3rd Grade - Gateway 1

​The materials reviewed for enVision Mathematics Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. In instances where above-grade-level content is assessed, the teacher could easily omit or modify questions. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments.

The series is divided into topics that include a Topic Assessment, available for online and/or paper and pencil delivery, and a Topic Performance Task. Additional assessments include a Grade 3 Readiness Test; Basic-Facts Timed Tests; four Cumulative/Benchmark Assessments addressing Topics 1–4, 1–8, 1–12, and 1–16; and Progress Monitoring Assessments A–C. Assessments can be found in the digital teacher interface and the Assessment Sourcebook online or in print. The materials include an ExamView Test Generator allowing teachers to build customized tests.

Examples of items that assess grade-level content include:

• Topic 3, Online Assessment, Problem 10, “Part A Mary bought 5 packages of soap. Each package has 6 bars of soap. Each bar of soap weighs 3 ounces. Which expression gives the total weight of the soap Mary bought? Select all that apply. 6\times5\times3, 2\times8\times7, 3\times6\times5, 2\times6\times4, 6\times3\times5” (3.OA.5)

• Topic 9, Assessment, Problem 1, “Find the sum of 458 and 342. Use place value and find the sums of the hundreds, tens, and ones.” Students are provided a table with columns labeled hundreds, tens, and ones. (3.NBT.2)

• Topic 12, Performance Task, Problem 3, “Divide the number line into the number of equal parts of the cake. Then mark a dot on the number line to show the part of the cake that Bruno frosted. Write the fraction that he frosted.” Students are provided a number line with only zero and one labeled. (3.NF.2)

• Topics 1-16, Cumulative/Benchmark Assessment, Problem 17, “Maya plans to serve dinner at 6:00 P.M. It takes Maya 20 minutes to iron her clothes, 45 minutes to clean up the house, and 50 minutes to prepare dinner. If Maya wants to iron before cleaning and preparing dinner, what time should she start ironing her clothes? Use a number line to show your reasoning.” (3.MD.1)

Examples of above grade-level assessment items that could be modified or omitted include, but are not limited to:

• Topic 2, Performance Task, Problem 6, “Carlos reads 10 pages every day. The book he is reading has 46 pages. How many days will it take him to finish his book? Complete the chart and explain your answer.” This question requires students to calculate with remainders in the solution. (4.NBT.6)

• Topics 1–4, Cumulative/Benchmark Assessment, Problem 13, “A coach brought a cooler with 20 bottles of water for the baseball team. Each player gets the same number of bottles of water. There are 9 players on the team. Which statement is true?” This question requires students to calculate with remainders in the solution. (4.NBT.6)

The materials reviewed for enVision Mathematics Grade 3 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding. During Independent Practice, students work with problems in various formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• In Topic 1, Topic 5 and Topic 14, students engage in extensive work with grade-level problems to meet the full intent of 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities). In Topic 1, Lesson 1-1, Additional Practice, Problem 10, students represent a word problem involving repeated addition of equal groups as an equivalent equation using multiplication. “Misha buys 4 boxes of 6 markers each. He writes this addition equation to show how many markers he buys: 6 + 6 + 6 + 6 = 24. What multiplication equation can Misha write to represent this situation?” In Lesson 1-4, Guided Practice, Problem 3, students solve word problems that involve dividing a given quantity into equal shares. In Problem 3, students draw a picture to answer the question, “Fifteen bananas are shared equally by 3 monkeys. How many bananas does each monkey get?” In Lesson 1-6, Visual Learning Bridge, students choose appropriate tools to solve problems. Given a 3 by 6 array of light bulbs, students consider the problem, “A hardware store has boxes of 18 light bulbs. 3 light bulbs cost $4. How much does it cost to buy a whole box of light bulbs? Choose a tool to represent and solve the problem.” In Topic 5, Lesson 5-4, Problem Solving, Problem 8, students complete a bar diagram and write an equation to solve the word problem, “Jodie has 24 flowers in her garden. She wants to give an equal number of flowers to 4 families in her neighborhood. How many flowers will each family get?” In Topic 14, Lesson 14-8, Independent Practice, Problem 6, students use multiplication to solve a word problem. “Omar is shipping 3 boxes. Each has a mass of 8 kilograms. What is the total mass of all of the boxes?”

• In Topic 11, students engage in extensive work with grade-level problems to meet the full intent of 3.OA.8 (Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding). In Lesson 11-1, Problem Solving, Problem 8, students use addition/subtraction and an equation with a letter standing for the unknown quantity to solve the problem, “Matt had 327 plastic bottles for recycling. He recycled 118 bottles on Monday. He recycled 123 bottles on Tuesday. How many bottles does Matt have left to recycle? Use representations such as bar diagrams or equations to model with math. Use letters to represent the unknown quantities. Estimate to check your work.” In Lesson 11-2, Independent Practice, Problem 4, students use multiplication, division and a letter to represent the unknown quantity within an equation to solve for the cost of each item. “Arif saves $4 each week. After 6 weeks, he spends all the money he saved on 3 items. Each item costs the same amount. How much does each item cost?” In Lesson 11-3, Visual Learning Bridge, students review how to solve two-step problems. “Jill can rent a car and GPS device for $325 for 7 days. What is the cost to rent the car for a week without the GPS device? Use estimation to check the answer.”

• In Topics 12 and 13, students engage in extensive work with grade-level problems to meet the full intent of 3.NF.3 (Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size). In Topic 12, Lesson 12-3, Problem Solving, Problem 8, students compare drawings of a whole table given the image of a half-table, choose which drawing is correct, and explain. “Ronnie and Gina were shown \frac{1}{2} of a table. They each drew a picture of the whole table. Whose drawing could be correct? Explain.” Provide is a picture of the table, Ronnie’s drawing of the whole table, and Gina’s drawing of the whole table. In Topic 13, Lesson 13-1, Convince Me!, students consider fractions bars that represent 1 whole and equivalent halves: one half, two quarters, and four eighths (all shown). “In the examples above, what pattern do you see in the fractions that are equivalent to \frac{1}{2}? What is another name for \frac{1}{2} that is not shown?”  In Lesson 13-2, Practice Buddy: Additional Practice, Problem 7, students use a number line and write fractions to determine if \frac{1}{4} and \frac{2}{8} represent the same length. “Brandon and Ellen had the same length of yarn. Brandon used \frac{1}{4} of his yarn to tie a couple of sticks. Ellen used \frac{2}{8} of her yarn to tie a couple of straws. Did they use the same amount of​ yarn? Draw a number line and write the fractions to show your answer.”

• In Topic 15, students engage in extensive work with grade-level problems to meet the full intent of 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.) In Lesson 15-1, Guided Practice, Problem 2, students “draw two different quadrilaterals that are NOT rectangles, squares, or rhombuses.” In Problems 3-6, students write as many special names as possible for each of four quadrilaterals. Pictured are a parallelogram, a rectangle, a rhombus, and a square. In Lesson 15-2, Reteach to Build Understanding, Problem 2, students look for ways three shapes in Group 1 and three shapes in Group 2 are alike and different. Students consider attributes such as the length of the sides and angles. In Lesson 15-3, Assessment Practice, Problem 14, students consider four polygons labeled A to D, name one attribute that they all share, and name an attribute that “A and D have but B and C do not.”  In Lesson 15-4, Solve & Share, students draw shapes that match the three given clues. “Draw shapes that match all of these clues. Use math words and numbers correctly to name each shape and explain how your shapes match the clues. Clue 1: I am a polygon with 4 sides. Clue 2: I am a polygon with 4 right angles. Clue 3: My area is 12 square units.”

The materials reviewed for enVision Mathematics Grade 3 meet expectations for that, when implemented as designed the majority of the materials address the major clusters of each grade. The materials devote at least 65% of instructional time to the major clusters of the grade.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 14 out of 16, which is approximately 88%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87 out of 104, which is approximately 84%.

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 115 out of 144, which is approximately 80%. 

A lesson-level analysis is most representative of the materials since the lessons include major work, supporting work connected to major work, and assessments embedded within each topic. As a result, approximately 84% of the materials focus on the major work of the grade.

The materials reviewed for enVision Mathematics Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher’s Edition, Lesson Overview, Coherence, Cross-Cluster Connections on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed in a document titled “Scope and Sequence.” Examples of connections include:

• Topic 7, Lesson 7-3 connects the supporting work of 3.MD.B (Represent and interpret data) to the major work of 3.OA.A (Represent and solve problems involving multiplication and division). In Problem Solving, Problems 6–8, students create a bar graph to display data and use the bar graph they created to answer word problems. “ In 6–8, use the table at the right. 6. Make a bar graph to show the data. 7. Construct Arguments Which two kinds of movies received about the same number of votes? Explain how to use your bar graph to find the answer. 8. Each movie ticket costs $8. Jo buys tickets for the number of people who voted for science fiction. How much change does she get from $50?” The materials show a table, “Favorite Kind of Movie,” which indicates four kinds of movies and the corresponding number of votes.  

• Topic 9, Lesson 9-4 connects the supporting work of 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic).  In Lesson 9-4, Reteach to Build Understanding, Problem 3, students work through a 3-step procedure to break apart a subtraction problem using place value. “Find 678 - 387. Break apart the subtraction problem by place value. Write the steps you used.” Students begin by writing 387 as 300 + 80 + 7. In Step 1, students subtract the hundreds: 600 - 300; in Step 2, students start with 378 and subtract the seven tens and then the remaining ten: 378 - 70 - 10; in Step 3, students start with 298 and subtract the 7 ones: 298 - 7. 

• Topic 15, Lesson 15-1 connects the supporting work of 3.G.A (Reason with shapes and their attributes) to the major work of 3.NF.A (Develop understanding of fractions as numbers). In Solve & Share, students identify, sketch, and describe quadrilaterals using fractional parts. “Fold a square piece of paper to make the fold lines as shown. Find as many different quadrilaterals as you can using the fold lines and the edges of the square paper. Sketch each quadrilateral you find and describe it. The area of each small triangle on the paper represents a unit fraction. Write the unit fraction, and then find what fraction of the whole square each of your quadrilaterals represents.” The materials provide an image of a paper folded to form a rhombus, rectangles, squares, and triangles.

The materials reviewed for enVision Mathematics Grade 3 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.

There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. These connections are listed for teachers in the Topic Overview, Scope and Sequence, and Teacher Guides within each topic. Examples include:

• In Topic 2, Lesson 2-2 Problem Solving, Problems 23–25, students represent and solve problems involving multiplication while solving problems involving the four operations that include identifying and explaining patterns in arithmetic. “In 23–25, use the table to the right. 23. Reasoning The library is having a used book sale. How much do 4 hardcover books cost? Draw a number line to show the answer. 24. Higher Order Thinking How much more would Chico spend if he bought 3 hardcover books rather than 3 paperback books? Show how you found your answer. 25. Maggie bought only magazines. The clerk told her she owed $15. How does Maggie know the clerk made a mistake?” The materials show a boy holding a sign that itemizes the prices of items at the Library Book Sale. Students draw a number line to illustrate 4 \times 9, show the difference between 3 \times 9 and 3 \times 5, and explain how multiples of 2 cannot equal 15. This connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic).

• In Topic 3, Lesson 3-2, Reteach to Build Understanding, Problem 4, students use the Distributive Property to break apart unknown facts with 3 or 4 as a factor.  “A bookshelf has 4 shelves with 8 books on each shelf. The total number of books is 4 \times 8. Use 2s facts to find the total number of books on the shelves.” The materials show 2 groups of 2 arrays of 8 counters and the equations: 4 \times 8 = (2 \times 8) + (___), 4 \times 8 = ___ + ___, 4 \times 8 = ___ “There are ___ books on the shelves.” This connects the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division) to the major work of 3.OA.C (Multiply and divide within 100). 

• In Topic 6, Lesson 6-2, Problem Solving, Problems 8 and 9, students find areas using unit squares and addition or multiplication. “8. Construct Arguments Riaz estimates that the area of this figure is 45 square units. Martin estimates the area is 48 square units. Whose estimate is closer to the actual measure? Explain.” The materials show a rectangle and 1 square unit. “9. Higher Order Thinking Theo wants to cover the top of a small table with square tiles. The table is 12 square tiles long and 8 square tiles wide. How many tiles will Theo need to cover the table?” This connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.MD.C (Geometric measurement: understand concepts of area and relate area to multiplication and to addition).

• In Topic 16, Lesson 16-3, Problem Solving, Problem 14, students find the missing side in a perimeter problem that includes a composite figure of two different rectangles. “The floor of Novak’s room is shown below. It has a perimeter of 52 feet. Write an equation to find the missing side length in Novak’s room.” The image of the room is labeled with the dimensions 13 ft, x ft, 3 ft, 7 ft, 10 ft, and 13 ft. This connects the supporting work of 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) to the supporting work of 3.MD.D (Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures). 

The materials reviewed for enVision Mathematics Grade 3 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.

Prior and Future connections are identified within the Teacher Edition Math Background: Focus, Math Background: Coherence, and Lesson Overview. Examples of connections to future grades include:

• Topic 1, Lesson 1-1 connects 3.OA.1 (Interpret products of whole numbers) to work in future grades. In Lesson 1-1, “students use repeated addition to determine the total number of objects in equal-sized groups. The answer to a multiplication problem or the total number of objects found when multiplying the factors is the product.” In Grade 4, Topic 6, “students will extend their understanding of multiplication to comparison situations.”

• Topic 8 connects 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) to work in future grades. In Topic 8, students use properties of addition and place-value concepts for mental math strategies. In Grade 4, Topic 2, “students will use the standard algorithm to fluently add and subtract multi-digit numbers.”

• Topic 15, Lessons 15-2 and 15-3 connects 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories) to the work of future grades. In Lesson 15-2, students show, “they can start with shapes in two different categories and then look for common attributes to see if the shapes also belong to a larger category.” In Lesson 15-3, students, “start with a group of shapes in a certain category and then look for differences in attributes to see if some of the shapes belong to smaller categories.” In Grade 4, Topic 16, students “will classify triangles based on their side lengths and/or angle measures. They will classify quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.”  

Examples of connections to prior knowledge include:

• Topic 4, Lesson 4-6 connects 3.OA.9 (Identify arithmetic patterns, and explain them using properties of operations) to the work of previous grades. In Grade 2, Topic 1, students used related facts to connect addition and subtraction; in Topic 2, students explored even and odd numbers, learning “that an even number of objects can be put into two equal-sized groups.” In this lesson, students “learn that all even numbers are multiples of 2. They learn that an even number can be divided by 2 with none left over, but an odd number can’t.”

• Topic 11, Lesson 11-1 connects 3.OA.8 (Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding) to the work of previous grades. In Grade 2, students “represented problems using bar diagrams and equations with a question mark for the unknown value. They also solved 2-step problems.” Lesson 11-1 introduces “ students to the use of letters to represent unknown quantities. In the rest of the topic, students continue to use letters to represent unknown quantities.” Students also “learn that the first step for solving a 2-step problem is to identify and solve the hidden question. They see that they need to use that approach as they solve the 2-step problems throughout the topic.”

• Topic 14, Lesson 14-1 connects 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes) to the work of previous grades. In Grade 2, “students learned to tell time to the nearest 5 minutes and they learned about patterns with 5 as a factor.” In this lesson, students “apply their knowledge of counting by 5s (and 1s) to tell time to the nearest minute.”