Grade 5CAP

Grade 5 - Common Core MathPlacing the Standards in the Math

Curriculum

July/August 2012

Danielle Brennan – Cap CoordinatorJane Hodge

Lissette Pellegrino

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Table of ContentsAbstract ......................................................................... 3

Rationale ......................................................................... 4

Content Emphasis by Cluster .................................... 5-9

8 Common Core Practices ……………………………………….. 10-14

Additional Practice Word Problems …………………….. 15-27

Bar Model Word Problems......................................... 28-29

Common Core Standards............................................. Addendum 1

Grade 5 Pacing Calendar…………………………………………… Addendum 2

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AbstractGrade 5

Fifth Grade Mathematics Common CoreJuly 2012

This CAP was developed to provide greater focus on mathematical experiences in the classroom. Emphasis is on Common Core Standards for Mathematical Content and Fluency in Grade 5. The Common Core fosters a greater in-depth understanding of mathematical concepts and their connections to everyday life. The curriculum, instruction and assessment should reflect the focus and emphasis of the standards. The major content (70%) emphasis in each standard is integrated with additional (20%) and supporting (10%) emphasis tying it all together to achieve fluency and cohesive understanding. The major focus in fifth grade is multiplication, division and fractions with greater emphasis placed on the depth of ideas, time required to master and importance to future mathematics readiness. The focus is in building skills within, and across grades, developing speed and fluency to know it, do it, and use it in real world situations.

Additionally, this CAP includes a teacher friendly pacing calendar with some recommendations for bringing the Mathematics Common Core Learning Standards to life in mathematics instruction through sense-making, reasoning, arguing and critiquing, and modeling, etc.

Finally, there is direct advice for teaching the mathematical practices in ways that foster greater focus and coherence for real world applications.

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RationaleGrade 5

Fifth Grade Mathematics Common CoreJuly 2012

The Mathematics Common Core Learning Standards focus on major content emphasis with fewer, key topics, while building skills within and across grades developing fluency and cohesive understanding. The Common Core practices were developed to help students apply math in real world situations, knowing which math to use for each real world situation. Students will be prepared to use core math facts faster and be able to apply math in the real world.

Our purpose is to provide a concise curriculum calendar identifying the major, and additional, and supporting clusters as a guide to inform instructional decisions regarding time and other resources with varying degrees of emphasis by cluster. This will allow the focus on the major math work for the grade to open up the Standards for Mathematical Practice in the mathematical instruction.

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Emphases in Common Core Standards for Mathematical ContentKindergarten – Grade 8March 12, 2012Content Emphases by Cluster

Describes content emphases in the standards at the cluster level for each grade. These are providedbecause curriculum, instruction and assessment at each grade must reflect the focus and emphasis ofthe standards.Not all of the content in a given grade is emphasized equally in the standards. The list of contentstandards for each grade is not a flat, one dimensional checklist; this is by design. There are sometimes‐strong differences of emphasis even within a single domain. Some clusters require greater emphasisthan the others based on the depth of the ideas, the time that they take to master, and/or theirimportance to future mathematics or the demands of college and career readiness. In addition, anintense focus on the most critical material at each grade allows depth in learning, which is carried outthrough the Standards for Mathematical Practice. Without such focus, attention to the practices wouldbe difficult and unrealistic, as would best practices like formative assessment.

Therefore, to make relative emphases in the standards more transparent and useful, the NY MathEmphases designate clusters as Major, Additional and Supporting for the grade in question. To say that some things have greater emphasis is not to say that anything in the standards can safely beneglected in instruction. Neglecting material will leave gaps in student skill and understanding and mayleave students unprepared for the challenges of a later grade. The assessments will mirror the messagethat is communicated here: Major Clusters will be a majority of the assessment, Supporting Clusters willbe assessed through their success at supporting the Major Clusters and Additional Clusters will beassessed as well. The assessments will strongly focus where the standards strongly focus.

In addition to identifying the Major, Additional and Supporting Clusters for each grade, suggestions aregiven in each grade for ways to connect the Supporting Clusters to the Major Clusters of the grade. Thus,rather than suggesting even inadvertently that some material not be taught, there is direct advice forteaching it in ways that foster greater focus and coherence.

Finally, the following are some recommendations for using the cluster level emphases:‐

Do … • Use the guidance to inform instructional decisions regarding time and other resources spent onclusters of varying degrees of emphasis.

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• Allow the focus on the major work of the grade to open up the time and space to bring the Standardsfor Mathematical Practice to life in mathematics instruction through sense making, reasoning,‐arguing and critiquing, modeling, etc.• Evaluate instructional materials taking the cluster level emphases into account. The major ‐work of the grade must be presented with the highest possible quality; the supporting work of the grade should indeed support the major focus, not detract from it.

• Set priorities for other implementation efforts taking the emphases into account, such as staffdevelopment; new curriculum development; or revision of existing formative or summative testing at the state, district or school level.

Don’t …

• Neglect any material in the standards. (Instead, use the information provided to connect Supporting Clusters to the other work of the grade.)

• Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

• Use the cluster headings as a replacement for the standards. All features of the standards matter — from the practices to surrounding text to the particular wording of individual content standards. Guidance is given at the cluster level as a way to talk about the content with the necessary specificity yet without going so far into detail as to compromise the coherence of the standards.

Explanations of terms used:

Major Clusters – areas of intensive focus, where students need fluentunderstanding and application of the core concepts (approximately 70%).

Supporting Clusters – rethinking and linking; areas where some material is being covered, but in a way that applies core understandings(approximately 20%).

Additional Clusters – expose students to other subjects, though at a distinct, level of depth and intensity (approximately 10%).

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Grade 4Major Supporting AdditionalOperations and AlgebraicThinking

▪ Use the four operations with whole numbers to solve problems.

Number and Operations in BaseTen

▪ Generalize place value understanding for multi digit‐ whole numbers.

▪ Use place value understanding and properties of operations to perform multi digit‐ arithmetic.

Number and Operations –Fractions

▪ Extend understanding of fraction equivalence and ordering.

▪ Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

▪ Understand decimal notation for fractions, and compare decimal fractions.

Operations and AlgebraicThinking

• Gain familiarity with factors and multiples. 3

Measurement and Data

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

• Represent and interpret data. 4

Operations and AlgebraicThinking

o Generate and analyze patterns.

Measurement and Data

o Geometric measurement: understand concepts of angles and measure angles.

Geometry

o Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Depth Opportunities:

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NBT 5, 6; NF 1, 3, 4 3Work in this cluster supports students’ work with multi digit arithmetic as well as their work with fraction equivalence.‐4The standard in this cluster requires students to use a line plot to display measurements in fractions of a unit and to solve problems involving addition and subtraction of fractions, connecting it directly to the Number and Operations – Fractions clusters.

Grade 5Major Supporting AdditionalNumber and Operations in BaseTen

▪ Understand the place value system.

▪ Perform operations with multi digit whole numbers‐ and with decimals to hundredths.

Number and Operations –Fractions

▪ Use equivalent fractions as a strategy to add and subtract fractions.

▪ Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Measurement and Data

▪ Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Measurement and Data

• Represent and interpret data.5

• Convert like measurement units within a given measurement system. 6

Operations and AlgebraicThinking

o Write and interpret numerical expressions.

o Analyze patterns and relationships.

Geometry

o Graph points on the coordinate plane to solve real world and mathematical‐ problems.

o Classify two dimensional‐ figures into categories based on their properties

Depth Opportunities:NBT 1, 6; NF 2, 4; MD 5

5The standard in this cluster provides an opportunity for solving real world problems with operations on fractions,‐connecting directly to both number and Operations – Fractions clusters.6Work in these standards supports computation with decimals. For example, converting 5 cm to .05 m involvescomputation with decimals to hundredths.

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Grade 6Major Supporting AdditionalRatios and ProportionalRelationships

▪ Understand ration concepts and use ration reasoning to solve problems.

The Number System

▪ Apply and extend previous understandings of numbers to the system of rational numbers.

▪ Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Expressions and Equations

▪ Apply and extend previous understandings of arithmetic to algebraic expressions.

▪ Reason about and solve one- variable equations and Inequalities.

▪ Represent and analyze quantitative relationships between dependent and independent variables.

Geometry

• Solve real world and‐ mathematical problems involving area, surface area, and volume.

Statistics and Probability

o Develop understanding of statistical variability.

o Summarize and describe distributions.

The Number System

O Compute fluently with multi‐ digit numbers and find common factors and multiples.

Depth Opportunities:RP 3; NS 1; NS 8; EE 3, 7

7In this cluster, students work on problems with areas of triangles and volumes of right rectangular prisms, which

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connects to work in the Expressions and Equations domain. In addition, another standard within this cluster asksstudents to draw polygons in the coordinate plane, which supports work with the coordinate plane in the NumberSystem domain.

Mathematics: Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

1. Make sense of problems and persevere in solving them.Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

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2. Reason abstractly and quantitatively.Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others.Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments ofothers. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

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4. Model with mathematics.Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically.Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

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6. Attend to precision.Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure.Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning.Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over

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and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line

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through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Additional Word Problems

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5OA Operations and Algebraic Thinking

5OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Adriana has 32 blue blocks. When she mixes them with her red blocks, there are 94 blocks in all. Which equation, when solved, will show how many red blocks Adriana has?

r + 94 = 3232 – r = 9432 + 94 = r32 + r = 94

5OA.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.

"There are 19 people on each train car and 4 people waiting in the train station."

Complete the table to show how the number of people, p, depends on the number of train cars, t.

Function: p = 19t + 4

t p3 61456

5NBT Number and Operations in Base Ten

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5NBT.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 1/10 of what it represents in the place to its left.

In 1.6, which digit is in the tenths place?

 

5NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal

point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

A university bookstore ordered 50 shipments of notebooks. There were 70 notebooks in each shipment. How many notebooks did the bookstore order in all?

notebooks 

5NBT.3 Read, write, and compare decimals to thousandths.

In 1,720.8694, which digit is in the tenths place?

5NBT.4 Use place value understanding to round decimals to any place.

Estimate the sum by rounding each number to the nearest whole number and then adding.

4.62 + 2.33

The sum is approximately . 

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102044269181963

755634948239807

777793073541638

5NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm

There are 97 bags filled with coins. There are 59 coins in each bag. How many coins are there in all?

coins

A new school bought pencils for all of the classrooms. There are 8 pencils in each package, and each box of pencils contains 5 packages. How many pencils are there in 3 boxes?

pencils

5NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

A photographer needs to mail 54 photographs to a newspaper in another town. If she can put 6 photographs in each envelope, how many envelopes will the photographer need to use?

envelopesA boy wants to purchase 600 green marbles. If there are 3 green marbles in each bag, how many bags of marbles should the boy buy?

bags 

A real estate agent has $72 to spend on newspaper ads. If each ad costs $18, how many ads will the real estate agent be able to buy?

newspaper ads 

5NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of

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796577785061791

177182547322385

operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

A pencil case usually costs $6.32. Today it is on sale for $1.84. If Jonah buys the pencil case today, how much will he save?

$

Dontrell bought 8.74 ounces of chocolate. 5.11 ounces of it was milk chocolate and the rest was dark chocolate. How much dark chocolate did Dontrell buy?

ounces 

Each sheet of metal is 0.7 inches thick. If Vikram stacks 9 sheets on top of each other, how thick will the stack be?

inches 

Each coin weighs 2.9 grams. How much do 3 coins weigh all together?

grams 

If 5 cherry popsicles cost $3.50 and the price of each popsicle is the same, how much does each popsicle cost?

$Each cement block weighs 0.4 kilograms. How much do 3 blocks weigh in total?

kilograms 

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224498163536738

177571283593888

736513928307752

640892106623810

784648196215375

360450508844136

195254646660325

It costs $11.34 to buy 6 ice cream sundaes. If the sundaes all have the same price, how much does it cost to buy 1 sundae?

$Rufus spent $1.75 to buy 5 spools of yellow thread. The spools all had the same price. How much did each spool cost?

$Over the past few years, Curtis has made 6 trips to visit the amusement park. He drove 981 kilometers in all. How far did Curtis drive on each trip?

kilometers 

A soda factory produced 8.6 liters of root beer in 5 minutes. How much root beer, on average, did the factory produce each minute?

liters 

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304338432658953

5NF Number and Operations-Fractions

5NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Starting from scratch, Belle finished 1/3 of a reading assignment Monday afternoon and another 1/3 of it on Tuesday afternoon. What fraction of the reading assignment was done by Tuesday night?

Simplify your answer.

 of the reading assignment

Last year, Seth grew 3/4 of an inch and his brother grew 1/2 of an inch. How much more did Seth grow than his brother?

Simplify your answer.

 inches 

Ramon's chemistry textbook weighs 9 3/5 pounds and his geometry textbook weighs 6 1/5 pounds. How much more does the chemistry textbook weigh than the geometry textbook?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

 pounds 

While waiting for her family to finish shopping, Gianna wandered around the mall. She spent 3/7 of an hour in a game store, 5/7 of an hour in clothing store, and 6/7 of an hour in a shoe store. In all, how many hours did Gianna spend wandering around the mall?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

hours 

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897118079458491

619003128017599

169515339364182

871149308300737

Taryn's aunt gave her a box of chocolates as a graduation gift. The box contained 7/9 of a pound of chocolate squares, 4/9 of a pound of chocolate coins, and 1/9 of a pound of chocolate caramels. How many pounds of chocolates were in the box in total?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

pounds 

Divide. Simplify your answer and write it as a proper fraction or as a whole or mixed number.

25

 ÷ 4  =

Professor Cook weighed two pieces of metal for an experiment. The piece of iron weighed 12 3/5 pounds and the piece of aluminum weighed 3 1/5 pounds. How much more did the piece of iron weigh than the piece of aluminum?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

 pounds

5NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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519552270677056

Complete the table. Simplify each answer and write it as a proper fraction or as a whole or mixed number.

Rule: multiply by 23

In Out06 4915

Multiply. Simplify your answer and write it as a proper fraction or as a whole or mixed number.

10  × 13

 =

5NF.4.b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

A square mirror has sides that are 3 feet long. What is the mirror's perimeter?

feet 5NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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285268593171123

Last week, Marcos's Fruit Stand sold 1/3 of a box of oranges. Down the road, Bruce's Fruit Stand sold 1/2 as many boxes of oranges as Marcos's did. How many boxes of oranges did Bruce's Fruit Stand sell?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

boxes 

Last week, Hector ran 4 4/5 miles. This week, he plans to run 3 times as far as last week. How many miles does Hector plan to run this week?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

miles 

Last week, Carlie spent 3 1/4 hours watching television. Martha watched television for 1 1/2 times as many hours as Carlie did. How many hours did Martha spend watching television?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

hours 

At the farmers' market, Isaac bought 11/12 of a bag of Red Delicious apples and 7/12 of a bag of Gala apples. How many more bags of Red Delicious apples did Isaac purchase?

Simplify your answer.

 bags

 

5NF.7.a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

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566552044823757

370160634501491

493877587578037

180136858105776

Divide. Simplify your answer and write it as a proper fraction or as a whole or mixed number.

25

 ÷ 2  =

5NF.7.b Interpret division of a whole number by a unit fraction, and compute such quotients.

Divide. Simplify your answer.

3  ÷ 12

 =

5NF.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Mrs. Hamilton had 1/2 of a cherry pie left over. She split the leftover pie evenly between her 2 children. What fraction of a pie did each child get?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

of a pie  5MD Measurement and Data

25

236181137445833

5MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Convert. Simplify your answer and write it as a proper fraction or as a whole or mixed number.

pints = 1

4 of a gallon

2 gal 1 pt + 3 gal 4 pt = gal pt

5MD.3.a A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

What is the volume of this object?

___cubic units

5MD.5.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as

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would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

What is the volume of this object?

___cubic units

5MD.5.c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

What is the volume of this object?

___cubic units

5G Geometry5G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Which words describe this shape? Choose all that apply.

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692707004699773

quadrilateral

trapezoidsquare

rhombus

Bar Model Word Problems

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1. Flora needs ⅜ yard of blue ribbon and ⅛ yard of red ribbon to make a bow for a present she is wrapping. How much ribbon does Flora need in all?

2. Campers go to Ridgeline Camp for one week sessions. During the first week of camp, there were 112 campers. During the second week, there were 15 fewer campers than in the first week. How many campers were at camp during both weeks?

3. The town Sean lives in has a population of 48,968 people. The town Debra lives in has a population of 73,815 people. How many more people live in Debra’s town?

4. Pete’s Pizza sold 65,182 pizza pies the first year they were open. They sold

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58,458 pizza pies the second year. What was the total number of pizza pies sold during the first two years of business?

5. Zoey has 8⅓ feet of blue yarn and 4⅔ feet of green yarn. How much more blue yarn does Zoey have than green yarn?

6. Mika and Shelly were playing a video game. Mika scored 65,324 points and Shelly scored 46,789 points. How many more points did Mika score than Shelly?

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