The materials reviewed for Math in Focus: Singapore Math Grade 5 do not 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 9 (Paper) states, “What is the value of 23 - 5 × (7 - 3)?” Show your work and write your answer in the space below.” (5.OA.1)

• In Chapter Test 2, Section B, Item 8 (Online) states, “Share 5 fruit tarts equally among 8 children. What fraction of a fruit tart will each child receive? Show your work and write your answer in the space below.” (5.NF.3)

• In Cumulative Review 2, Section C, Item 22 (Paper) states, “Three boys recorded their long jump distances. Eric jumped 6 centimeters further than Daniel. Eddie jumped 0.12 meters further than Eric. The three boys jumped a total of 5.19 meters. How far did Eddie jump?” (5.MD.1)

• In the Mid-Year Benchmark Assessment, Section B, Item 22 (Online) states, “Divide 7,001 by 57. Show your work and write your answer in the space below.” (5.NBT.6)

• In Chapter Test 8, Section A, Item 3 (Paper) states, “Which statements about the shape are correct? Choose the two correct answers. [A picture of a kite is shown.] A) It is a kite. B) It is a rhombus. C) It has two pairs of parallel sides. D) It has two pairs of equal sides. E) Its opposite sides are equal.”  (5.G.3)    

The provided assessments also assess above-grade assessment items that could not be removed or modified without impacting the structure or intent of the materials. Examples include:

• In Chapter Test 9 (Online), all assessment items are aligned to 6.RP.1 (Understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities). For example, Section A, Item 2 states, “What is the missing number?  3:7 = 12: ___ A) 16, B) 21, C) 28, D) 40.”

• In Chapter Test 10 (Online), all assessment items are aligned to 6.RP.3c (Find a percent of a quantity as a rate per 100 [e.g., 30% of a quantity means 30/100 times the quantity]; solve problems involving finding the whole, given a part and the percent). For example, Section A, Item 5 states, “There are 100 red and blue beads in a box. 30 of the beads are blue. What percent of the beads are red beads?”

• In Cumulative Review 4, Section A, Item 8 (Online) states, “There are 800 people at a carnival. 64% of them are adults. How many people are adults? A) 512, B) 486, C) 482, D) 480.” This item assesses 6.RP.3c (Find a percent of a quantity as a rate per 100 [e.g., 30% of a quantity means 30/100 times the quantity]; solve problems involving finding the whole, given a part and the percent).

• In the End of Year Benchmark Assessment (Online), 11 of the 40 assessment items align to above-grade-level standards. For example, Section B, Item 20 states, “Express $\frac{140}{700}$ as a percent.” (6.RP.3c)

The materials reviewed for Math in Focus: Singapore Math Grade 5 do not 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, Hands-on 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 1.4, Multiplying and Dividing by 2-Digit Numbers Fluently, students multiply multi-digit whole numbers. In the Engage activity on page 45, students begin by using place value chips to multiply. The problem states, “What is 56 × 3? What is 56 × 20? How do you use your answers to find 56 × 23? Explain your reasoning. Can you use the same method to find 549 × 28? What is another way to find the answer? Explain your thinking to your partner.” In Learn, Problem 1, page 45, students multiply using the standard algorithm. The problem states, “Multiply 63 by 28.” Try, Problem 1, page 47, students practice multiplying by a 2-digit number, “97 × 53.” In Independent Practice, Problem 5, page 59, students multiply and estimate to check that each answer is reasonable. The problem states, “235 × 21 = ____.” Students engage with extensive work to meet the full intent of 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm).

• In Section 2.1, Fractions, Mixed Numbers, and Division Expressions, students solve problems involving equal shares resulting in fractional answers. Engage, page 113, states, “Divide two square pieces of paper into three equal parts each. Put the pieces into equal groups. How many ways can you do it? How can you name each group? Now do the same in another way.” In Try, Problem 2a, page 116, students divide bars into equal pieces and write the fraction. The problem states, “Share 2 granola bars equally among 3 children. What fraction of a granola bar does each child receive? 2 ÷ 3 = ____. Each child receives ____ of a granola bar.” In Learn, Problem 1, page 117, students rewrite division expressions as mixed numbers. The problem states, “Mr. Davis made 5 pancakes. The pancakes were divided equally among his 4 children. How many pancakes did each child receive?” There are four colored pies (representing pancakes) divided into four equal parts included in the problem. Two colored rectangles are included in the problem. In Independent Practice, Problem 4, page 121, students “Express each division expression as a fraction in simplest form. Rewrite the fraction as a mixed number if necessary, 18÷ 8 = ___.” Students engage with extensive work to meet the full intent of 5.NF.3 (Interpret a fraction as division of the numerator by the denominator $$(\frac{a}{b}=a÷b)$$. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem). 

• In Section 7.1, Making and Interpreting Line Plots, students make and interpret line plots with fractional data, and solve problems involving fractions. In Engage, page 73, students measure lengths and create a data display of the measurements. The materials state, “Measure each piece of ribbon in inches. Now, record the length of each piece of ribbon in feet. Then create a data display. Share with your partner how you did it.” Ten pieces of ribbon with different lengths are provided with the problem. In Try, Problem 1, page 75, students make and interpret line plots. The problem states, “The tally chart (provided) shows the weights of the raisins in 12 bags of trail mix. Use the data to fill in the table and make a line plot.” In Independent Practice, Problem 2, page 77, states, “The table (provided) shows the weights of 10 wedges of cheese. Use the Line plot in 1 to answer 2 and 3. What is the total weight of the 10 wedges of cheese?” Students engage with extensive work to meet the full intent of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit $$(\frac{1}{2}, \frac{1}{4}, \frac{1}{8})$$. Use operations on fractions for this grade to solve problems involving information presented in line plots).

• In Section 7.3, Number Patterns and Graphs, students identify and extend number patterns and the relationship between two sets of numbers. In Engage, Problem 1, page 91, students find a rule in a number pattern. The problem states, “Look at each number pattern. a) 2, 4, 8, 16, …, b) 2, 3, 5, 8, 13, … Discuss with your partner how you can find the rules of the patterns.” In Learn, Problem 1, page 94, students generate patterns from a table and draw graphs. The problem states, “Two water bottles A and B are being filled at two different taps. Bottle A is filling at a rate of 50 milliliters of water every second. Bottle B is filling at a rate of 25 milliliters of water every second. The tables show the total amount of water in the two water bottles during the first 5 seconds. How much water is in each bottle after 4 seconds?” In Try, Problem 1, page 98, students generate patterns and draw graphs. The problem states, “Complete the number pattern. Then, plot each point on a coordinate plane and make a line graph. Car A consumes 1 gallon of gas for every 35 miles it travels. Car B consumes 2 gallons of gas for every 60 miles it travels.” Two tables and a graph are shown for cars A and B showing the gas each car consumed (gal) and distance traveled (mL). In Independent Practice, Problem 2 on page 101, students identify the rule in each pattern. A table showing the pattern is given “Pattern: 26, 52, 104, 208, 416, … Rule: _______.” Students engage with extensive work to meet the full intent of 5.OA.3 (Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane). 

• In Section 8.2, Classifying Polygons, students classify polygons using a hierarchy based on properties. In Engage, page 131, students draw and describe four sided shapes. The materials state, “Draw 2 different shapes with four equal sides. How are they the same? How are they different?” In Learn, Problem 1, page 131, students classify polygons. The problem states, “When all sides of a polygon are equal and all the angles within the polygon are equal, the polygon is called a regular polygon.” In Try, Problem 5, page 134, states, “Write trapezoid, parallelogram, rectangle, rhombus, kite, or square.” In Independent Practice, Problem 3, page 135, states, “Name each polygon. Identify whether each is a regular polygon. Name ______ Is this a regular polygon? ______. “ A picture of an octagon is provided. Students engage with extensive work to meet the full intent of 5.G.4 (Classify two-dimensional figures in a hierarchy based on properties).

Materials do not provide students the opportunity to engage with the full intent of some grade-level standards. Examples include:

• Students are not provided the opportunity to engage with the full intent of 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 $$\frac{1}{10}$$ of what it represents in the place to its left). For example, in Section 1.1, Numbers to 10,000,000, Try, Problem 9, page 15, students read and write numbers to 10,000,000 in expanded form, standard form, and word form. The problem states, “Complete each expanded form. 2,300,598 = 2,000,000 + _____ + 500 + 90 + 8.” In Independent Practice, Problem 7, page 17, students read numbers in standard form and write them in word form. The problem states, "Write each number in word form: 1,215,905 _________.” According to the CCSS Correlations Chart in the Teacher Manual, page T71, this standard is addressed in Chapter 4 on nearly every page, but no evidence of this standard is present in the student work. Additionally, students do not have extensive work with problems involving an explanation of how digits are $$\frac{1}{10}$$ of what they represent to their place to its left. Students read and write numbers up to 10,000,000 in standard, expanded, and word form. Therefore, students do not have the opportunity to engage with the full intent of 5.NBT.1.

• Students are not provided the opportunity to engage with the full intent of 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). Students only work with metric unit conversions. There is no evidence of conversions with customary units of measurements, intervals of time, money; or solving real-world problems using these conversions. For example, Section 5.8, Converting Metric Units, Engage, Problem 1, page 416, states, “What is 1 centimeter in meters? What is 8 centimeters in meters? What are two ways to find the answer?” In Learn, Problem 3, page 417, states, “Convert 2,500 grams to kilograms.” According to the CCSS Correlations Chart, Teacher Manual on page T7, this standard is also addressed on pages 27-42, 57, 55-62, and 63j-64 of the Student and Teacher Editions. However, there is no evidence that students work with customary units on these pages. Therefore, students are not given the opportunity to engage with the full intent of 5.MD.1. 

Materials do not provide extensive work with all standards. Example include:

• The materials do not provide extensive work with 5.NBT.3a (Read and write decimals to thousandths using base-ten numerals, number names and expanded form). Section 4.1, Understanding Thousandths, contains limited opportunities for students to write decimals to thousandths using expanded form. Additionally, students do not have the opportunity to write decimals in expanded form using fractions. In Try, Problem 10, page 298, students practice expressing thousandths as decimals. The problem states, “Fill in each blank 5 + 0.3 + 0.07 + 0.004 =_____.” Students have limited opportunities to read or write decimals with number names, write decimals to thousandths using expanded form, and write decimals in expanded form using fractions. Therefore, students do not have the opportunity to engage with extensive work of 5.NBT.3a.