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Main Curriculum Tie:
Background For Teachers:
Enduring Understanding (Big Ideas):
Ways to Gain/Maintain Attention (Primacy):
Note: Throughout the lesson, have students read and say all rational numbers in this lesson identifying the place value, for example saying, “three tenths”, rather than merely saying “point 3”.
Lesson segment 1: How do I use estimation to determine reasonableness?
The worksheet, “Estimating Fractions and Decimals by Rounding”, will provide the basis for class discussion.
Students have been studying estimation in previous years. You may want to review and practice rounding and estimating decimals by having them make the three-flap Foldable (attached), playing The Price Is Right, and Skillboard for Compatible Numbers.
The “Price Is Right” Estimation Relay
Objective: Students will use appropriate methods for estimating reasonableness in decimal computations.
Skillboard Game For Estimating Quotients Using Compatible Numbers
Objective: Students will use compatible numbers to estimate when dividing decimals.
The answers for these estimated problems will be 0-9. There are two forms of each correct answer on each skillboard, though they may be written as expressions rather than the actual quotient. For example, if the best estimated quotient is 3, the students will find two expressions on their board that are equivalent to three such as 3 x 1 and 6/2, or 12/4 and 9-6. Explain this to the students.
Write “compatible numbers, and quotient” on the board. Review estimating quotients using compatible numbers by modeling and referring to the vocabulary:
Show a problem on the transparency as listed below. Have partners discuss together how to use compatible numbers to estimate. Each partner tries to find one expression that is equivalent to the best estimated quotient on the skillboard and places that digit marker on the expression. Then, show the second problem on the overhead and repeat until you have shown all nine problems.
All the digits 0-9 will be used except one. At the end of the game, those pairs who have the correct digit marker left off the board win.
Assignment: Remind students to write an example for each of the methods of estimating discussed in segment 2 on their Foldable, and finish of any part of the Decimals With Color Tiles or Estimating Decimals and Fractions worksheet that needs to be finished. Assign any additional appropriate text practice.
Lesson Segment 3: What operation is needed to find the answer? What different symbols are used to indicate different operations? How can I predict whether the answer to a problem using fractions or decimals will be an increase or a decrease of the original value? How can I use estimation to determine reasonableness?
Write the following questions on a transparency:
Student teams may work together to sketch a model, write math symbols, and answer the questions on the transparency as you write the words below. Rotating roles help build accountability in the activity: a leader (keep folks on task), a gatekeeper (makes sure all ideas are treated with respect), an encourager (invites each person to contribute), and a scribe(writes on a team board or Smart Pal so class can see team ideas). Have teams rotate roles, so each person take the role at least once.
Write each of the following As they look for a way to show each of the following (except for the whole) 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 check their answers with a calculator after they have used the manipulative and sketched.
After teams have been given time to model, sketch, write the problem and set up math symbols, teacher selects a person from a team to show the class what the team did on the team board or Smart Pal. Class discussion about different approaches or responses and justification for their thinking should follow each problem below.
Work with students to complete the “Investigating Operations With Fractions” paper.
Using a Color Tile or other counter to represent the value of a decimal, help students visualize operations with decimals. Remind then that multiplication means repeated addition and division means repeated subtraction or how many of in the total.
Discuss and work with students on “Decimal Operations With Color Tiles” (attached)
Lesson segment 4: Practice predicting and estimating.
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