Updates and Tape Diagrams STEM and Instructional Resources Coach’s Meeting 2/15/2013 UPDATES K- Counting and Cardinality, K-5 Operations and Algebraic Thinking Counting and Cardinality are Operations and Algebraic Thinking are about understanding and using numbers. Progressions in Operations and Algebraic Thinking deals with basic operations- the quantitative relationships they model, the kinds of problems they can be used to solve, as well as their mathematical properties and relationships. The Progression describes concepts, properties and relationship that extend to other number systems, to measures, and to algebra. The Progressions are designed to help students extend arithmetic beyond whole number and understand and apply expressions and equations in later grades. Operation Progression Addition Subtraction Multiplication Division Commutativity and associativity of addition and multiplication Distributivity of multiplication over addition. Computational methods - strategies Counting and Cardinality Saying counting words Subitizing Counting and counting on Spoken number words to written base-ten numerals to base-10 system Operations and Algebraic Thinking Grades K-2 Methods used for solving single-digit addition and subtraction problems Working within 5, 10, 20 Representing and solving new type of problem situation (compare) Representing and solving the subtypes for all unknowns in all positions Extend addition and subtraction problem solving beyond 10, to problems within 20 Related addition and subtraction equations Two step word problems 3-5 Operations and Algebraic Thinking Common types of multiplication and division situations Levels in problem representation and solution: making and counting all quantities repeated counting on use of the associative and/or the distributive property to compose and decompose Using a letter for the unknown quantity, the order of operations, and two-step word problems for all operations 3-5 Operations and Algebraic Thinking Multiplication Comparison Factors, multiples, and prime and composite numbers Generating and analyzing patterns Connections to NF and NBT in Grades 3-5 Model Drawing Grade 1 Sarah collected 8 more shells than Penny. Penny collected 7 shells. How many shells did they collect altogether? Milking It for All It’s Worth! What is the difference in the number they collected? How many more would Penny need to collect to have more than Sarah? How many would Sarah have to lose to have fewer than Penny? Model Drawing Grade 2 Noah and Luca had the same number of comic books. Noah gave 3 to a friend, while Luca bought 5 more to add to his collection. How many more comic books did Luca have than Noah? Milking It for All It’s Worth! What’s the least number of books they could have to start? If they each had 10 books to start, how may books would they have now? If they each had 100 books to start, how many books would they have now? Model Drawing Grade 3 During a roadside clean-up, Manny collected 4 times as much litter as Henny. If they collected 15 pounds of litter altogether, how many pounds of litter did Manny collect? Milking It for All It’s Worth! How much did Manny collect? How much did Henny collect? What is the difference in the amount each collected? Model Drawing Grade 4 In one 4th grade class, 2/7 of the students wear glasses. If there are 21 students in the class, how many do not wear glasses? Milking It for All It’s Worth! How many wear glasses? How many do not wear glasses? How many more students do not wear glasses than do? What is 1/3 the number who do not wear glasses? Model Drawing Grade 5 Keisha bakes a pan of brownies for a family picnic. She takes 1/2 of the brownies to the picnic. At the picnic, her family eats 3/8 of the whole pan of brownies. What fraction of the whole pan of brownies doe Keisha bring back from the picnic? (pg. 312 Go Math) Milking It for All It’s Worth! How much less than ½ the brownies did her family eat? Any other questions? Model Drawing Grade 6 $240 was shared in the ration of 2 : 3 :1 by Jay, Nick, and Mandy. How much money did each one get? Milking It for All It’s Worth! What is the difference in the amounts each one shared? How much would each get if they shared $360? Additional questions??? There were 120 boys at the school assembly. There were 15 more girls than boys. How many students were at the assembly altogether? Chad and Jamie collect baseball cards. Both boys started the summer with the same number of cards. Chad lost 8 cards and Jamie collected another 13 cards. How many more cards does Jamie have than Chad now? Partitive Division The basketball team has 80 students signed up. The Coach divided them into 4 equal teams. How many students are on each team? Go Math Example, Gr. 4, Ch. 2, P37 Juan, Steve, and Gabriella bought a total of 30 markers at an art store. Juan bought 3 more markers than Steve. Gabriella bought 7 times as many markers as Steve. How many markers did each buy? Working with Fractions There were 75 swimming pools at a local store. If 3/5 of the pools were sold during one hot summer day, how many pools were left for sale after that day? One or Two Variable There are 30 glass jars in a box. 2/6 of them are broken. How many glass jars are not broken? Fraction within a Fraction Akia earned $30 babysitting Friday night. She spent half of the money on a new pair of shoes, and she spent 1/3 of the remaining money on lunch. Does she have enough money to also buy a CD that costs $12.98? Carol made 300 cookies for a bake sale. She sold ¾ of the cookies in the morning and 2/3 of the remainder in the afternoon. How many cookies did Carol have leftover? Three-fifths of the students in class have brown eyes. There are 7 more students with brown eyes than without brown eyes. How many student are in the class? Working with Ratios Cracker and cookies are ordered for snack at a ratio of 3:1. If 100 snacks were ordered, how many were cookies? Challenge Problem A father is four times as old as his son now. If the father was 46 years old 2 years ago, find the son’s age now. Where the Operations and Algebraic Thinking Progression is Heading Connection to the Number System Connection to Expressions and Equations

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