4th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 78% |
|---|---|
Criterion 1.1: Focus | 4 / 6 |
Criterion 1.2: Coherence | 7 / 8 |
The materials reviewed for Math in Focus: Singapore Math Grade 4 partially meet expectations for focus and coherence. For focus, the materials partially meet expectations for assessing grade-level content and providing all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials meet expectations for coherence and consistency with the CCSSM.
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 in Focus: Singapore Math Grade 4 partially meet expectations for focus as they 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 in Focus: Singapore Math Grade 4 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
Summative assessments provided by the materials include Chapter Tests, Cumulative Reviews, and Benchmark Assessments and are available in print and digitally. According to the Preface of the Math in Focus: Assessment Guide, "Assessments are flexible, teachers are free to decide how to use them with their students. ... Recommended scoring rubrics are also provided for some short answer and all constructed response items to aid teachers in their marking." The following evidence is based upon the provided assessments and acknowledges the flexibility teachers have in administering them in order to understand their students' learning.
The provided assessments, found in the Assessment Guide Teacher Edition, assess grade-level standards. Examples include:
In Chapter Test 1, Section B, Item 8 (Paper) states, “Store A earns $10,347. Store A earns $1,255 more than Store B. How much do the two stores earn in all? Show your work and write your answer in the space below.” (4.NBT.4)
In Chapter Test 2, Section B, Item 9 (Online) states, “Mr. Jones has 3,250 grams of blueberries. His neighbor gives him another 2,750 grams of blueberries. He uses 5,250 grams of blueberries to make some jelly. He then divides the remaining blueberries equally among his 3 children. How many grams of blueberries does each child receive? Show your work and write your answer in the space below.” (4.OA.3)
In Chapter Test 3, Section A, Item 4 (Online) states, “Which pairs of fractions show a correct comparison? Choose the two correct answers. A) \frac{2}{3}>\frac{1}{4} B) \frac{3}{5}<\frac{3}{8} C) \frac{4}{5}>\frac{3}{4} D) \frac{3}{8}>{2}{3} E) \frac{1}{10}>\frac{7}{10}.” (4.NF.2)
In Chapter Test 6, Section B, Item 7 (Paper) states, “Michael bent a 40-inch wire into a square. What is the area inside the square? Show your work and write your answer in the space below.” A picture of a square is shown. (4.MD.3)
In Chapter Test 8, Section C, Item 11 (Paper) states, “Jason says that the shape below is a rectangle. Do you agree with Jason? Explain.” (4.G.2)
The provided assessments also assess above-grade assessment items that could be removed or modified without impacting the structure or intent of the materials. Examples include:
In Chapter 4 Test, Section A, Item 5 (Online) states, “A number has two decimal places. It is 1 when rounded to the nearest whole number. What could the number be? Choose the three correct answers. A) 1.19, B) 1.24, C) 1.48, D) 1.59, E) 1.67, F) 1.88.” This item assesses 5.NBT.4 (Use place value understanding to round decimals to any place).
In the Mid-Year Benchmark Assessment, Section A, Item 9 (Online) states, “What is the product of 753 and 19? A) 7,110, B) 7,530, C) 13,887, D) 14,307.” This item assesses 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm).
In Chapter Test 6, Section B, Item 6 (Paper) states, “Find the area of the shaded parts of the figure. Show your work and write your answer in the space below.” (An image of a rectangle with labeled sides of 8m and 10m is provided. There is an unshaded parallelogram cutting the rectangle into 2 trapezoids.) This item assesses 6.G.1 (Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems).
In the End-of-Year Benchmark Assessment, Section A, Item 6 (Paper) states, “What is the missing number? 20 + 3 + 0.05 = ___ A) 2.35, B) 20.35, C) 23.05, D) 23.5.” This item assesses 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used).
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 in Focus: Singapore Math Grade 4 partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Materials provide opportunities for students to engage in grade-level problems during Engage, Learn, Think, Try, Activity, and Independent Practice portions of the lesson. Engage activities present an inquiry task that encourages mathematical connections. Learn activities are teacher-facilitated inquiry problems that explore new concepts. Think activities provide problems that stimulate critical thinking and creative solutions. Try activities are guided practice opportunities to reinforce new learning. Activity problems reinforce learning concepts while students work with a partner or small group. Independent Practice problems help students consolidate their learning and provide teachers information to form small group differentiation learning groups.
The materials provide students extensive work with grade-level problems to meet the full intent of some grade-level standards. Examples include:
In Section 2.2, Quotients and Remainders, students find quotients and remainders in division problems. In Engage, Problem 1, page 121, students use counters to solve equal sharing problems. The problem states, “Share 11 red counters with your partner. How did you do it? Draw a sketch to explain your thinking.” In Try, Problem 1, page 122, students work in pairs to find quotients and remainders. The problem states, ”Write each division quotient and remainder. 21 ÷ 8 = __ R __ , Quotient = __ , Remainder = __ .” In Independent Practice, Problem 1, page 123, students use pictures to divide. The problem states, “Divide 18 keychains equally among 7 children. How many keychains are left? 18 ÷ 7 + __, Quotient = __, Remainder = __ , So 18 ÷ 7 = __. Each child receives keychains. There are _ keychains left.” Eighteen keychains are shown. Students engage with extensive work to meet the full intent of 4.NBT.6 (Find whole-number quotients and remainders with up to four-digit dividends and one-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).
In Section 3.1 Equivalent Fractions, students use multiplication and division to find equivalent fractions and write a fraction in simplest form. In Engage, Problem A, page 231, students use models to show equivalent fractions. The problem states, “Use fraction circles or fraction strips to show $$\frac{1}{2}$$ in two ways.” In Learn, Problem 3, page 232, students use division to find equivalent fractions. The problem states, “You can also find equivalent fractions by simplifying fractions. You simplify a fraction by dividing the numerator and denominator by the same number.” Two sets of visual fraction models are shown. In Hands-On Activity, Problem 1, page 233, students use strips of paper to find equivalent fractions. The problem states, “Your teacher will give you two strips of paper. Use them to form a pair of equivalent fractions. Paste the strips in the box.” Two fraction strips are shown. In Try, Problem 7, page 235, students write fractions in simplest form. The problem states, “Write each fraction in simplest form, $$\frac{8}{12}=\frac{\Box}{3}$$.” In Independent Practice, Problem 7, page 238, states, “ Find the next eight equivalent fractions, $$\frac{1}{5}$$ = __ = __ = __ = __ = __ = __ = __ = __ .” Students engage with the extensive work to meet the full intent of 4.NF.1 (Explain what a fraction $$\frac{a}{b}$$ is equivalent to a fraction $$\frac{n×a}{n×b}$$ by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions).
In Section 4.5, Fractions and Decimals, students express a fraction as a decimal and a decimal as a fraction. In Engage, Problem A, page 383, students use a number line to express a fraction as a decimal. The problem states, “Draw a number line with endpoints 0 and 1. Mark a point ot show $$\frac{1}{2}$$ on your number line. What decimal does the point represent? Explain your thinking to your partner.” In Learn, Problem 3, page 384, students express fractions as decimals. The problem states, “Express $$3\frac{4}{5}$$ as a decimal.” In Try, Problem 1, page 386, students express decimals as fractions on a number line. The problem states, “Express each decimal as a fraction or mixed number in simplest form, 0.4 = ___.” In Learn, Problem 1, page 387, students add tenths and hundredths by converting fractions to decimals. The problem states, “A table is $$\frac{7}{10}$$ meter long. A bench is $$\frac{81}{100}$$ meter long. Find the total length of the table and the bench. Express your answer as a decimal.” Students engage with extensive work to meet the full intent of 4.NF.6 (Use decimal notation for fractions with denominators 10 or 100).
In Section 7.4, Finding Unknown Angles, students solve real-world problems by using addition or subtraction to find unknown angle measures. In Try, Problem 1, page 216, states, “The measure of ∠XOY is 125o and the measure of ∠YOZ is $$15\degree$$. Find the measure of ∠XOZ.” In Engage, page 219, students “Fold a square piece of paper along the diagonal. What can you say about the new angles formed in the corners? What are the measures of the new angles? How do you know?” In Try, Problem 2, page 220, states, “Ms. Mitchell has a square piece of cloth. She wants to cut the cloth as shown to make a pattern. What is the measure of ∠y?” In Independent Practice, Problem 4, page 222, students find missing angle measures. The problem states, “Silvana buys a paper fan during a carnival. Find the measure of ∠LTN.” Students engage with extensive work to meet the full intent of 4.MD.7 (Recognize angle measure as additive).
In Section 8.1, Classifying Triangles, students classify triangles by their angle measures. In Hands-on Activity, Problem 2, page 261, students work in pairs to classify triangles. The problem states, “Sort the triangles by their angle measures and complete the table below. Write the letter of each triangle in the correct group.” In Try, Problem 1, page 262, states, “Which of these triangles is right, obtuse, or acute? Use a protractor to help you. Measure of ∠PRQ = __$$\degree$$, Measure of ∠PQR = __$$\degree$$, Measure of∠QRP = __$$\degree$$. Triangle PQR is an/an __ triangle.” In Independent Practice, Problem 2, page 264, states, “Circle the triangle that does not belong in each set. Explain.” Three acute triangles and one obtuse angle triangle are shown. Students engage with extensive work to meet the full intent of 4.G.2 (Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size and recognize right triangles as a category, and identify right triangles).
Materials do not provide students the opportunity to engage with the full intent of some grade-level standards. For example:
Students are not provided the opportunity to engage with the full intent of 4.NF.3b (Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation). According to the the Common Core State Standards Correlations, page T73, 4.NF.3b is addressed in Section 3.4, Mixed Numbers; Section 3.5, Improper Fractions (page 267); and 3.6, Renaming Improper Fractions and Mixed Numbers (page 275). In, Section 3.5, Improper Fractions, Learn, Problem 4, page 269, states, “Write an improper fraction for the shaded parts. Express the fraction in simplest form.” In these two sections, students work with reducing fractions, mixed numbers, and simplifying improper fractions. However, students are not “decomposing a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation or justifying decompositions by using a visual fraction model.”
Materials do not provide extensive work with some grade-level standards. Examples include:
The materials do not provide extensive work with 4.NBT.1(Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right). According to the Common Core State Standards Correlations, page T71, this standard is addressed in Section 1.1, Numbers to 100,000, page 11 and Section 1.2, Numbers to 1,000,000, page 19. In these sections, students work with place value, understanding the value of a digit and writing numbers in a variety of forms. Students do not have the opportunity to engage with extensive work of 4.NBT.1.
The materials do not provide extensive work with 4.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction by a whole number). In Sections 3.8 and 3.9, 4.NF.4a, b, and c are addressed. In Section 3.8, Multiplying Fractions and Whole Numbers, students have the opportunity to multiply a whole number and a fraction, and relate the product to a multiple of a unit fraction. For example, in the Independent Practice, Problem 5 states, “$$3 × \frac{1}{6}$$.” Problem 6, “$$11 × \frac{2}{3}$$.” In Section 3.9, Real-World Problems: Fractions, students have the opportunity to solve real-world problems involving multiplying whole numbers and fractions. For example, in the Independent Practice, Problem 10 states, “Solve. Draw a bar model to help you. Ethan walks $$\frac{5}{6}$$ kilometer to th bus stop each morning. How far does he walk in 5 days?” Problem 11 states, “Solve. Draw a bar model to help you. Mr. Brown spends $$\frac{2}{3}$$ hour gardening every day. How long does he spend gardening in one week?” Per the Math in Focus 2020 Comprehensive Alignment to CCSS: Grade 4, these are the two lessons that address 4.NF.4a, b, c, and d. Therefore, students do not have the opportunity to engage in extensive work with 4.NF.4a, b, and c.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Math in Focus: Singapore Math Grade 4 meet expectations for coherence. The majority of the materials, when implemented as designed, address the major clusters of the grade, and the materials have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials also 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 partially have content from future grades that is identified and related to grade-level work and 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 in Focus: Singapore Math Grade 4 meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.
There are 9 instructional chapters, of which 4.5 address major work of the grade, or supporting work connected to major work of the grade, approximately 50%.
There are 82 sections (lessons), of which 46.5 address major work of the grade, or supporting work connected to major work of the grade, approximately 57%.
There are 151 days of instruction, of which 102.5 days address major work of the grade, or supporting work connected to the major work of the grade, approximately 68%.
A day-level analysis is most representative of the instructional materials because the days include all instructional learning components. As a result, approximately 68% 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 instructional materials reviewed for Math in Focus: Singapore Math Grade 4 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Examples include:
Section 2.6, Multiples, connects the supporting work of 4.OA.4 (Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number…) to the major work of 4.NF.2 (Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as $$\frac{1}{2}$$. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, eg.., by using a visual fraction model). This connection is evident in Problems 1 and 2 on page 185. Problem 1 states, “Find the first common multiple of 2 and 3.” Problem 2 states, “How can you use the answer in Problem 1 to compare $$\frac{1}{2}$$ and $$\frac{2}{3}$$?”
Section 3.9, Real-World Problems: Fractions, connects the supporting work of 4.MD.4 (Make a line plot to display a data set of measurements in fractions of a unit $$(\frac{1}{2}, \frac{1}{4}, \frac{1}{8})$$ Solve problems involving addition and subtraction of fractions by using information presented in line plots) with the major work of 4.NF.3c (Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction and or by using properties of operations and the relationship between addition and subtraction). In Independent Practice, Problem 3, page 316, students use data charts to solve problems involving addition and subtraction of fractions by answering the question. Problem 4 states, “Answer the question. Zoe planted some seeds. After two months, she recorded the heights of the plants.” Students are provided a pre-filled table to create a fraction line plot to answer Problems 7, 8, and 9a. Problem 7 states, “What is the difference in height between the shortest and tallest plants?” Problem 8 states, “What is the sum of the heights of the shortest and tallest plants?” Problem 9a states, “Three plants grew $$\frac{3}{4}$$ feet How much did they grow in all?”
Section 5.1, Length in Customary Units, connects with supporting work of 4.MD.1 (Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit) to the major work of 4.NBT.5 (Multiply a whole number of up to four digits by a one-digit whole number…). In Try, Problem 1, page 10, states, “Practice measuring length in feet and inches. Write each length in inches. You can use a table to help. 3 ft = __$$\bigcirc$$__=____in.”
Section 6.1, Area and Unknown Sides connects supporting work of 4.MD.3 (Apply the area and perimeter formulas for rectangles in real world and mathematical problems) to the major work of 4.NBT.6 (Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors as students solve area problems that require division). In Independent Practice, Problem 10, page 128, states, “The area of a rectangular pool is 225 square meters. The width of the pool is 9 meters. a. Find the length of the pool. b. Find the perimeter of the pool.”
Section 7.4, Finding Unknown Angles, connects supporting work of 4.MD.7 (Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems) to the major work of 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm). In Try, Problem 1, page 220, students “Practice solving real-world problems involving unknown angles. Find each unknown angle. Vijay used a rectangular piece of cardboard and a triangular piece of cardboard to make a model of a house. The measure of ∠PTQ is 35$$\degree$$. What is the measure of ∠PTS?”
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 instructional materials for Math in Focus: Singapore Math Grade 4 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.
Examples of connections between major work and major work and connections between supporting work and supporting include:
Section 1.6, Real-World Problems: Addition and Subtraction, connects the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic) to the major work of 4.OA.A (Use the four operations with whole numbers to solve problems, as students use bar models to solve real-world addition and subtraction problems). In Independent Practice, Problem 1, page 73, states, “A construction company needed 15,010 tiles to completely cover the lobby of a building. Some tiles were laid on the first week and 7,823 tiles were laid on the second week. At the end of the second week, 1,950 tiles were left. How many tiles were laid on the first week?”
Section 2.7, Real World Problems: The Four Operations, connects the major work of 4.OA.A (Use the four operations with whole numbers to solve problems) to the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic, as students solve multi-step story problems involving the four operations). In Independent Practice, Problem 2, page 202, states, “Kimberly made some bookmarks to sell for charity. She kept 1,022 bookmarks aside and bundled the rest equally in packs of 3. She sold all the bookmark packs for $4 each, and earned $3,704 for the charity. How many bookmarks did Kimberly make?”
Section 4.1, Understanding Tenths, connects the major work of 4.NF.A (Extend understanding of fraction equivalent and ordering) to the major work of 4.NF.C (Understand decimal notation for fractions and compare decimals fractions, as students explore tenths with fraction models). In Independent Practice, Problem 1, page 353, students “Write the decimal represented by the shaded part in each figure.” An image with a circle divided into tenths with three of the tenths shaded is provided.
Section 4.5 Fractions and Decimals, connects the major work of 4.NF.B (Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers) to the major work of 4.NF.C (Understand decimal notation for fractions, and compare decimal fractions, as students add fractions and express the answer as a decimal). In Try, Problem 1, page 388, students “Add. Express each answer as a decimal. $$\frac{3}{10} + \frac{49}{100}$$.”
Section 7.2, Drawing Angles to 180o, connects supporting work 4.G.A (Draw and identify lines and angles, and classify shapes by properties of their lines and angles) to supporting work 4.MD.C (Geometric measurement: understand concepts of angle and measure angles, as students draw and identify angles by understanding concepts of angle measurement). In Try, Problem 4, page 201, students “Join the marked endpoint of each ray to one of the dots to form an angle with the given value. Then, label the angle. Measure of ∠b = 80$$\degree$$.” The included drawing shows a horizontal ray with two points (one at the vertex, the other near the arrow). There are two dots located above the vertex. Students must determine which of the two dots will provide the correct angle measure when connected.
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 in Focus: Singapore Math Grade 4 partially 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.
Materials relate grade-level concepts to prior knowledge from earlier grades. Prior Knowledge highlights the concepts and skills students need before beginning a new chapter. The section What have students learned? states the learning objectives and prior knowledge relevant to each chapter. The Math Background identifies the key learning objectives and provides an overview of how prior work connects with grade level work. Examples include:
In Teacher Edition, Chapter 3, Fractions and Mixed Numbers, Chapter Overview, Math Background, page 221A, connects prior work of 3.NF.A with grade-level work of 4.NF.B.3c. It states, “In earlier grades, students have learned to represent fractions pictorially, as a sum of unit fraction, and on a number line. Students have learned how to find equivalent fractions and compare and order fractions less than one. Students will be familiar with the term like fractions. In this chapter, they add and subtract unlike fractions with and without renaming. The unlike fractions at this grade level are restricted to denominators that are multiples of one of them (called related fractions), so that only one fraction needs to be renamed. They will also be introduced to the concept of fractions of a set, and will apply this knowledge to multiply a fraction by a whole number.”
In Teacher Edition, Chapter 4, Decimals, Recall Prior Knowledge, page 342, connects prior work of 3.NF.A with grade-level work of 4.NF.6. It states, “In Grades 3 and 4, students learned to read, write, and identify fractions of a whole, interpret pictorial representations of mixed numbers, and use multiplication and division to find equivalent fractions. They used number lines and place value to round numbers to the nearest ten and learned to add like fractions.”
In Teacher Edition, Chapter 5, Conversion of Measurements, Chapter Overview, Math Background, page 1A, connects prior work of 3.MD.2 to grade-level work of 4.MD.1. It states, “In earlier grades, students learned to measure length, weight, and capacity using metric and customary units of measurement. They learned to convert metric and customary units from larger to smaller units. Students estimated and measured length to the closest $$\frac{1}{2}$$ and $$\frac{1}{4}$$ inch. In this chapter, students will further their understanding of length, mass, weight, and volume. They will understand that, when converting from larger to smaller units, a greater number of smaller units is needed, so they must multiply. They will also learn how to use and convert metric measurements for length, mass, weight, and volume.”
In Teacher Edition, Chapter 6, Area and Perimeter, Chapter Overview, Math Background, page 101A, connects prior work of 3.MD.C and 3.MD.D to grade-level work of 4.MD.3. It states, “In Grade 3, students gained an understanding of the concepts of perimeter and area. They learned to find the perimeter and area of squares and rectangles on grid paper. In this chapter, students learn to find the area and perimeter of figures using formulas.”
In Teacher Edition, Chapter 8, Polygons and Symmetry, Chapter Overview, Math Background, page 255A, connects prior work of 3.G.1 to grade-level work of 4.G.2 and 4.G.3. It states, “In Grade 2, students explored plane shapes, learning to identify and describe the properties of both curved and straight-sided figures. In Grade 3, students build on their knowledge to classify shapes by identifying like properties. In this chapter, students will apply their knowledge of angles to define acute, obtuse, and right triangles. They will learn how to classify polygons based on whether the figures have sides of equal lengths or are parallel, for example.”
Within the Chapter Overview, Learning Continuum, materials relate grade-level concepts to upcoming learning but do not identify content from future grades. The section What will students learn next? states the learning objectives from the following chapter (or grade) to show the connection between the current chapter and what students will learn next. However, there is no specific correlation made to how the standards connect. The online materials do not include the standard notation. Examples include:
In Teacher Edition, Chapter 2, Multiplication and Division, Learning Continuum, What will students learn next?, page 89G, states, “In Grade 5 Chapter 1, students will learn: Multiplying and dividing by 2-digit numbers fluently (5.NBT.5, 5.NBT.6), Real-world problems: four operations of whole numbers (5.OA.1). In Course 1 Chapter 1, students will learn: Common factors and multiples (6.NS.4).”
In Teacher Edition, Chapter 4, Decimals, Learning Continuum, What will students learn next?, page 341E, states, “In grade 5, Chapter 5, students will learn: Four operations with decimals (5.NBT.2, 5.NBT.7).”
In Teacher Edition, Chapter 6, Area and Perimeter, Learning Continuum, What will students learn next?, page 101E, states, “In Grade 5 Chapter 6, students will learn: Volume of rectangular prisms (5.MD.5). In Course 1 Chapter 10, student will learn: Area of triangles (6.G.1, 6.EE.2c), Area of parallelograms and trapezoids (6.G.1, 6.EE.2c), Area of other polygons (6.G.1, 6.EE.2c).”
In Teacher Edition, Chapter 7, Angle and Line Segments, Learning Continuum, What will students learn next?, page 171E, states, “In grade 5, Chapter 8, students will learn: Classifying triangles (5.G.3).”
In Teacher Edition, Chapter 9, Tables and Line Graphs, Learning Continuum, What will students learn next?, page 309E, states, “In Grade 5 Chapter 7, students will learn: Making and interpreting line graphs (5.MD.2), In Course 1 Chapter 12, students will learn: Collecting and tabulating data. (6.SP.1, 6.SP.5a, 6.SP.5b), Dot plots and number lines (6.SP.2, 6.SP.4), Histograms (6.SP.4).”
Indicator 1g
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.