3rd Grade - Gateway 2

The instructional materials reviewed for JUMP Math Grade 3 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single- and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The materials include limited opportunities for students to independently engage in the application of nonroutine problems. Most problems are routine in nature and provide few opportunities for students to independently demonstrate the use of mathematics flexibly. 

The instructional materials have few opportunities for students to engage in non-routine application throughout the grade level. There is little variety in situational contexts/problem types. Engaging applications include single- and multi-step word problems presented in a context in which the mathematics is applied; however, these problems are often routine, and students have few opportunities to engage with non-routine application problems. Examples of routine application problems include:

• Teacher Resource, Part 1, Unit 4, Lesson OA3-25, Extensions, Item 5, “In the school parking lot there are 2 rows of parking spots with 3 parking spots in each row. a. How many parking spots are there? b. If each car has 4 wheels, how many wheels are in the parking lot when it is full?” (3.OA.3)
• Teacher Resource, Part 1, Unit 8, Lesson OA3-54, Extensions, Item 2, “A basketball league has 42 players with 6 players on each team. A second basketball league has 5 teams with 8 players on each team. Which league has more players? Which league has more teams? Use any tools you think will help. Write your answer as a full sentence.” (3.OA.8)
• Teacher Resource, Part 2, Unit 2, Lesson NF3-5, Extensions, Item 5, “Rani has 8 packs of 5 pens each. How many packs would she have if the same pens were put into packs of 20 pens each? Use a picture or use number sentences.” (3.OA.3)

Few opportunities for non-routine applications of mathematics are provided in the extensions and in the Assessment and Practice Books. Examples include:

• Teacher Resource, Part 1, Unit 5, Lesson OA3-36, “Karen has 6 pets. Some are cats and the rest are birds. Her pets have 14 legs total. How many cats and birds does she have?” 
• Student Resource, Assessment & Practice Book, Part 2, Lesson MD3-21 “It takes Mindy 2 minutes to serve 1 person at a coffee shop. How much time does it take her to serve 25 people? Mindy started her shift at 9:05 a.m. She served 25 people before a break. When did she take the break?” (3.MD.1)

The instructional materials reviewed for JUMP Math Grade 3 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

The curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials emphasize fluency, procedures, and algorithms. 

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

• Conceptual Understanding: Student Resource, Assessment & Practice Book, Part 1, Lesson OA3-24, Item 2, “Count the rows. Count the dots in one row. Write a multiplication sentence. Find the answer by skip counting. (Model shows two rows of 4 dots, students must identify 2 rows, 4 dots in each row, then write a multiplication equation 2x4=8.)” Students build conceptual understanding of 3.OA.1 by working with arrays.
• Procedural Skill and Fluency: Student Resource, Assessment & Practice Book, Part 2, Lesson NBT3-16, includes 9 problems of this type: “2 x 3 = ___; 2 x 30 = ___.” The same lesson includes 9 addition problems of this type: “5 x 70= ____.” Students complete many problems related to multiplication of one-digit whole numbers by multiples of 10 to develop fluency.
• Application: Student Resource, Assessment & Practice Book, Part 1, Lesson OA3-25, Item 1, “Use skip counting to find out how many legs the animals have. (A table with a bird, lion, ant, and octopus is present. Students are given the number of legs for one animal, and must skip count to say how many legs for 2, 3, 4, and 5 of each type of animal.)” Students solve problems related to multiplication concepts.

Examples of where conceptual understanding, procedural skill and fluency, and application are presented together in the materials include:

• Student Resource, Assessment & Practice Book, Part 1, Lesson NBT3-10, Item 1, “Find the sum by drawing the blocks and adding the digits. a. 24 + 15  b. 62 + 21 #2 Add the numbers by adding the digits. Start in the ones place. a. 23+12  b. 48 + 21” Students develop both conceptual understanding and fluency related to 3.NBT.2 while they model addition with regrouping using base ten blocks; students also practice the standard algorithm for addition with regrouping. 
• Student Resource, Assessment & Practice Book, Part 1, Lesson OA3-26, Item 8, “A table is 32 inches long. How long are two tables?” Students use both conceptual understanding and application to solve the problem. 
• Student Resource, Assessment & Practice Book, Part 2, Lesson MD3-33, Item 7, “Tina’s lawn is a rectangle 9 yards long and 8 yards wide. What is the area of Tina’s lawn in square yards?” Students use both conceptual understanding and application to divide rectangles into square units to find area, then application of this procedure to solve word problems.

The instructional materials reviewed for JUMP Math Grade 3 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MPs 4 and 5.

Examples of the materials carefully attending to the meaning of some MPs include:

• MP1: Teacher Resource, Part 1, Unit 1, Lesson OA3-7, Extensions, Item 5, “The following T-tables give the number of blocks used to build a structure. The same number of blocks was added each time. Fill in the missing numbers.“ Students make sense of problems and persevere in solving them as they analyze relationships of given numbers in a T-table in order to complete the missing numbers.
• MP2: Teacher Resource, Part 1, Unit 1, Lessons OA3-4, Extensions, Item 1, “Extend the pattern. Create a word problem that goes with the number pattern. a. 65, 56, 47, 38; b. 101, 91, 81, 71.” Students reason abstractly and quantitatively to continue a number pattern, then to contextualize the pattern by creating a word problem. 
• MP6: Teacher Resource, Part 1, Unit 6, Lesson MD3-6, Extensions, students create a precise mathematical drawing to accompany a story.
• MP7: Teacher Resource, Part 1, Unit 4, Lesson OA3-17, Extensions, Item 5, “Will the pattern give a total that is even or odd? Explain. a. even + even + even; b. odd + odd + odd; c. odd + even + even; d. odd + odd + even; e. odd + even + odd; f. even + odd + odd.” Students look for patterns and structures when adding three or more numbers.
• MP8: Teacher Resource, Part 1, Unit 8, Lesson OA3-44, Extensions, Item 3, “a. write a story about nickels to explain why (3 x 5) + (4 x 5) = 7 x 5; b. write a story about dimes to explain why (3 x 10) + (4 x 10)= 7 x 10; c. write a story about quarters to explain why (3 x 25) + (4 x 25) = 7 x 25; d. How can you use pretend coins to explain why (3 x18) + (4 x 18)= 7 x 18; e. Do you think the same type of story will work with any number? Explain.” Students look for and express regularity in applying the distributive property to the 7s times table.

For MP4, students are given models to use and have few opportunities to develop their own mathematical models. In addition, students have few opportunities to compare different models in problem contexts. Examples include:

• Teacher Resource, Part 1, Unit 1, Lesson OA3-4, Extensions, Item 3, “Read the following problem: Jim gives $3 to charity every month. In January, he has $26. After how many months will he have $5 left? a. Solve the problem using a number line. b. How does your picture show the answer to the question? Discuss with a partner.” Students are given a number line to use instead of developing their own model.
• Teacher Resource, Part 2, Unit 7, Lesson MD3-31, Extensions, Item 4, “Six cars fit end-to-end along a fence. The cars take up the entire fence. Each car is 9 feet long. The fence is divided into 3 equal sections. How long is each section of the fence? Show your answer using equations.” This problem has a model given to the students, then requires the students to answer using equations.

For MP5, students are given few opportunities to use tools strategically, as they are most often given the tools to use for a problem. Examples include: 

• Teacher Resource, Part 1 Unit 7, Lesson OA3-29, Extensions, Item 4, “Add. Use mental math or paper and pencil. Explain your choice. a. 234 + 10 b. 99 + 372 c. 658 + 274.”
• Teacher Resource, Part 2, Unit 4, Lesson NBT3-18, Extensions, Item 3, “Jun plants flowers in an array. His garden has the same number of rows and columns. Marla plants flowers in another array. Her garden has one more row than Jun’s garden and one fewer column. Who planted more flowers? Do you think the answer will always be the same? Explain why or why not. Use one or more of these tools: arrays, number lines, a T-table.”

The instructional materials reviewed for JUMP Math Grade 3 partially meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. 

There are few opportunities in the Teacher Resource or the Assessment & Practice for students to construct viable arguments or analyze the arguments or the work of others. MP3 is identified in the margins of the lesson. Examples of where the materials prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:

• Teacher Resource, Part 1, Unit 2, Lesson NBT3-12, Extensions, Item 6: “Display a hundreds chart and the following square: (32,33, 42, 43). a. Add the two top numbers then add the two bottom numbers. How do the sums compare? Write a statement. Check two other squares on the hundreds chart. Is the same statement true? b. Add the top left and bottom right numbers. Then add the top right and bottom left numbers. How do the two sums compare? Write a statement. Check two other squares on the hundreds chart. Is the same statement true? c. Choose a statement from part a or b. In pairs explain why your statement is true and use two different squares as examples. Do you agree with each other? Decide why or why not. d. Do you think your statement will be true for any square? Explain.” Students construct viable arguments, justify their thinking, and analyze the reasoning of others related to patterns on the hundreds chart.
• Teacher Resource, Part 1, Unit 3, Lesson OA3-11, Extensions, Item 4: “a. Look at your answers to extension 1. In pairs explain why you can use the answer to 38 + 5 to get the answer to 380 + 50. Do you agree with each other? Discuss why or why not.” After completing mental math addition exercises, students discuss strategies for mental math and analyze the strategies of others. 
• Teacher Resource, Part 2, Lesson NBT3-18, Extensions, Item 3 “Jun plants flowers in an array. His garden has the same number of rows and columns. Marla plants flowers in another array. Her garden has one more row than Jun’s garden and one fewer column. Who planted more flowers? Do you think the answer will always be the same? Explain why or why not…” Students construct a viable argument.

Examples where the materials miss opportunities to prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:

• Teacher Resource, Part 1, Unit 3, Lesson OA3-9, Extensions, “Display a calendar for the current month. Have students find and explain as many patterns as they can.” Students do not construct viable arguments or analyze the arguments of others. 
• Teacher Resource, Part 2, Unit 8 Lesson MD3-41, Extensions, Item 3, “a. Start by drawing a square on grid paper so that it has 6 rows and 6 columns. Take away a row, then add a column. Repeat until you have 4 shapes altogether. b. Does the perimeter get bigger, smaller, or stay the same? Explain.” Students do not construct viable arguments or analyze the arguments of others. 
• In Student Resource, Assessment & Practice Book, Part 2, Lesson NBT3-22, Item 2a, students are asked to find the equations that are not correct. Then in part 2b students are asked to, “Explain how you found the answer.” Students could solve all of the equations, or they could estimate like the previous problem. Students do not construct viable arguments or analyze the arguments of others. Students circle the correct equations and explain how they found the answer, which could be by adding or subtracting.
• Teacher Resource, Part 2, Lesson NBT3-19, Extensions, Item 2 “390 + 425 is about 400 + 400 = 800. Without adding the actual numbers, say if the answer is more than 800 or less than 800. Explain your thinking.” Students do not construct a viable argument or analyze the arguments of others. 
• Teacher Resource, Part 2, Unit 5, Lesson MD3-13, Extensions, Item 3 “Find 270 ÷ 6. Explain how you know your answer is correct.” In the Teacher Resource, it says if the students “articulate their reasoning” that meets MP3. Students do not construct a viable argument or analyze the arguments of others.

The instructional materials reviewed for JUMP Math Grade 3 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher guidance and questions are found in the lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments, and in other lessons, teachers are provided questions and sentence stems to facilitate students in analyzing the arguments of others, and to justify their answers. Also, on page A49 in the “How to use the lesson plans flexibly” states, “When students work with a partner, many of them will benefit from some guidance, such as displaying question or sentence stems on the board to encourage partners to understand and challenge each other’s thinking, use of vocabulary, or choice of tools or strategies, For example: 

• I did ___ the same way but got a different answer. Let’s compare our work. 
• What does ___ mean?
• Why is ___ true? 
• Why do you think that ___ ?
• I don’t understand ___. Can you explain it a different way?
• Why did you use ___? (a particular strategy or tool)
• How did you come up with ___? (an idea or strategy)”

These sentence stems are used consistently during the Lessons and Extensions. 

Examples where teachers are provided guidance to engage students in constructing viable arguments and/or analyze the arguments of others include, but are not limited to:

• Teacher Resource, Part 1, Unit 1, Lesson OA3-6, Extensions, Item 5, “For part c, encourage partners to ask questions to understand and challenge each other’s thinking.”
• Teacher Resource, Part 2, Unit 1, Lesson G3-8, Extensions, Item 4, “Encourage partners to ask questions to understand and challenge each other’s thinking (MP.3) and choice of strategy (MP.5) - see page A-49 for sample sentence and question stems to guide students.”
• Teacher Resource, Part 2, Unit 5, Lesson MD3-19, Extensions, Item 4, ”Encourage partners to ask questions to understand and challenge each other’s thinking (MP.3) and use of terminology.”

Within lessons, the teacher materials are not always clear about how teachers will engage and support students in constructing viable arguments or critiquing the reasoning of others. Materials identified with the MP3 standard often direct teachers to “choose a student to answer” or “have a volunteer fill in the blank.” Questions are provided but often do not encourage students to deeply engage in MP3. In addition, although answers are provided, there are no follow up questions to help redirect students who didn’t understand. Examples include:

• Teacher Resource, Part 1, Unir 6, Lesson MD3-8, Extensions Item 1, “a. Jack says: The rectangle below has 3 rows, and the first row has 3 squares. The area of the rectangle is 9 squares because 3 x 3 = 9. (a picture is shown) Do you agree or disagree with his thinking? Explain. b. Rani says: There are 3 columns, with 5 squares in each column. The area of this rectangle is 15 square units because 3 x 5 = 15. Is she correct? Explain. c. What is the area of the rectangle? Explain how you know.” The teacher asks students to explain, but the materials do not give any other suggestions to the teacher. 
• Teacher Resource, Part 2, Unit 4, Lesson NBT3-19, Extensions, Item 2, “390 + 425 is about 400 + 400 = 800. Without adding the numbers, say if the actual answer is more than or less than 800. Explain your thinking.” The teacher asks students to explain, but the materials do not give any other suggestions to the teacher. 
• Teacher Resource, Part 2, Unit 5, Lesson MD3-13, Extensions, Item 3, “Find 270 / 6. Explain how you know your answer is correct.” The teacher asks students to explain, but the materials do not give any other suggestions to the teacher.

The instructional materials reviewed for JUMP Math Grade 3 partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials; however, while vocabulary is identified throughout the materials, there is no explicit direction for instruction of the vocabulary in the teacher materials of the lesson. Examples include, but are not limited to: 

• Vocabulary is identified in the Terminology section at the beginning of each unit.
• Vocabulary is identified at the beginning of each lesson.
• The vocabulary words and definitions are bold within the lesson.
• There is not a glossary.
• There is not a place for the students to practice the new vocabulary in the lessons.
• Teacher Resource, Part 1, Unit 1, Lesson OA3-1, Vocabulary, materials use the term “gap” instead of “difference”, which is not accurate terminology.