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Title Designing Jewelry Grade 3 SBAC Assessment Claim Claim #1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Claim #2: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. SBAC Assessment Target Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace. Model with mathematics using a variety of methods. Learning Goal Demonstrate understanding of number relationships and principles underlying the structure of the number system. Apply understanding of properties of multiplication and the relationship between multiplication and division when multiplying and dividing. Represent and solve problems involving multiplication and division. Item Type Constructed Response, Performance Task Standards 3.OA.3: Use multiplication and division within 100 to solve word problems. 3.OA.5: Apply properties of operations as strategies to multiply and divide. 3.OA.6: Understand division as an unknown-factor problem. Practice(s) 1, 2, 3, 4, 6, 7 Depth of Knowledge 1,2,3 Task Overview In Parts One, Two, Three, and the Performance Task, students will construct justifications in words, diagrams, and symbols to support their problem solutions as they relate to the number relationships and properties when multiplying and dividing. Tasks will increase in level of rigor, as well as mirror the corresponding progression of conceptual understanding. The final Performance Task will require students will demonstrate increasing ability to make use of structure inherent in the number system to generate unique solutions to an open question. Students will demonstrate increasing fluency when multiplying and dividing within one hundred in the Performance Task. Third Grade – Module 2 Designing Jewelry Part One: Children are learning to make jewelry during summer camp. 1. Jenna plans to make pearl necklaces which have 24 pearls each. If 6 pearls are in one package, how many packages will she need to make necklaces for 10 friends? Show your work and explain your thinking. 2. Taj decides to create another style of a 24-bead necklace which uses beads in packs that hold 8 each. How many people can receive necklaces if he buys 12 packs? Show your work and explain your thinking. 3. a. The craft supply room also has loose beads. Trayvon chooses blue beads that come in scoops of 4 and red beads in scoops of 8. Unfortunately, the Craft Teacher spills Trayvon’s bag and can only tell Trayvon that she picked up 48 beads. What are the possible amounts of each color he may have chosen? 4. b. Demonstrate your solution(s) using a diagram, chart, number sentence, and/or a picture. c. Explain in words how you know your solution(s) would be possible. Describe any patterns you notice between more than one possible solution. Part Two: In a Native American village, children are experts at making beautiful beaded belts. 4.a. Each belt is four strings wide. Draw a total of 20 green beads with an equal number on each string. ________________________________________________ G rr r ________________________________________________ ________________________________________________ ________________________________________________ Write a multiplication sentence that describes your picture of the green beads. b. Add two yellow beads to each string. How many yellow beads did you draw? Write a multiplication sentence that describes your picture of the yellow beads. c. What is your total number of beads? d. Write a number sentence that describes all the beads in your picture. Use parentheses to combine the multiplication sentences from 1c and 1e. ( ) + ( )= Part Three: At the village, every child is making a belt to celebrate the return of spring. 5. a. If four beads make a line across the four strings, ________________________________________________ G rr rG ________________________________________________ rr rG ________________________________________________ rr r ________________________________________________ G rr design yourr own belt using one group of green beads and one group of yellow beads for a total of 60 beads. Remember: Keep your green and yellow beads in lines of four. Draw a picture of your belt. b. Write a number sentence that shows the number of green and yellow beads in each group. c. Use words and numbers to describe your belt. Performance Task Design three different belts using green and yellow lines of beads with a total of 60 beads each. Remember that the belts must be four beads wide. 6.a . Draw your three belts. Include a number sentence under each belt. b. Describe the belts’ patterns using numbers, symbols, and words. Designing Jewelry Credit for specific aspects of performance should be given as follows: 1. 40 packages Show work and explain thinking (may include a correct process but incorrect arithmetic) 2. 4 people Show work and explain thinking (may include correct process but incorrect arithmetic) 3. a. Solutions must include: Quantities of blue- bead scoops whose products are multiples of 4 Quantities of red- bead scoops whose products are multiples of 8 Products of blue bead scoops and red bead scoops must have a sum of 48 when added together Points Total Points 1 point 1 point 2 points 1 point 1 point 2 points 1 point for solution 4 points (Possible solution): 2 blue scoops and 5 red scoops (Possible solution): 4 blue scoops and 4 red scoops b. Solution(s) may be presented in a chart, diagram, picture, number sentence. For example: Number Sentence: (2 x 4) + ( 5 x 8) = 48 1 point for representation (chart, etc) c. Explanation: Look for phrases such as: Blue groups are all made by multiplying by 4 Red groups are all made by multiplying by 8 48 can be divided into equal groups by sets of 4 and sets of 8 As blue scoops increase by 2 groups, red scoops decrease by 1 group 4. a. Diagram of necklace drawn correctly. Number sentence: 4 x 5 = 20 b. 8 beads; 4 x 2 = 8 c. 28 beads d. (4 x 5 ) + ( 4 x 2 )= 48 2 points for explanation of math reasoning Accept all solutions that include multiples of 4 in a range of groups from 1 to 14. Total number of beads for both green and yellow beads must be equivalent to 60 Example: 14 groups of 4 green beads and 1 group of 4 yellow beads is equal to 60 beads total , or (14 x 4) + (1x 4) = 60 Use properties to decompose into simpler numbers: 14 x 4= 4 x 14 (Commutative Property) and (4x 2)x 7 = 56 (Associative Property) a. Diagram/picture of the belt b. Correct number sentence corresponds to the diagram c. Explanation of why the belt can be made with two colors of beads and 60 beads 6 . a. Accept all solutions that will fit on a belt 4 strings wide, have two colors, and have 60 beads total Student must include an appropriate corresponding number sentence to describe each belt. Each belt must be unique. b. Student must explain the relationship between the belts’ designs 1 point 1 point 1 point 1 point 5. 4 points 3 points 1 point 1 point 1 point 1 point/belt 1 point/ belt for each number sentence 1 point/belt 3 points 3 points 3 points (color arrangement and quantities) and the number sentence used to describe them using words. for each explanation in words Total Points 24 points