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6 th Grade Big Idea 3. Teacher Quality Grant. Big Idea 3: Write, interpret, and use mathematical expressions and equations. MA.6.A.3.1: Write and evaluate mathematical expressions that correspond to given situations.
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6th Grade Big Idea 3 Teacher Quality Grant
Big Idea 3: Write, interpret, and use mathematical expressions and equations. • MA.6.A.3.1: Write and evaluate mathematical expressions that correspond to given situations. • MA.6.A.3.2: Write, solve, and graph one- and two- step linear equations and inequalities. • MA.6.A.3.5 Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent. • MA.6.A.3.6 Construct and analyze tables, graphs, and equations to describe linear functions and other simple relations using both common language and algebraic notation.
Big idea 3: assessed with Benchmarks • Assessed with means the benchmark is present on the FCAT, but it will not be assessed in isolation and will follow the content limits of the benchmark it is assessed with. • MA.6.A.3.3 Work backward with two-step function rules to undo expressions. (Assessed with MA.6.A.3.1.) • MA.6.A.3.4 Solve problems given a formula. (Assessed with MA.6.A.3.2, MA.6.G.4.1, MA.6.G.4.2, and MA.6.G.4.3.)
Big Idea 3: Prerequisite knowledge • Order of Operations • Fractions and ratios • Decimals • Percent
Be able to write an algebraic expression for a word phrase or write a word phrase for an expression. Writing Algebraic Expressions
Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions. Since we do not know the can weight of the Chihuahua we can represent it with the variable c =c So then we can write the Great Dane as 40c or 40(c).
Notes • In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.
Addition Phrases: • More than • Increase by • Greater than • Add • Total • Plus • Sum
Subtraction Phrases: • Decreased by • Difference between • Take Away • Less • Subtract • Less than* • Subtract from*
Multiplication Phrases: • Product • Times • Multiply • Of • Twice or double • Triple
Division Phrases: • Quotient • Divide • Divided by • Split equally
Notes • Multiplication expressions should be written in side-by-side form, with the number always in front of the variable. • 3a 2t 1.5c 0.4f
Notes • Division expressions should be written using the fraction bar instead of the traditional division sign.
Modeling a verbal expression • First identify the unknown value (the variable) • Represent it with an algebra tile • Identify the operation or operations • Identify the known values and represent with more tiles
Modeling a verbal expression • There is no unknown value • More means addition • The known values are: Lula 10 books and Kelly 4 more Example: Lula read 10 books. Kelly read 4 more books then Lula. 10 +4 10 books 4 books
Singapore math introduction • Level 1 • Level 2 • Level 3 • Enrichment • Links for other strategies
Examples • Addition phrases: • 3 more than x • the sum of 10 and a number c • a number n increased by 4.5
Examples • Subtraction phrases: • a number t decreased by 4 • the difference between 10 and a number y • 6 less than a number z
Examples • Multiplication phrases: • the product of 3 and a number t • twice the number x • 4.2 times a number e
Examples • Division phrases: • the quotient of 25 and a number b • the number y divided by 2 • 2.5 divide g
Example games • Snow man game • Millionaire game
Examples 12f • converting f feet into inches • a car travels at 75 mph for h hours • the area of a rectangle with a length of 10 and a width of w 75h 10w
Examples i • converting i inches into feet • the cost for tickets if you purchase 5 adult tickets at x dollars each • the cost for tickets if you purchase 3 children’s tickets at y dollars each 12 5x 3y
Examples • the total cost for 5 adult tickets and 3 children’s tickets using the dollar amounts from the previous two problems 5x + 3y = Total Cost
Example Great challenge problems are located on the website bellow: Challenges
PROBLEM SOLVING What is the role of the teacher?
“Through problem solving, students can experience the power and utility of mathematics. Problem solving is central to inquiry and application and should be interwoven throughout the mathematics curriculum to provide a context for learning and applying mathematical ideas.” NCTM 2000, p. 256
Instructional programs from prekindergarten through grade 12 should enable all students to- • build new mathematical knowledge • through problem solving; • solve problems that arise in • mathematics and in other contexts; • apply and adapt a variety of • appropriate strategies to solve • problems; • monitor and reflect on the process of • mathematical problem solving.
Teachers play an important role in developing students' problem-solving dispositions. • They must choose problems that engage • students. • They need to create an environment that • encourages students to explore, take risks, share failures and successes, and question one another. • In such supportive environments, students develop the confidence they need to explore problems and the ability to make adjustments in their problem-solving strategies.
Three Question Types • Procedural • Conceptual • Application
Procedural questions require students to: • Select and apply correct operations or procedures • Modify procedures when needed • Read and interpret graphs, charts, and tables • Round, estimate, and order numbers • Use formulas
Sample Procedural Test Question • A company’s shipping department is receiving a shipment of 3,144 printers that were packed in boxes of 12 printers each. How many boxes should the department receive?
