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Grade 5 UNIT 5: Addition and Multiplication with Volume and Area Suggested Number of Days for Entire UNIT: 25

|Essential Question |Key Concepts |Cross Curricular Connections |

|When would area and volume need to be calculated in real life? |Concepts of Volume |Science: Have students create a healthy diet using exact serving |

| |Volume and the Operations of Multiplication and Addition |measurements. Extend: Bring in some foods that students can |

|Unit Vocabulary |Area of Rectangular Figures with Fractional Side Lengths |measure out so that they gain a better understanding of portion |

|Base Bisect Cubic units |Drawing, Analysis, and Classification of Two-Dimensional Shapes |size. |

|Height Hierarchy Unit cube | | |

|Volume of a solid Angle | |Other: Use online resources and knowledge of volume to design a |

|Area Attribute Cube | |water park. |

|Degree measure of an angle | | |

|Face Kite Parallel lines | | |

|Parallelogram Perpendicular | | |

|Perpendicular bisector Plane | | |

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|*Assessments | | |

|Mid-Module Assessment: After Section B | | |

|(2 days, included in Unit Instructional Days) | | |

|End-of-Module Assessment: after Section D (2 days, included in Unit | | |

|Instructional Days) | | |

| | | |

| Unit Outcome (Focus) |

|Students will understand that volume can be measured by finding the total number of same size units required to fill the space without gaps or overlaps. They will measure necessary attributes of shapes in |

|order to determine area and volume to solve real world mathematical problems. |

|In this 25-day unit, students work with two- and three-dimensional figures. Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume |

|formula for right rectangular prisms. The second half of the unit turns to extending students’ understanding of two-dimensional figures. Students combine prior knowledge of area with newly acquired |

|knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths. They then engage in hands-on construction of two-dimensional shapes, developing a foundation |

|for classifying the shapes by reasoning about their attributes. This unit fills a gap between Grade 4’s work with two-dimensional figures and Grade 6’s work with volume and area. |

UNIT 5 SECTION A: Concepts of Volume Suggested Number of Days for SECTION: 3

|Essential Question |Key Concept |Standards for Mathematical Practice |

|When would volume need to be calculated in real |Explore volume by building with and counting unit cubes. |Make sense of problems and persevere in solving them |

|life? |Find the volume of a right rectangular prism by packing with cubic units and counting. |Reason abstractly and quantitatively |

| |Compose and decompose right rectangular prisms using layers. |5. Use appropriate tools strategically |

| | |6. Attend to precision |

| | |7. Look for and make use of structure |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Section A, students extend their spatial |5.MD.3 |Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A. A cube with side length 1 unit, |( |

|structuring to three dimensions through an |(DOK 1) |called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. | |

|exploration of volume. Students come to see | |B. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. (PS – 2) | |

|volume as an attribute of solid figures and | | | |

|understand that cubic units are used to measure | |Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (PS – 5 & 6) | |

|it (5.MD.3). Using improvised, customary, and | | |( |

|metric units, they build three-dimensional |5.MD.4 | | |

|shapes, including right rectangular prisms, and |(DOK 1) | | |

|count units to find the volume (5.MD.4). By | | | |

|developing a systematic approach to counting the | | | |

|unit cubes, students make connections between | | | |

|area and volume. | | | |

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UNIT 5 SECTION B: Volume and the Operations of Multiplication and Addition Days for SECTION: 6

|Essential Question |Key Concept |Standards for Mathematical Practice |

|When would volume need to be calculated in real |Use multiplication to calculate volume. | |

|life? |Use multiplication to connect volume as packing with volume as filling. |Make sense of problems and persevere in solving them |

| |Find the total volume of solid figures composed of two non-overlapping rectangular prisms. |Reason abstractly and quantitatively |

| |Solve word problems involving the volume of rectangular prisms with whole number edge lengths.|Make sense of problems and persevere in solving them |

| | |Reason abstractly and quantitatively |

| |Apply concepts and formulas of volume to design a sculpture using rectangular prisms within |5. Use appropriate tools strategically |

| |given parameters. |6. Attend to precision |

| | |7. Look for and make use of structure |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Concrete understanding of volume and |5.MD.3 |Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A. A cube with side length 1 unit, |( |

|multiplicative reasoning come together in Section|(DOK 1) |called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume | |

|B as the systematic counting from Section A leads| |B. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. (PS – 2) | |

|naturally to formulas for finding the volume of a| | | |

|right rectangular prism (5.MD.5). Students | |Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | |

|solidify the connection between volume as packing| |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| |

|and volume as filling by comparing the amount of |5.MD.5 |the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent | |

|liquid that fills a container to the number of |(DOK 1) |threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. |( |

|cubes that can be packed into it. This | |b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number | |

|connection is formalized as students see that 1 | |edge lengths in the context of solving real world and mathematical problems. | |

|cubic centimeter is equal to 1 milliliter. | |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. (PS – 1 & 4). | |

UNIT 5 SECTION C: Area of Rectangular Figures with Fractional Side Lengths Suggested Number of Days for SECTION: 6

|Essential Question |Key Concept |Standards for Mathematical Practice |

|When would area need to be calculated in real |Find the area of rectangles with whole-by-mixed and whole-by-fractional number side |4. Model with mathematics |

|life? |lengths by tiling, record by drawing, and relate to fraction multiplication |7. Look for and make use of structure |

| |Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths by| |

| |tiling, record by drawing, and relate to fraction multiplication. | |

| |Measure to find the area of rectangles with fractional side lengths. | |

| |Multiply mixed number factors, and relate to the distributive property and the area | |

| |model. | |

| |Solve real world problems involving area of figures with fractional side lengths using | |

| |visual models and/or equations. | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Section C, students extend their |5.NF.4b |Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. |( |

|understanding of area as they use rulers and set|(DOK 2) |b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction | |

|squares to construct and measure rectangles with| |side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side | |

|fractional side lengths and find their areas. | |lengths to find areas of rectangles, and represent fraction products as rectangular areas. | |

|They apply their extensive knowledge of fraction| | | |

|multiplication to interpret areas of rectangles | |Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or | |

|with fractional side lengths (5.NF.4b) and solve| |equations to represent the problem. | |

|real world problems involving these figures | | | |

|(5.NF.6), including reasoning about scaling |5.NF.6 | |( |

|through contexts in which volumes are compared. |(DOK 2) | | |

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UNIT 5 SECTION D: Drawing, Analysis, and Classification of Two-Dimensional Shapes Suggested Number of Days for SECTION: 6

|Essential Question |Key Concept |Standards for Mathematical Practice |

|How can you classify two dimensional figures |Draw trapezoids to clarify their attributes, and define trapezoids based on those |Make sense of problems and persevere in solving them |

|based on their properties? |attributes. |Reason abstractly and quantitatively |

| |Draw parallelograms to clarify their attributes, and define parallelograms based on |Make sense of problems and persevere in solving them |

| |those attributes. |Reason abstractly and quantitatively |

| |Draw rectangles and rhombuses to clarify their attributes, and define rectangles and |5. Use appropriate tools strategically |

| |rhombuses based on those attributes. |6. Attend to precision |

| |Draw kites and squares to clarify their attributes, and define kites and squares based |7. Look for and make use of structure |

| |on those attributes. | |

| |Classify two-dimensional figures in a hierarchy based on properties. | |

| |Draw and identify varied two-dimensional figures from given attributes. | |

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|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Students make use of structure to build a |5.G.3 |Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.|( |

|logical progression of statements and explore |(DOK 1) |For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. (PS – 7) | |

|hierarchical relationships among 2 dimensional | | | |

|shapes. | |Classify two-dimensional figures in a hierarchy based on properties. (PS – 7) | |

| |5.G.4 | |( |

| |(DOK 2) | | |

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|Possible Activities |

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|MULTIPLICATION STORIES: Challenge students to create a story involving the following fraction problems: 2/3 x 1⁄4; 1/5 x 1⁄2; 3/4x1⁄8; and 3/8 x 1⁄3. Extend: Have students share story problems with other |

|students with different problems and see if they can find the answer. Have students defend their answer by drawing a picture and using multiplication to reason about whether their answer makes sense. |

|Students can also create a comic strip depicting their story. |

|AREA WORD PROBLEMS: Ask students to use a rectangular grid to represent a rectangular area and show that the area is the same as would be found by multiplying the side lengths. Additional problems and |

|solutions can be found online. Ex: A rectangle is 4 meters long and half a meter wide. What is the area? Problems and solutions of rectangular arrays can be found at K-. |

|Click on 5th Grade in the left menu and scroll down until you find Area Word Problems with Fractional Side Lengths. |

|Resources |

|MULTIPLYING AND DIVIDING FRACTIONS BY DIVIDING RECTANGLES: Challenge students to solve multiplication and division of fractions using virtual fraction models at . Choose Divide or |

|Multiply from the top menu. This site allows students to practice dividing fractions by showing them visually what it looks like in a circle or on a line. |

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|Online video lessons and practice questions that align with: |

|NYS Common Core Standard 5.NF.4B: |

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|Engage NY Grade 5 Module 5 Link: |

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|Possible Activities |

|VOLUME EXPLORATION: Provide students with interlocking unifix cubes (ask a primary teacher for some). Ask students to make a simple rectangular prism 3 x 2 x 2. Have them count the cubes to find the volume.|

|Repeat this process again with dimensions 4 x 3 x 2. Give students time to recognize that counting the units is the same as multiplying the length width and height. Ask the students to create a rectangular |

|prism with a base area of 12 and height of 3. Prisms might look different, but they should come up with the same answer. Discuss why the volumes are the same even though some look different. Help them |

|understand that the base area of a rectangular prism x height is the same as counting the units to find the volume. Extend: Have students explore surface area. If unifix cubes are not available, this |

|activity can also be modeled online. A great interactive volume site: . Select Interactivate from the Activities & Lessons menu. Choose Activities under learners. Select Geometry from the top|

|menu and scroll down to find Surface Area and Volume and Activity. |

|COMPARING FISTS: Fill a container about halfway with water. Make a mark with masking tape to show the water level. Have each student make a fist and put it in the water. Mark the water level on the |

|container and take the fist out. The difference between the tape marks indicates the volume of students’ fists. Record the result of each student. Extend: Challenge students to graph all the results and ask|

|questions regarding the data. Explain to students that when Archimedes, the ancient Greek mathematician, hopped in the bathtub, he noticed that the water rose a certain amount, and realized that he had just|

|discovered the way to measure volume. He was so excited he ran down the street naked shouting, “Eureka!” (That’s Greek for “I’ve found it!”). Examples and more information on Cube Nets can be found at |

|illuminations.. Choose Activities and select 6-8. Click on Search. Scroll down to Cube Nets Activity. |

|CUBE NETS: A net is a two-dimensional figure that can be folded into a three-dimensional object. Provide students with paper and scissors and see which of the nets will form a cube. Examples of nets are 6 |

|unit squares horizontally; four squares horizontally with three squares at end vertically. More examples and information can be found online. |

|VOLUME WORD PROBLEMS: Challenge students to create their own volume word problems for others to solve. Ex: A rectangular solid measuring 9" by 12" by 16" is painted blue. The solid is then cut up into |

|1-inch cubes. How many of the 1-inch cubes have blue on exactly one side? Explain in detail how you found your answer using words, numbers, and/or pictures. (Answer: 616) |

|Resources |

|ONLINE ORDER OF OPERATIONS INTERACTIVE GAME: Challenge students to arrange number cards using different operations to make 24. There are multiple levels and students love the challenge! |

|. Select Math Games. Scroll down to Algebra and click on Make 24. |

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|Online video lessons and practice questions that align with: |

|NYS Common Core Standard 5.MD.3: |

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|NYS Common Core Standard 5.MD.4: |

|NYS Common core Standard 5.MD.5: |

|Possible Activities |

|FIGURE FAMILY TREE: Give students a list of figures and their properties, such as polygons – a closed plane figure formed from line segments that meet only at their endpoints; quadrilaterals – a four-sided polygon; |

|rectangles – a quadrilateral with two pairs of congruent parallel sides and four right angles; rhombi – a parallelogram with all four sides equal in length; square – a parallelogram with four congruent sides and four |

|right angles; a quadrilateral – a four-sided polygon; parallelogram – a quadrilateral with two pairs of parallel and congruent sides; rectangle – a quadrilateral with two pairs of congruent and parallel sides and four |

|right angles; a rhombus – a parallelogram with all four sides equal in length; square – a parallelogram with four congruent sides and four right angles. Ask students to find out what figures share the same properties. |

|Guide them by asking, is a square a rectangle, or is a rectangle a square? Have them explain their thinking. Then ask them to create a “family tree” to show the hierarchy of the figures based on their properties. Can a|

|figure be in more than one branch? Encourage rich mathematical discussions when sharing their “family trees”. Classification games can be played online. Online games for classifying different polygons based on their |

|characteristics can be found at math-. Click on Geometry Games and scroll down to Polygon Game near the bottom. |

|JEOPARDY! Arrange students in groups; each group decides on a team name. Draw a grid on your whiteboard (or overhead) with relevant categories. Create questions at various levels of difficulty to ask students. Each |

|group gets points when they answer the questions correctly. Jeopardy examples can be found online. Great Jeopardy examples are located at math-. Click on Middle School Games on the left. Select 6th Grade |

|Math Games and click on Factors and Multiples (LCM and GCF). Or click on Decimal Games from the left menu and scroll down until you find the Decimals Jeopardy Game (All Decimal Operations). |

|Enrichment Activities |

|ARCHIMEDES' PUZZLE: Challenge students to research the famous mathematician Archimedes and the Stomachion, an ancient tangram-type puzzle. This puzzle is believed by some to have been created by Archimedes, it consists|

|of 14 pieces cut from a square. The pieces can be rearranged to form other interesting shapes. Students can share with the class or write a report on their findings. An interactive lesson is available online. |

|Interactive lessons about Archimedes can be accessed at illuminations.. Select Lessons and choose grades 6-8, Geometry, then select Search. Scroll down to Archimedes' Puzzle. |

|PETALS AROUND THE ROSE GAME: A puzzle involving five dice and a non-standard pattern is used to promote problem-solving skills. Say: “The name of the game is Petals Around the Rose. The name is important. I will roll |

|five dice, and I will tell you how many petals appear.” Roll the dice so that all students can see the results. If possible, use transparent dice on the overhead projector, or virtual dice on the white board, so that |

|all students can see the roll. After each roll, tell the students how many petals are showing. Challenge students to try to discover the pattern. If some students figure it out, tell them to write it down (do not call |

|out answer) and submit to teacher in secrecy. (Answer: The number of petals is determined by the number of dots around the center dot on the dice) Directions and other examples can be found online. EX: If 5,3,3,3,2 |

|is rolled, inform students that there are ten petals. Continue rolling dice and telling them the number of petals. Directions and examples for “Petals Around the Rose” can be found at illuminations.. Choose |

|Lessons from the main menu and select 3rd-5th grade. Click Search and scroll down to find Petals Around the Rose Game. |

|Resources |

|ONLINE ORDER OF OPERATIONS INTERACTIVE GAME: Challenge students to arrange number cards using different operations to make 24. There are multiple levels and students love the challenge! . |

|Select Math Games. Scroll down to Algebra and click on Make 24. |

|Online video lessons and practice questions that align with: |

|NYS Common Core Standard 5.G.3: |

|NYS Common Core Standard 5.G.4: |

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