Middle School Math East Coweta Middle September 25

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Middle School Math East Coweta Middle September 25, 2012

Middle School Math East Coweta Middle September 25, 2012

Agenda § Visual tools for thinking Tape diagrams Double number lines § § §

Agenda § Visual tools for thinking Tape diagrams Double number lines § § § Resources Grade-level discussions Vertical teaming Textbook evaluation timeline Wrap-up Coweta Committed to Student Success

Instructional sequence Concrete Model with objects Representational Model the problem with drawings, tables, graphs

Instructional sequence Concrete Model with objects Representational Model the problem with drawings, tables, graphs Coweta Committed to Student Success Abstract Represent problems with equations

Representational Drawing pictures that represent concrete objects provides a bridge to help students connect

Representational Drawing pictures that represent concrete objects provides a bridge to help students connect concrete representations to the abstract world of mathematical symbols. Coweta Committed to Student Success

Standard MCC 6. RP. 3 Use ratio and rate reasoning to solve realworld and

Standard MCC 6. RP. 3 Use ratio and rate reasoning to solve realworld and mathematical problems, e. g. , by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Coweta Committed to Student Success

What is it? Tape diagram. A drawing that looks like a segment of tape,

What is it? Tape diagram. A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model. – CCSS Glossary, p. 87 Coweta Committed to Student Success

Using tape diagrams with ratios The ratio of the length of the red ribbon

Using tape diagrams with ratios The ratio of the length of the red ribbon to the blue ribbon is 7: 4. If the red ribbon is 21 cm long, find the length of the blue ribbon. 21 cm 3 3 3 3 3 The blue ribbon is 12 cm long. Coweta Committed to Student Success 3 3

On your own … § Abby and Keisha shared $35 in the ratio of

On your own … § Abby and Keisha shared $35 in the ratio of 4: 3. How much money did Abby receive? Abby received $20. § The ratio of the weight of box A to the weight of box B is 5: 3. If the weight of box A is 40 pounds, find the total weight of the two parcels. The total weight of the two parcels is 64 pounds. Coweta Committed to Student Success

Double number lines § Double number lines are useful when a problem involves two

Double number lines § Double number lines are useful when a problem involves two different quantities. § Draw a pair of empty parallel number lines that are “hinged” at 0. § Label the number lines and mark off the corresponding quantities. Coweta Committed to Student Success

Double number lines example § There are 4 apples on each plate. If there

Double number lines example § There are 4 apples on each plate. If there are 6 plates, how many apples are there altogether? The two different quantities are apples and plates. 0 4 8 12 16 20 24 ? apples plates 0 1 2 3 4 5 6 There are 24 apples altogether. Coweta Committed to Student Success

Could you use a tape diagram? § There are 4 apples on each plate.

Could you use a tape diagram? § There are 4 apples on each plate. If there are 6 plates, how many apples are there altogether? 4 4 4 There are 24 apples altogether. Coweta Committed to Student Success 4

Using tape diagrams with % § There are 14 candies in a bag that

Using tape diagrams with % § There are 14 candies in a bag that is 20% full. How many candies are in the full bag? 20% 14 14 100% There are 70 candies in a full bag. Coweta Committed to Student Success 14

Using DNL with % § There are 14 candies in a bag that is

Using DNL with % § There are 14 candies in a bag that is 20% full. How many candies are in the full bag? 0 14 28 42 56 70 part percentage 0 20% 40% 60% 80% Coweta Committed to Student Success 100%

… or even a function table § There are 14 candies in a bag

… or even a function table § There are 14 candies in a bag that is 20% full. How many candies are in the full bag? Percentage Part 0% 20% 40% 60% 80% 100% 0 14 28 42 56 70 Coweta Committed to Student Success

Tape diagrams § $72 8 = $9 9 books 9 9 9 sports equipment

Tape diagrams § $72 8 = $9 9 books 9 9 9 sports equipment 9 3 = 27 Carlton had $27 left. Coweta Committed to Student Success 9 9

Double number lines example § 0 m 2 pints 0 Coweta Committed to Student

Double number lines example § 0 m 2 pints 0 Coweta Committed to Student Success

Double number lines example § 0 m 2 pints 0 Coweta Committed to Student

Double number lines example § 0 m 2 pints 0 Coweta Committed to Student Success

On your own … § 0 m 2 pints 0 Coweta Committed to Student

On your own … § 0 m 2 pints 0 Coweta Committed to Student Success

On your own … § 0 m 2 pints 0 Coweta Committed to Student

On your own … § 0 m 2 pints 0 Coweta Committed to Student Success

On your own … § 0 m 2 pints 0 Coweta Committed to Student

On your own … § 0 m 2 pints 0 Coweta Committed to Student Success

On your own … § 0 m 2 pints 0 Coweta Committed to Student

On your own … § 0 m 2 pints 0 Coweta Committed to Student Success

On your own … § 0 m 2 pints 0 Coweta Committed to Student

On your own … § 0 m 2 pints 0 Coweta Committed to Student Success

Visual thinking tools What we need to keep in mind about these representations is

Visual thinking tools What we need to keep in mind about these representations is that they are supposed to be students’ thinking tools, not just teachers’ explanation tools. – Dr. Tad Watanabe Kennesaw State University Coweta Committed to Student Success

Edmodo, intranet, shared drive ns atio d n u o al f u t

Edmodo, intranet, shared drive ns atio d n u o al f u t p nce ound o c h for r t s a g e k l m c Core ining ba nd examp n o m nta o c ers a Com h n i c a a m te by do ation for me a s m e r info in th n is. t s o t n en tio are a s m stud t i r n fo ats. u n i e m r h e t o h al f ut t , so n b h o i , a t t s ’ a U ia nt From as Georg f represe r so t o l orde t with a e r g

Unit pretests on intranet These pretests can be used “as is” or they may

Unit pretests on intranet These pretests can be used “as is” or they may be adapted as you feel is appropriate for your students. Coweta Committed to Student Success

CRCT materials As soon as these are posted, I will put them on the

CRCT materials As soon as these are posted, I will put them on the intranet and send you an email that they are there. Coweta Committed to Student Success

Grade-level discussions § What have you done already? § What’s been successful? challenging? §

Grade-level discussions § What have you done already? § What’s been successful? challenging? § How are you approaching the next unit? Coweta Committed to Student Success

Vertical teaming § Looking at possibilities for vertical teaming opportunities using feeder school patterns

Vertical teaming § Looking at possibilities for vertical teaming opportunities using feeder school patterns 5 th and 6 th grade teachers 8 th and 9 th grade teachers § Input on meeting dates, times, and locations needed Coweta Committed to Student Success

Textbook evaluation timeline § September Create textbook evaluation form. Ask publishers to begin sampling

Textbook evaluation timeline § September Create textbook evaluation form. Ask publishers to begin sampling books to schools. § October – January/February Teachers complete evaluations. Parents/community members complete evaluations. § February Get evaluations from schools. Eliminate to three potential series. § March Hear presentations from publishers; choose series. § March/April Submit choice(s) for school board approval. Coweta Committed to Student Success

Wrap-up § Questions/concerns/suggestions/needs? § Upcoming meetings Date October 23 December 4 January 29 March

Wrap-up § Questions/concerns/suggestions/needs? § Upcoming meetings Date October 23 December 4 January 29 March 5 Location Evans Lee Madras Smokey Road Coweta Committed to Student Success