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Main Curriculum Tie:
Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
Discuss the starter asking students how they predicted, what surprised them and what inferences they might make about operations n > 1 and when n < 1. Ask whether 3 and 12 are compatible numbers (3 is a factor of 12) and review that mental division can be done more easily if the numbers are compatible numbers.
Lesson Segment 1: Fractions-How can patterns, models, and pictures be used to estimate and check for reasonableness when performing operations with fractions and decimals? How do algorithms for operations with fractions help us compute efficiently?
Give each team a fraction manipulative such as Fraction Tiles or Fraction Towers. Give them a sheet of graph paper for sketching. Put a transparency on the overhead with these questions:
Problem Solving Questions (Transparency)
You can use rotating roles to build accountability in the following activity: a manipulator, two coaches, and a checker and an encourager. As they look for a way to show each of the following, discuss the answers to the questions on the transparency. Help the students build the models. Then, have them sketch the model and represent the problem mathematically and write out words for the operation involved.
Have them show each:
Practice With Fractions
Using these words you can work with the students to model and sketch simple fraction computations. The attached “Using Area Models for Adding and Subtracting Fractions”, and “Using Area Models for Multiplying and Dividing Fractions” worksheets can guide you through using an area model, but similar ideas can be applied if you would rather use Fraction strips or Fraction Equivalency Towers. As you work through each problem with the class, review how to set up algorithms for computing with fractions and discuss their efficiency and accuracy over models or sketching.
Help the students work through the attached worksheet, “Investigating Operations With Fractions”, Investigating Operations With Fractions, to practice answering the transparency questions. They will need help showing or sketching a model for the fractions involved.
You may find more practice is needed on operations with fractions as well as conceptual ideas for mixed numbers and improper fractions. Two additional worksheets have been attached for this: “Picturing Fraction Operations”, and “Mixed Numbers”
Game for practicing algorithms: Fraction Operation Basketball
Journal: Complete the “Computing With Fractions Journal Page” Cornell Notes.
Lesson Segment 2: Decimals-How can patterns, models, and pictures be used to estimate and check for reasonableness when performing operations with fractions and decimals? How do algorithms for operations with fractions help us compute efficiently?
Use “Modeling Decimal Computations” worksheet as a guide for class discussion. When working with multiplication of decimals, use length and width for an area.
Make transparency copies of several newspaper ads to be used for the following game. Put an ad on the overhead for each question in the game. When picturing multiplication with decimals, count the decimal along the width and length and shade the area common to both numbers.
Lesson Segment 3: Practice in Estimating and Computing, and determining reasonableness
Game: Price Is Right Race
Teams work together to answer the four questions on the transparency for each question. They should actual costs. Each person on the team records the answers to the four transparency questions on their own assignment paper.
After the students have had a couple of minutes to work with their teams to discuss methods without using a calculator and to record their work, the teacher selects a person from each team to go their whiteboard space to write the items they selected, and show the team’s reasoning. The first four teams to get this information on the board earn a point. Teams with the highest points at the end of the game will win.
Teacher uses the ads to determine what to fill in blanks with.
Have student pairs play the following game to explore patterns in operations:
Rational Numbers Operations War
Two players will play against another two players, so that each player has a partner to discuss options with. Have each group cut out the 32 cards. (attached). Have the students place the cards in two stacks: Decimals and Fractions. Shuffle the cards. Each pair draws two cards from either stack they choose, fractions or decimals. Choosing any one operation from +, −, x, ÷, the pairs arrange their two cards in either order to create an expression with the greatest possible value. They should write both theirs and their opponent’s expressions on their assignment. The pair whose expression has the greatest value collects all four cards and sets them aside. This continues until all cards have been drawn. The player who has collected the greatest number of cards wins the game.
Lesson Segment 4: Summarizing
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