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:

 Goal Your goal is to purchase the ‘in’ hoodie, by convincing your guardian to buy it for you today because it is only on sale for one day, at J Crew. Role You want the hoodie to fit in with your peers.  You know your guardian always likes the idea of a bargain as s/he is thrifty. Therefore you have to convince your guardian that s/he is saving x amount of money by buying it today, as the sale price includes up to 3 discounts. Audience Your mother /father / guardian, as they have the money needed to purchase the hoodie. Situation J Crew have this particular hoodie on sale for one day only.  You therefore need to prove to your guardian that by buying today, they could save x amount of money.  You know that your guardian likes to think about things, therefore you need to record your thinking, so they can go back to your explanation multiple times before making their final decision. Product You are to show your guardian how much money they are saving by purchasing the hoodie today.  Not only will it include an oral explanation, but you need to record the savings they will make in some form. For example, a spreadsheet, a tutorial demonstrating how all the discounts affect the price  - it is up to you.

OTHER EVIDENCE:

Learners  will show they have achieved Stage 1 goals by demonstrating their understanding through the Six Facets of Understanding...

 Explain Their reasoning behind their solutions to every problem based lesson Interpret What information they have been given, and what is needed to solve the problem Apply What operational / mathematical skills they need to solve the problem Have perspective To visualize how the problem could be solved, and how it can be solved in different ways, depending on the perspective that it has been interpreted. Therefore considering various possibilities, choose the best method to reach the determined goal. Empathize Be able to put themselves into the situation to be able to understand various perspectives, therefore enabling them to choose the best solution possible for the given problem so the most people involved are satisfied with the outcome. Have self-knowledge Be able to build on their prior knowledge, and be aware of their best learning style eg. manipulatives, paper to solve the specific problem, taking time to reflect and consider alternative options if the answer doesn’t seem correct.  Know it is ok to make mistakes to move forward.

Stage 3- Learning Plan

 Time Frame Learning Events Progress Monitoring Depends As this is a very individualized class,  the students work at their own rate, at their level, on whichever skill they need to develop (identified from the pre-test), therefore time is dependent on their mastery and depth of understanding. Likewise, how the student wishes to practice their skill is dependent upon the way they prefer to learn, therefore they are given a choice of paper / on-line games or hands on manipulatives/ partner games to choose from to reinforce their current learningAs this is individualized, within the lesson time frame, a student will have one on one with a teacher, which may include a mini lesson, on-going formative feedback, and practice - this may be individually or with a partner or small group. Formative feedback will be given dailyEach student will be involved in demonstrating the transfer of their new skills / knowledge to  solve an authentic problem using problem based learning and the problem solving framework  - this may be individually / partner / group, depending on the situation

 Resources / Materials:Link to teacher resource of menu created for student options to reinforce their learning of a specific skill.  This is modified, then shared with students via google doc. Main Websites  for resources - mathalicious, Robert Kaplinsky,  Yummy math, illuminations for mini lessons, problem based learning activitiesProblem solving framework taken from R. KaplinskyNLVM - national library of learning virtual manipulativesFraction manipulatives