number pairs. c. What simple relationship exists between each x and y coordinate? d. Why do you think this relationship is there? (Where does it stem from?)” Students use number patterns to create coordinates that they then plot on the coordinate plane.
Worktext 5-B, Chapter 7: Fractions: Add and Subtract, Mixed Review Chapter 7, connects the supporting work of 5.MD.A (Convert like measurement units within a given measurement system.) to the supporting work of 5.G.A (Graph points on the coordinate plane to solve real-world and mathematical problems.). For example, Question 4, “Make a line graph of the baby’s weight.” A 3 column table is provided . Column 1 is labeled “Week” and has the following information: 0, 1, 2, 3, 4, 5, 6, and 7. Column 2 is labeled “Weight” and has the following information: 6 lb 14 oz, 6 lb 12 oz, 6 lb 14 oz, 7 lb, 7lb 2 oz, 7 lb 4 oz, 7 lb 6 oz, and 7 lb 7 oz . Column 3 is labeled “Weight in ounces” and is blank. Students convert the weights into ounces and then graph the data on the chart.
Worktext 5-B, Chapter 9: Geometry, Volume of Rectangular Prisms, connects the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to the hundredths.) to the major work of 5.MD.C (Geometric measurement: understand concepts of volume.). For Example, Question 11, “John’s room is 12 ft x 18 ft and it is 9 ft high. The family plans to lower the ceiling by 1 foot. a. What will the volume of the room be after that? b. How much volume will the room lose?” Students use the standard algorithm for multiplication to solve multi-digit whole number volume problems.
The following connections are entirely absent from the materials:
No connection is made between the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths) to the major work of 5.NF.B (Apply and extend previous understanding of multiplication and division.).
No connections are made to the major work of 5.NF.A (Use equivalent fractions as a strategy to add and subtract fractions.).
Indicator 1f
Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The materials reviewed for Math Mammoth Grade 5, Light Blue Series, do not meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. While some references to future or earlier grade work does occur in the introduction lesson, these references are limited, and are not always related to grade-level concepts or work. The materials include a Common Core Alignment Document that lists the grade-level standards addressed in each lesson, however, the document does not include information regarding the progression of the lesson standards between grade-level bands.
An example within the materials that relates grade-level concepts to future grade content:
Worktext 5-A, Chapter 5: Graphing, Introduction, connects the grade-level work of 5.OA.3 to the future work of 8.F.1. It states, “students study simple number patterns (number rules), and plot points produced by the rule. This concept will later on lead to the study of functions (in 8th grade and beyond).”
There are some examples of references to future grade content, however these references are not always identified and/or related to grade-level work. Examples include, but are not limited to:
Worktext 5-A, Chapter 2: Large Numbers and the Calculator, Introduction, “Concerning exponents and powers, the focus is on powers of ten (such as 102, 105 , 108 and so on), which is what the student should master in this grade level. If your student has difficulties with exponents in general, there is no need to worry. Exponents and powers are taught from scratch again in Math Mammoth grade 6.”
Worktext 5-B, Chapter 7: Fractions: Add and Subtract, Introduction, “In 5th grade, students study most aspects of fraction arithmetic: addition, subtraction, multiplication, and then in some special cases, division. Division of fractions is studied in more detail in 6th grade.”
There are some examples of references to prior grade learning, however not all references relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include, but are not limited to:
Worktext 5-A, Chapter 1: The Four Operations, Introduction, “Next, we review multi-digit multiplication, starting with partial products (including a geometric visualization), and then going on to the standard multiplication algorithm with more digits than in 4th grade…Lastly, we study the topics of divisibility, primes, and factoring. Students review or learn the common divisibility rules for 2, 3, 4, 5, 6, 9, and 10. In prime factorization, we use factor trees. The topic of finding factors is review from 4th grade.”
Math Mammoth Grade 5 Alignment to the Common Core Standards, Worktext 5-A, Chapter 2: Large Numbers and the Calculator, “Note: there is no numbered standard for adding and subtracting whole numbers in 5th grade, but the standards document states in the introduction part for 5th grade that students ‘finalize fluency with multi-digit addition, subtraction, multiplication, and division.While rounding and estimating are not mentioned in the standards for 5th grade, since students learn and use bigger numbers in this chapter than they did in 4th grade, I feel it is good to review and practice them one more time.”
Indicator 1g
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.