5th Grade - Gateway 2

The instructional materials reviewed for JUMP Math Grade 5 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 2, Lessons NF5-27, Practice Word Problems, “a. Three people share $$\frac{5}{8}$$ of a cake equally. What fraction of the cake does each person get? b. Eight people share $$\frac{1}{2}$$ pounds of chocolate equally. How much chocolate does each person get? c. Four people share $$\frac{3}{4}$$ of a meat pie. What fraction of the pie does each person get?” It is important to note that four, nearly identical problems, are offered in the Assessment and Practice, Part 2, Lesson NF5-27, Items 4-9. 
• Teacher Resource, Unit 1, Lesson G5-4, Exercises, Item 3, “A helicopter set out from Grants Pass, OR, flew to Eugene, OR, and then flew to Willamette National Forest. How far did it fly?”
• Teacher Resource, Part 1, Unit 7, Lesson MD5-9,Extensions, Item 1, “A small box of rice weighs 1,362g and cost $5.60. A large bag of rice weighs 2.27kg and cost $9. How much do 5 small bags boxes weigh and cost? How much do 3 large bags weigh and cost? Which combination is a better buy?”
• Teacher Resource, Part 1, Unit 6, Extensions, Item 5, “In November, the students in Grade 5 class read 88 fiction books and 38 non-fiction books. They read one third as many books in December. How many books did they read in November and December altogether?”

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 7, Lesson MD5-4, Extensions, Item 2, “John has a strip of paper 1cm long and 2cm wide. He folds the strip so that it has a crease down its center. How can John use this strip as a benchmark to make each of these measurements? a. 5 cm; b. 3 cm; c. 1 cm”
• Teacher Resource, Part 2, Unit 5, Lesson MD-13, Extensions, Item 2c, “A car is traveling on a road with the distance markers shown in part 2a. At the first marker, the driver sees a reason to brake. Halfway to the other marker, the car crashes. A police officer is examining the scene of the crash. The speed limit for the road is 70 mi/hr. Was the car traveling at the speed limit or not? Explain.”

The instructional materials reviewed for JUMP Math Grade 5 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 NBT5-42, Item 2, “Write the decimal in expanded form using words and write the total number of thousandths.”
• Procedural Skill and Fluency: Student Resource, Assessment & Practice Book, Part 1, Lesson NBT5-24, includes 20 problems where students apply the algorithm step by step, then six problems where they complete a multiplication problem with all steps of the algorithm. Students practice the stages of the algorithm to multiply 3-digit numbers by 2-digit numbers.
• Application: Student Resource, Assessment & Practice Book, Part 2, Lesson NF5-26, “Kim has $$\frac{5}{3}$$ cups of paint. She uses $$\frac{3}{4}$$ of it to paint a shelf. a. How much paint did she use? b. Did Kim use more or less than 1 cup of paint? How do you know?”

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 NBT5-26, Item 7, “In some countries it costs only $18 to buy lunch for a child for an entire year. a. How much money is needed to pay for lunch for a school of 354 children for the entire year? b. A generous donor gave $5,000 to the school. How much more money is needed to feed all the children for one year?” Students use the multiplication algorithm to solve word problems related to multiplication. 
• Teacher Resource, Part 1, Unit 6, Lesson NBT5-46, Item, 12, “The mass of a dime is 2.268 g and the mass of a quarter is 5.670 g. What is the total mass of one dime and two quarters?” Conceptual understanding and application are engaged within this problem.
• Teacher Resource, Part 2, Unit 2, Lesson NF5-22, Item 9, ”Farah made apple juice. She used $$\frac{3}{5}$$ of a bag of apples on Saturday. She used $$\frac{1}{2}$$ of the rest of the apples on Sunday. What fraction of the bag did Farah use on Sunday? Reduce your answer to lowest terms.” Students engage conceptual understanding by using fraction models, engage procedural skills to solve equations multiplying two fractions, and apply these mathematics to solve word problems involving multiplication of fractions.

The instructional materials reviewed for JUMP Math Grade 5 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 2, Lesson NBT5-5, Extensions, Item 5, “Hannah writes two number sequences. The first sequence starts at 0. Any term in the second sequence is always 5 less than the next term in that sequence. Each term in the second sequence is 10 more than the same term in the first sequence. Write a rule for each sequence.” Students have the opportunity to make sense of problems and design appropriate solution pathways.
• MP2: Teacher Resource, Part 1, Unit 3, Lesson NBT5-15, Extensions, Item 6, “Use any tool such as play money, base-10 blocks, or sketches of these to model and solve the multiplication. Explain how your model shows the multiplication. a. 40 x 10 b. 32 x 10 c. 57 x 100.” Students reason quantitatively to represent abstract problems.
• MP6: In Teacher Resource, Part 1, Unit 5, Lesson NF5-14, students attend to precision when subtracting fractions with unlike denominators as they calculate a common denominator and then carry out the subtraction operation.
• MP7: Teacher Resource, Part 1, Unit 3, Lesson NBT5-15, Extensions, Item 2: “Find as many answers as you can using multiples of 10 for each question. a. __ x __ = 40,000; b. __ x __ = 120,000” Students look for and make use of structures when working with multiples.
• MP8: Teacher Resource, Part 1, Unit 2, Lesson NBT5-1, Item 3, “Nina and Sal save their allowance to donate to charity. Nina starts with $500 and Sal starts with $360. They both get $20 per week. When they are ready to donate, Nina has $1000. How much money do they donate all together? Explain how you know.” Students apply repeated reasoning to extend a sequence and solve word problems. 

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 2, Lesson NBT5-8, Extensions, Item 2, “Amy and Jin sell cookies to raise money for charity. There are 15 cookies in each box. Amy starts with 518 boxes and Jin starts with 372 boxes. They each sell 12 boxes a day. After a certain number of days, Jin has 300 boxes left. How many boxes does Amy have left? Find the answer using sequences. Show your work and write your answer as a complete sentence.”
• Teacher Resource, Part 2, Unit 6, Lesson MD5-29, Extensions, Item 2, “a. Mandy coaches a baseball team. She has a pizza party for her team and spent $95.95 for 5 pizzas. Each pizza cost the same amount. Three of the pizzas were vegetarian. One of the vegetarian pizzas had pineapple on it. How much did the vegetarian pizzas cost? b. Which facts did you not need to use in part a? Explain.” The students are not developing their own models or comparing different models.

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 3, Lesson NBT5-35, Extensions, Item 2, “a. Use long division to find 656 / 8. Use money, base-10 blocks, or sketches of these, to explain each step. b Create a story problem about sharing money or base ten blocks that matches the division. Explain what each step in the long division is in your story problem.”
• Teacher Resource, Part 2, Unit 4, Lesson NBT5-59, Extensions, Item 4, “Use money or base-10 blocks and math words like regrouping, hundredths, and tenths to explain why 4.65 x 3 = 13.95.”
• Teacher Resource, Part 2, Unit 7, Lesson G5-18/G5-19, Extensions, Item 2, “Nancy has one large cubic box and one small cubic box. To measure the volume of each, she fills them with cubic blocks, each measuring 1 cubic foot. She uses 91 blocks altogether and the blocks fill the boxes perfectly. How much larger is the larger box than the smaller box? Use one or more of these tools: a number line, a pan balance, base-10 blocks, a ruler, a T-table, connecting cubes, grid paper, pattern blocks, pencil and paper sketches.”

 The instructional materials reviewed for JUMP Math Grade 5 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 3, Lesson NBT5-19, Extensions, Item 3, “Look at the following statement: If you multiply a whole number by 10,000, the number of zeros in the product will be ___. a. Rani says the blank should be 4, since there are 4 zeros in 10,000. Do you agree with Rani?”
• Teacher Resource, Part 2, Unit 2, Lesson NF5-31, Extensions, Item 3, “John adds $$\frac{2}{5}$$ + $$\frac{5}{3}$$ = $$\frac{7}{8}$$. What mistake did he make? How can you tell by estimating that the answer is correct? Explain.” 
• Teacher Resource, Part 2, Unit 6, Lesson MD5-30, Extensions, Item 4, “Tony says, ‘Since there are 1,000 millilites in a liter, millileters must be bigger than liters.’ Explain why you agree or disagree with Tony’s reasoning.”
• Teacher Resource, Part 2 Unit 4, Lesson NBT5-57, Extensions, Item 5, “To multiply 3.2 and 7.1, Tessa multiplies 32 and 71 first. She then moves the decimal in the product two places to the left because the rule says to add the number of places after the decimal point to each factor. Tesa knows the rule, but she doesn’t understand why the rule works.” Part a helps guide the student. Part b. “In pairs, explain your answers to part a. Do you agree with each other? Discuss why or why not.”

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 6, Lesson NBT5-39, Extensions, Item 2 “a. Is there a largest power of 10? Explain. b. Is there a smallest decimal fraction? How do you know?” Students do not construct a viable argument or analyze the arguments of others, only explain the solution.
• Teacher Resource, Part 1, Unit 5, Lesson, NF5-17, Extensions 6: “a. Find: $$\frac{1}{2}$$ of 2, $$\frac{1}{3}$$ of 3, $$\frac{1}{4}$$ of 4, $$\frac{1}{5}$$ of 5, $$\frac{1}{}$$ of 6, $$\frac{1}{7}$$ of 7. Do you see a pattern? Predict $$\frac{1}{384}$$ of 384. Explain your reasoning. b. Find the fractions of a number. Explain your result. $$\frac{2}{3}$$ of 3, $$\frac{3}{5}$$ of 5, $$\frac{8}{9}$$ of 9, $$\frac{7}{15}$$ of 15, $$\frac{8}{11}$$ of 11” Students do not construct a viable argument or analyze the arguments of others, only explain the solution.

 The instructional materials reviewed for JUMP Math Grade 5 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 3, Lesson NBT5-20, Extensions, Item 4, “Encourage partners to ask questions to understand and challenge each other’s thinking. See page A-49 for sample sentence and question stems to guide students.”
• Teacher Resource, Part 1, Unit 5, Lesson NF5-18, Extensions, Item 2, “Encourage partners to ask questions to understand and challenge each other’s thinking and use of math words. See page A-49 for sample sentence and question stems to guide students.”
• Teacher Resource, Part 1, Unit 5, Lesson NF5-19, Extensions, Item 2, “Encourage partners to ask questions to understand and challenge each other’s thinking. See page A-49 for sample sentence and question stems to guide students.”

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, Unit 6, Lesson NBT5-40, Extensions, Item 1, “NOTE: Encourage students to try examples in an organized way to look for a pattern.” The teacher is encouraged, but not given any samples. 
• Teacher Resource, Part 1, Unit 2, Lesson NBT5-12, Extensions, Item 3, “a. What is the greatest seven-digit number you can create so that the number is a multiple of 5 and the millions digit is worth 200 times as much as the ten thousands digit? b. In pairs, explain how you know that your answers in part a) are correct. Do you agree with each other? Discuss why or why not.” The teacher asks students to explain, but the materials do not give any other suggestions to the teacher. 
• Teacher Resource, Part 2, Unit 2, Lesson NF5-31, Extensions, Item 3, "John adds$$\frac{2}{5}$$ + $$\frac{5}{3}$$ = $$\frac{7}{8}$$. What mistake did he make? How can you tell by estimating that the answer is incorrect? Explain." Teachers are provided an answer but teachers are not given direction on how to help students build an argument.
• Teacher Resource, Part 2, Unit 3, Lesson OA5-7, Extensions, Item 4, "The smallest non-zero place value in 15.70 is the tenths place. a. What is the smallest non-zero place value in the sum? a. 4.6 + 5.2 ... b. Rob adds two numbers whose smallest non-zero place value is the tenths place. When does the sum also have the tenths place as the smallest non-zero place value? Try several examples and make a conjecture, or guess, of what the rule is. c. In pairs, explain why your conjectures are true. Do you agree with your partner? Discuss why or why not. The materials provide answers but not directions to the teachers for how to guide the students in constructing an argument.

The instructional materials reviewed for JUMP Math Grade 5 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.