Unit Title Incorporating problem based learning when using operational and rational numbers Course(s) 4 final project Designed by Bettina Meyer Time Frame Varies depending on students ( 3 + weeks)

Stage 1- Desired Results

 Establish Goals5.8.2 Apply and adapt a variety of appropriate strategies to solve problems.5.8.3 Monitor and reflect on the process of problem solving. 6.1 The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals The student solves problems involving direct proportional relationships. The student is expected to: (B) represent percents with concrete models, fractions, and decimals (7.1) The student represents and uses numbers in a variety of equivalent forms. The student is expected to:  (B) convert between fractions, decimals, whole numbers, and percents CCSS 6.NS.4 –  GCF, LCMCCSS..5.NF.A.1 - +/- fractions with unlike denominatorsCCSS.5.NF.A.2    Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominatorsCCSS..5.NF.B.3 Interpret a fraction as division of the numerator by the denominatorCCSS 5.NF.4a-1, 4a-2, 4b-1,6-1,7a,7b,7c ; 6.NS,1-2- Multiplying and dividing with fractionsCCSS 5.NF.3-1, 3-2 Interpreting fractions

Transfer

 Learners will be able to....Apply their mathematical knowledge, skill and reasoning, specifically that of operational and rational numbers (fractions, decimals & percents), and problem solving strategies to determine and justify answers to authentic problemsApply their mathematical knowledge, specifically that of operational and rational number to their everyday lives

Meaning

 UNDERSTANDINGSLearners will understand that...Rational numbers can be represented as decimals, fractions, and percents Strategies can be used to simplify expressions and to compare and order rational numbers There are advantages and disadvantages to each type of representation (fractions, decimals, and percents)Sometimes the “correct” unit rate (i.e., fractions, decimals, and percents) is not the best solution to real world problemsTo compare fractions and decimals the numbers must be converted to the same form Essential QuestionsLearners will keep considering...Why do we need rational numbers?How are rational numbers used in our everyday lives?How are mathematical ideas interconnected and build on one another to produce a coherent wholeWhy do we need to compare rational numbers and which form is best to use given a specific situation?

Acquisition

 Learners  will know…Key Term definitions – unit rate, percent, decimal, mixed & improper fractions, rational number  The properties of rational numbers expressed in a variety of forms Strategies to convert between rational numbers.   When comparing fractions, a common denominator is essentialThere are key questions to ask when solving a problem Learners will be skilled at...Computing with rational numbers being expressed in a variety of forms  Determine if a solution is appropriate and moving beyond a particular problem by thinking of other situationsComputing the LCM, GCF to help solve problemsSimplifying fractions.  Generating equivalent forms of rational numbers.   Converting between fractions, decimals, whole numbersCalculating rational numbers using the 4 operationsIdentifying and calculating exponents and powers of numbersUsing various problem solving strategies to solve authentic problemsAsking themselves key questions when solving problems

Stage 2- Evidence

Learners will show that they understand by evidence of…

Set up a Sale Item  (from Yummymath.com)

GRASPS Task written in student-friendly language: