Task Name Task Type Grouping Strategy Content Addressed Standard(s) Arrays, Number Puzzles, and Factor Formative Assessment Lesson Individual/Small Group Understand differences between factors, multiples, prime & composite Skill to maintain- use task at your discretion MCC.4.OA.4 Equal to One Whole, More or Less Scaffolding Task Small Group/Partner Task Determining whether a fraction is Greater, Less, or Equal to 1 Skill to maintain- use task at your discretion MCC4.NF.2 Sharing Candy Bars Constructing Task Small Group/Partner Task Fractions as Division MCC5.NF.3 MCC5.NF.4 MCC5.NF.6 Sharing Candy Bars Differently Constructing Task Small Group/PartnerTask Fractions as Division MCC5.NF.3 MCC5.NF.4a MCC5.NF.6 Hiking Trail Constructing Task Individual/Partner Task Fractions of numbers, introducing operations with fractions MCC5.NF.3 MCC5.NF.4a *The Box Learning Task Partner/Small Group Task Fraction addition using models MCC5.NF.1 The Wishing Club Constructing Task Partner/Small Group Task Fraction Addition MCC5.NF.1 MCC5.NF.2 Fraction Addition and Subtraction Constructing Task Individual/Partner Task Fraction Addition and Subtraction MCC5.NF.1 MCC5.NF.2 Flip it Over Practice Task Group Task Building Fluency with Addition of Fractions MCC5.NF.1 Up and Down the Number Line Practice Task Small Group/Partner Task Building Fluency with Addition and Subtraction of Fractions MCC5.NF.1 Create Practice Task Small Group/Partner Task Building Fluency with Addition of Fractions MCC5.NF.1 Comparing MP3s Constructing Task Partner Task Multiplication of Fractions as an area model MCC5.NF.1 MCC5.NF.2 MCC5.NF.3 MCC5.NF.4 MCC5.NF.5 MCC5.NF.6
Measuring for a Pillow Performance Task Individual/Partner Task Using an area model to multiply and compare products based on factors MCC5.NF.4 MCC5.NF.5 MCC5.NF.6 Reasoning with Fractions Constructing Task Individual/Partner Task Determine the effect on a product, of multiplying a number by a factor greater than 1 and less than 1. MCC5.NF.4 MCC5.NF.5 *Sweet Tart Hearts Performance Task Group Task Problem solving by adding and multiplying fractions MCC5.NF.1 MCC5.NF.4 MCC5.NF.5 MCC5.NF.6 Where are the cookies? Formative Assessment Lesson Individual/Small Group Conceptualizing fractional parts of different wholes MCC5.NF.3 MCC5.NF.4 MCC5.NF.6 MCC5.NF.7 Dividing with Unit Fractions Constructing Task Partner Task Investigate dividing whole numbers by unit fractions and unit fractions by whole numbers MCC5.NF.7 Adjusting a Recipe Culminating Task Multiply, divide, add, and subtract unit fractions MCC5.NF.1 MCC5.NF.2 MCC5.NF.3 MCC5.NF.4 MCC5.NF.5 MCC5.NF.6 MCC5.NF.7 If you need further information about this unit visit the GaDOE website and reference the unit webinars.
These are halves These are thirds These are fourths These are fifths These are sixths These are sevenths These are eighths These are ninths These are tenths These are twelfths These are sixteenths These are eighteenths These are twentieths These are These are fiftieths These are hundredths
This task was developed to give students a real world application of multiplying fractions that would be engaging. It also allows students to take the concept of arrays, which they should have worked with extensively in their study of multiplication, and apply this familiar concept to another area of multiplication – fractions. The relationships between factor sizes and products can be discovered and generalized as students study partial products. Once students understand this relationship, they will be better able to attend to precision because they will know if their partial products are reasonable. Decomposition: Mixed Number = Whole number + Fraction (if fraction is a proper fraction) x Whole Number Fraction Whole Number > or = whole # < whole # > or = Fraction Fraction < whole # > or = Fraction < both Fractions Students should be allowed to draw representations of their thinking. This allows them to “talk through” their process which in turn enables students the opportunity to attend to precision as they explain and reason mathematically. Teacher Notes: Before the lesson, work with students on a number talk involving multiplication. Use the following problems, one at a time, giving think time and time to share after each one. Discuss strategies and give students opportunities to make connections to other areas in mathematics. Students should notice about the size of the product in relation to the factors. The use of “of” maybe helpful for students to visualize some of the problems. 2 x 4 x 4 or of 4 x or of x x or of x 4 or of 4 2 x 4 or 2 of 4
Is it possible to adjust the recipe to make 30 cookies? What would you have to do to the measurements of each of the ingredients? Explain how you would adjust your recipe to feed everyone in our class (don’t forget the teacher!) Is it possible to get the exact number of cookies for our class by adjusting the recipe? If not, adjust the recipe to get as close as possible (make sure everyone gets a cookie). Possible struggles students may have can be turned into wonderful inquiries! As students investigate the screen areas, you may notice them: Using array models or doubling ideas of multiplication to show how to double a recipe for some ingredients. multiplication of fractions algorithm. This strategy may promote discussion, so please allow students the freedom to make sense of this in the closing part of the lesson. Be on the lookout for students who, when working on halving the recipe, divide by ½ rather than by 2. This may be a lack of understanding of the concept of division. Scaffolding the students’ learning with thought provoking questions can help students strengthen conceptual understanding. Formative Assessment Questions How can you tell that your answer is correct? Does dividing by 2 (or ½) help solve this problem? How do you know? Did you develop a strategy to find your answers? Did you identify any patterns or rules? Explain! enough time has been devoted to the task, ask students to make recipe cards to prepare for the closing of the lesson. Recipe cards should be clear enough for others in the class to understand their thinking, but should not just be the figuring that was initially done copied over again. The recipe cards should be clear and concise presentations of any important ideas and strategies students wish to present. Some ideas to encourage discussion about in the presentations of student work: Estimation, using whole number estimates can help determine whether measurements of ingredients are in the ballpark. How fractions/mixed numbers are decomposed can make a difference. Students who use any algorithm should also show understanding of the algorithm used with some kind of model. DIFFERENTIATION: Extension Students can find their own recipes and determine the quantity of ingredients needed to: Double the recipe