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T OOLS /M ODELS FOR E NGAGE NY Vanessa Walker PVSD vwalker@pvsd.k12.ca.us

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Goal for tonight: To provide you with some background knowledge and provide an overview of the tools and models that your child will be using with the math curriculum.

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B ACKGROUND I NFORMATION

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P REPARING S TUDENTS FOR A LGEBRA T HROUGH N UMBERS AND O PERATIONS

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P REPARING S TUDENTS FOR A LGEBRA R EQUIRES T HREE S HIFTS IN M ATHEMATICS 1. Focus: Concentrate where the standards focus. 2. Coherence: Think across grades, and link to major topics. 3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.

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S OLID C ONCEPTUAL U NDERSTANDING Teach more than how to get the answer and instead support students ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application)

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S UPPORTING M ATHEMATICAL U NDERSTANDING

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E NGAGE NY M OST L ESSONS I NCLUDE : Fluency Practice - activity to build fluency in a concept Application Problem- word problems- apply math to daily life Concept Development- main objective of the lesson is taught here Problem Set- student practice sheet Student Debrief- provides students with the opportunity to discuss what they have learned Exit Ticket- formative assessment Homework- is just like the problem set

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V OCABULARY V OCABULARY : D ECOMPOSING & C OMPOSING N UMBERS Break numbers down into their sub-parts: This concept is used across grade levels. 1. Decompose numbers into tens 2. How any number can be created using a variety of addends (numbers). For example 5 can be represented by: 0+5; 1 + 4; 2+2 +1; 3 + 2; 5 +0;

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T OOLS /M ODELS OF E NGAGE NY Ten Frame (TK-3 rd ) Arrays & Area Models (1 st -5 th ) Base Ten Blocks & Bundles (K-2 nd ) Number Bonds (K-5 th ) Tape Diagram (1 st -5 th ) Number Line (K-5 th ) Number Path/Towers (TK-1 st ) Place Value Chart (2 nd -5 th ) Number Disks (2 nd -5 th )

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T EN F RAME A RRAYS & A REA M ODELS

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TK, Kinder & 1 st 5th Grade 2 nd -4 th Grade

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TK - 1 ST G RADE C OUNTING, A DDITION, & S UBTRACTION Uses the 5-frame & 10-frame to set the foundation of decomposing numbers

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2 ND G RADE R EPEATED A DDITION

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M ULTIPLICATION 3 RD G RADE 13 X 23

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M ULTIPLICATION 4 TH G RADE 26 x 34 34 (20 + 6) x (30 + 4) x 26 (6 x 34) + (20 x 34) 24 (6 x 4) + (6 x 30) + (20 x 4) + (20+ 30) 180 80 600 884 30 4 6 20 18 tens or 180 24 6 hundreds or 600 8 tens or 80

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D IVISION

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A NTS M ARCHING The ants are marching in the annual parade. There are 12 ants. They must march in equal rows and each row must have more than one ant. Show all the different ways the ants can march in the parade. How many different ways can they march? Explain your answer.

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N UMBER B ONDS (K 5 TH G RADE ) T APE D IAGRAMS (1 ST 5 TH G RADE ) P ICTORIAL REPRESENTATION OF PART - PART - WHOLE RELATIONSHIP

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N UMBER B OND P RIMARY G RADE

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N UMBER B OND U PPER G RADES 198 + 54 = 2 + 52 198 + 2 = 200 200 + 52 = 252

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T APE D IAGRAM B AR M ODELS USED FREQUENTLY WITH WORD P ROBLEMS

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John, Emma, and Alice each had 10 raisins. John ate 3 raisins, Emma ate 4 raisins, and Alice ate 5 raisins. How may raisins do they each have now? Write a number bond and a number sentence for each.

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Mathew has 14 blue marbles. His blue marbles make-up two-fifths of his total number of marbles. How many marbles does Mathew have? 2/5 14 2 = 14 1 = 7 5 = 5 x 7 = 35

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N UMBER L INE & P LACE V ALUE C HART (& N UMBER C HIPS )

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N UMBER L INE P RIMARY G RADES

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N UMBER L INE U PPER G RADES

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P LACE V ALUE C HART

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F LUENCY

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R EQUIRED F LUENCIES IN K-6

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W HAT S UPPORT C AN B E O FFERED AT H OME ? Continue to support students in memorizing basic math facts. Ask your child to review the days lesson by reviewing the problem set with them. Solve the problem using traditional methods then prove any added information. Read the newsletter that goes along with the topic. Homework should provide an opportunity for practice.

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TO HELP STUDENTS RETELL Questions to pose: How did you solve the problem? What did you do? What strategy did you use? What math words did you use or learn? What were the steps involved? What did you learn today? What do(es) __________________ mean to you ?

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Prompts to use: I solved the problem by The math words I used were The steps I followed were My strategy was successful because Explain to a young child or someone that wasnt involved Draw a picture to show how you solved the problem.

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PVSD W EBSITE HTTP :// WWW. PVSD. K 12. CA. US / SITE / DEFAULT. ASPX ?P AGE ID=1 HTTP :// WWW. PVSD. K 12. CA. US / SITE / DEFAULT. ASPX ?P AGE ID=1

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L ET S S OLVE S OME P ROBLEMS Bella spilled some pencils on the carpet. Bill came over to help her pick them up. Bill found 5 pencils under the desk and Bell found 4 by the door. How many pencils did they find together? Use a ten frame, draw a math picture, write a number sentence (equation) that tells about the story.

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M ULTIPLICATION : USE AN A RRAY TO S OLVE 26 X 48 40 8 20 20 x 40 = 800 20 x 8 = 160 6 x 40 = 240 6 6 x 8 = 48 1248

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R IGOR & D EPTH OF K NOWLEDGE (DOK)

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F RACTIONS 5 TH G RADE https://www.engageny.org/resource/grade-5- math-visual-model-representations-tape- diagram-and-area-model-5nf1-and-5nf4a