The materials reviewed for Math in Focus 2020 Grade 3 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 2, Section C, Item 11 (Paper) states, “Evan skipped 127 times in the first round of a competition. He skipped 75 more times in the second round. He said that the number of skips for the second round was 192. Explain Evan’s mistake. What number should have been recorded for the second round? Explain how you arrived at your answer.” (3.NBT.2)

• In Chapter Test 4, Section A, Item 12 (Paper) states, “James looks at the multiplication table of 6 and says that the answers to the multiplication equations are all even numbers. Explain whether James’ observation is true. What multiplication tables have equations with answers that are all even numbers?” (3.OA.9)

• In Cumulative Review 3, Section B, Item 18 (Online) states, “Claire wrote that $\frac{1}{4}>\frac{1}{3}$ and explained that it is because 4 is greater than 3. Is she correct? Explain. Write your answer and your work or explanation in the space below.” (3.NF.3d)

• In Chapter Test 10, Assessment Guide, Section A, Item 4 (Paper) states, ”Ruth went to a party for 135 minutes. Which of the following is equal to 135 minutes? A) 1 hour 35 minutes, B) 2 hours 15 minutes, C) 2 hours 75 minutes, D) 13 hours 5 minutes.” (3.MD.1) 

• In Chapter Test 12, Section B, Item 7 (Paper) states, “Is the shape a quadrilateral? Write ‘Yes’ or ‘No’ for each shape.  Hexagon:____ Parallelogram: ____ Rhombus: ____.” (3.G.1) 

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 2, Section B, Item 6 (Online) states, “6,359 + 2,178 =____ . Write your answer in the answer grid.” This item assesses 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm).

• In Chapter 2 Test (Paper), seven of the 12 assessment items align to 4.NBT.4 (Fluently add and subtract multi-digit whole numbers). For example, Section B, Item 8 states, “Ms. Carter saves $1,438. She saves $250 less than Ms. Jones. How much do they save in all?”

• In Chapter Test 3 (Paper), nine of the 12 assessment items are aligned to 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm). For example: Chapter Test 3, Section A, Item 2 states, “What is the difference between 7,794 and 1,704?” A) 6,054 B) 6,090 C) 7,620 D) 9,498.”

• In Chapter Test 5 (Online), 10 of the 12 assessment items are aligned to 4.NBT.5 (Multiply a whole number of up to four digits by a one-digit whole number). For example: 

  • In Section A, Item 5 states, “There are 176 pennies in each jar. How many pennies are there in 6 jars? A) 626, B) 1026, C) 1056, D) 2456.”

  • In Section A, Item 3 states, “Which expression could not be used to find the value of 549 × 3?” A) (500 × 3) + (40 × 3) + (9 × 3), B) (500 × 3) + (50 × 3) - (1 × 3), C) (500 × 3) + (50 × 3) - (2 × 3), D) (500 × 3) + (40 × 3) + (5 × 3) + (4 × 3).  

  • In Section A, Item 4 (Online) states, students are shown a vertical version of the multiplication problem 1? 8 × 2 = 296. Students answer, “What is the missing digit? A) 1, B) 2, C) 3, D) 4.” 

• In Cumulative Review 1, Section C, Item 23 (Online) states, “Alan has $20. He wants to buy some stationery from a store. Alan buys a few different items. He wants only one of each item. The 5 items are listed in a table, ‘Cost of Stationary,’ ranging in cost from $5.25 to $11.59. Which items should he buy so that he has the least change left? Explain how you arrived at your answer.” This item assesses 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using strategies based on the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used). 

• In Chapter Test 7, Section C, Item 10 (Online) states, “There were 24 people at a party. $\frac{3}{4}$ of the people at the party were children and the rest were adults. $\frac{1}{2}$ of the children wore party hats. How many children did not wear party hats? Show your work and write your answer in the space below.” This item assesses 4.NF.4c (Solve word problems involving multiplication of a fraction by a whole number). 

• In Chapter 8 Test (Online), 11 of the 12 assessment items align to 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit…). For example, Item 7 states, “A tank contains 7 liters 550 milliliters of water. How many milliliters of water does the tank contain? Show your work and write your answer in the space below.”

• In Chapter 12 Test (Paper), five of the 11 assessment items are aligned to 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…). For example, Item 6 states, “Use a number to complete the sentence. Write the answer in the blank. A rectangle has ___ pairs of parallel sides.”

• In the End-Of Year Benchmark Assessment, Section B, Item 37 (Paper) states, “Which angles are less than a right angle? Write your answers in the space below.” Included is an irregular hexagon with acute and obtuse angles; Angles A, B, C, D, E, and F are noted on the hexagon. This item assesses 4.G.1 (Identifying angles [right, acute, and obtuse]).

The materials reviewed for Math in Focus 2020 Grade 3 do not meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The 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 1.5, Rounding Numbers to the Nearest Hundred, students use number lines and place value to round numbers to the nearest hundred. In Engage, Problem A, page 47, students estimate or round numbers to the nearest hundred. The problem states, “Draw a number line starting at 300 and ending at 400, with intervals of 10. Choose 2 points that are nearer to 400. Compare your points with your partner. How are your points different from your partner’s?” In Hands-on Activity, Problem 3, page 49, students work with a partner to practice rounding numbers to the nearest hundred. The problem states, “Work in pairs. Round each number to the nearest hundred. ____ is ____ when rounded to the nearest hundred.” In Try, Problem 4, page 50, students mark numbers on a number line to help them round to the nearest hundred. The problem states, “Mark (x) each number on the number line. Then round each number to the nearest hundred. a) 350 is ____ when rounded to the nearest hundred, b) 460 is ____ when rounded to the nearest hundred, 510 is ____ when rounded to the nearest hundred.” A number line is shown with 300, 400, 500, 600 marked. In Independent Practice, Problem 6, page 54, students round to the nearest hundred without visual aids. The problem states, “Round each number to the nearest hundred. 450 ____.” Students engage with extensive work to meet the full intent of 3.NBT.1 (Use place value understanding to round whole numbers to the nearest 10 or 1000).

• In Section 4.1, Multiplying by 6, students use skip counting and properties of operations to multiply by 6. Engage, page 226, students use an known fact to help determine an unknown fact. It states, “What is 5 × 6? Draw a picture to show how you found the answer. How does knowing 5 × 6 help you find 7 × 6? Explain your thinking.” In Learn, Problem 1, page 226, students use known multiplication facts to find other multiplication facts. The problem states, “Use known multiplication facts to find other multiplication facts. 7 × 6 = ? You can use array models to show multiplication facts. Start with 5 groups of 6.” Students are shown how to use the distributive property to find 7 x 6. In Try, Problem 2, page 229, students practice multiplying by 6 using array models and known multiplication facts, “7 × 6 = ?, 5 × 6 = ___,  2 × 6 = ___, 7 × 6 = (5 × 6) + (2 × 6) = ___ + ___ = ___ .” In Independent Practice, Problem 3, page 232, states, “Find 5 groups of 6. 5 × 6 = ___.” Five pictures with six strawberries in baskets are shown. Students engage in extensive work to meet the full intent of 3.OA.1 (Interpret products of whole numbers).

• In Section 9.1, Area, students use square units to find the area of plane figures made of squares and half-squares. They then compare the area of plane figures and make plane figures of the same area. In Engage, page 119, students use square units to design shapes. The problem states, “Use 5 (squares) to create as many different figures as you can. Sketch each figure. How many figures did you create? Share your figures with your partner.” In Hands-on Activity, Problem 1, page 120, students work in pairs using square units to find the area. The problem states, “Use 4 square tiles to make as many different figures. Draw them below.” Try, Problem 1, page 121, students count square tiles to determine a figure’s corresponding area. The problem states, “Look at each figure and answer each question. How many square tiles make each figure? a) Figure A is made up of ___ square tiles, b) Figure B is made up of ___ square tiles, c) Figure C is made up of ___ square tiles.” In Independent Practice, Problem 5, page 127, students compare the area of figures. The problem states, “Look at each set of figures. Circle the figures that have the same area.” Students engage in extensive work to meet the full intent of 3.MD.5 (Recognize area as an attribute of plane figures and understand concepts of area measurement).

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 3.G.2 (Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole). For example, Section 7.3, Fractions as Part of a Set, Think, page 25, students work in pairs to read, write, and identify fractions of a set and find the number of items in a fraction of a set, “$$\frac{3}{8}$$ of the pupils in a class wear glasses. 9 pupils in the class wear glasses. How many pupils are there in the class?” In Learn, Problem 1, page 27, students use bar models to show fractions as part of a set. The problem states, “Ms. White had 12 oranges. She gave $$\frac{3}{4}$$ of the oranges to Cooper. How many oranges did she give to Cooper?” In Try, Problem 4, page 30, students use bar models to show fractions as part of a set. The problem states, “Find the value of each of the following. Draw a bar model to help you. $$\frac{7}{8}$$ of 16.” Students engage in solving problems involving multiplication of a fraction by a whole number, which are the expectations of fourth grade standard 4.NF.4c (Solve word problems involving multiplication of a fraction by a whole number). By engaging in the work of 4.NF.4c, students do not have the opportunity to engage with the full intent of 3.G.2.

Materials do not provide extensive work with some grade-level standards. Examples include:

• The materials do not provide extensive work with 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations). Chapter 4 contains sections: Multiplying by 6, Multiplying by 7, Multiplying by 8, Multiplying by 9, Multiplying by 11, and Multiplying by 12. There is no evidence of students using strategies or properties to understand multiplication facts for 0, 1, 2, 3, 4, 5, or 10, except for within the context of facts of 6, 7, 8, 9, 11, and 12. In the Teacher’s Manual, page 217C states, “What have students learned? In Grade 2 Chapter 8, students have learned: How to multiply (2.OA.4), How to divide. In Grade 2, Chapter 9, students have learned: Multiplying in any order (3.OA.5).” Students work with 3.OA.7 in Grade 2. In the Teacher's Manual, page 217 A, Math Background states, “Students have learned the basic meanings of equal groups of multiplication and division in Grade 2, where they were taught about multiplication as the addition of equal groups, and division as sharing equally. They have also learned the multiplication facts for 2, 3, 4, 5, and 10.”

• The materials do not provide extensive work with 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction). In Section 2.3, Adding Fluently Within 1,000, Independent Practice, Problems 1-16, students have the opportunity to add within 1,000. For example, Problem 9 states, “82 + 257 = ___.” Problem 10 states, “382 + 536 = ___.” Problem 11 states, “475 + 363 = ___.” In Section 3.2, Subtracting Fluently Within 1,000, Independent Practice, Problems 1-16, students have the opportunity to subtract within 1,000. For example, Problem 5 states, “461 - 355 = ___.” Problem 6 states, “367 - 184 = ___.” Problem 7 states, “809 - 433 = ___.” Per the Math in Focus 2020 Comprehensive Alignment to CCSS: Grade 3, these are the two lessons that address 3.NBT.2. Therefore, students do not have the opportunity to engage in extensive work with 3.NBT.2.

• The materials do not provide extensive work with 3.NBT.3 (Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place values and properties of operations). For example, Section 5.2,  Multiplying Without Regrouping, Try, Problem 1, page 329, students practice multiplying 3-digit numbers without regrouping, “210 × 4 = (200 × 4) + (10 × 4) + (0 × 4) = ___ + ___ + ___ = ___.” A number bond for 210 with 200, 10, and 0 is shown. In Independent Practice, Problem 8, page 332, students multiply 2-digit and 3-digit numbers by a 1-digit number, without regrouping using the vertical form, multiply, and then, fill in each corresponding letter to find the answer. The problem states, “The Williams family went for a vacation. Where did they go? (T) 23 x 2 = ___, (E) 31 × 3  = ___, (C) 124 × 2 + ___, (O) 112 × 2 = ___, (N) 212 × 4 = ___, (Y) 204 × 2 = ___, (R) 303 × 3 = ___, (K) 122 × 4 = ___, (W) 432 × 2 = ___. The Williams went to: ___, ___, ___, ___, ___, ___, ___.” Each blank space correlates to the solution for each of the letters to spell out where the family went on vacation. In Section 5.3, Multiplying with Regrouping, Engage, Problem 1, page 333, students multiply 3-digit numbers with regrouping. The problem states, “Mia uses (counters) to show 3 groups of 15. How many (counters) does she have? She then places the (counters) on the ones column of a place-value chart. Regroup them in two ways. Explain your thinking.” In Recall Prior Knowledge, Problem 1a, page 362, students multiply by a 1-digit number without regrouping, “21 × 4 = ?” In these sections, students multiply a whole number of up to four digits by a one-digit whole number (4.NBT.5). Due to the amount of off grade level work, there is not extensive work with 3.NBT.3.

• The materials do not provide extensive work with 3.MD.2 (Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters and add, subtract, multiply or divide to solve one step word problems involving masses or volumes that are given in the same units). For example, in Section 8.1, Mass: Kilograms and Grams, Hands-on Activity, Problems 1-3, page 71, students measure mass in kilograms and grams. The problems state, (1) “Hold a 1-kilogram weight in one hand,“ (2) “Hold a completely filled 1-litre water bottle in the other hand. Compare its mass with the 1-kilogram weight. Fill in the blank with more or less. The completely filled 1-litre water bottle is ___ than 1 kilogram,” and (3) “Find its actual mass using a weighing scale. The actual mass of the filled 1-litre water bottle is ___ kilogram ___ grams.” In Section 8.2, Liquid Volume: Liters and Milliliters, Try, Problem 1, page 80, students practice measuring volume in liters and milliliters. The problem states, “Circle each correct unit of measure. A glass of juice: 200 liters/milliliters.” A picture of a glass of juice is shown. In Section 8.3 Real World Problems: One-Step Problems, Try, Problem 4, page 93, students practice solving one-step real-world problems involving measurement. The problem states, “A chef poured 9 cups of water into a pot. Each cup of water contained 240 milliliters of water. How much water did the chef put into the pot? Give your answer in liters and milliliters.” In all three sections students engage with 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit). By engaging in the work of 4.MD.1, students do not have the opportunity to engage in extensive work with 3.MD.2. Per the Math in Focus 2020 Comprehensive Alignment to CCSS: Grade 3, these are the two lessons that address 3.MD.2.