Rational Number Operations, Activity 7()(A) Activity Objective I can add, subtract, multiply, and divide fractions fluently. I can explain how to use estimation to determine if a solution is reasonable. Materials Fraction Operations Loop Fraction Operations Loop Cards Scissors Tape or glue Answer Key Expression 7 4 8 5 Solution 5 5 7 4 4 6 5 7 4 5 Debriefing Questions What steps did you take to simplify 7? Why? How are the two division problems similar? How are they different? Listen For... Use of the standard algorithm for fraction addition, subtraction, multiplication and division. Use of vocabulary: mixed number, simplify, reciprocal, denominator, numerator, and improper. Understanding of the order of operations. Communicating about Mathematics Students may respond by talking to a partner and recording a written response in the space provided. Possible sentence frame: I could use estimation. Listen/Look For... Understandings of the effects of rounding up or rounding down when compared to the actual answer, and use of benchmarking fractions to the nearest half. 05 Region 4 Education Service Center
Student Name: Date: Fraction Operations Loop. Simplify each expression on the Fraction Operations Loop Cards in the workspace provided below.. Tape the top of the card that contains the solution to the bottom of the card that contains the expression.. Continue this process for the remaining problems. 4. When complete, the taped cards should form a loop. My Workspace: Communicating about Mathematics Explain how you could use estimation to determine if your answers are reasonable. 05 Region 4 Education Service Center
Fraction Operations Loop Cards Cut along the dotted lines. Do not cut along the solid lines. 5 6 5 7 4 8 5 7 7 5 4 5 4 4 05 Region 4 Education Service Center
Rational Number Operations, Activity 6 7()(A) Activity Objective I can determine if a statement involving rational number operations is always, sometimes, or never true. Materials Always, Sometimes, or Never I can describe how my models illustrate that a statement involving integer operations is true or false. Answer Key Always Sometimes Never Statement A negative number plus a positive number is a negative number. The product of two integers will have the same sign as the quotient of the two integers. The difference between two positive numbers is The quotient of a number and its opposite is one. The product of two positive numbers is positive. The difference between two negative numbers is The sum of two positive numbers is positive. The product of a positive number and a negative number is positive. The sum of a number and its absolute value is zero. The product of a number and its absolute value is positive. Debriefing Questions What strategies did you use to determine if a statement was always, sometimes or never true? What examples did you use to test the statements about absolute value? What examples and non-examples did you use with the statements that are sometimes true? Listen For... Use of the vocabulary negative, positive, opposite, and absolute value. Use of examples and non-examples to justify how statements are classified. 05 Region 4 Education Service Center Communicating about Mathematics Students may respond by talking to a partner and recording a written response in the space provided. Possible sentence frame: My examples show that is sometimes true by. Listen/Look For... Connections between rules for integers and rules for rational numbers.
Student Name: Date: Always, Sometimes, or Never Determine if the statements below are always, sometimes or never true. Place a check mark in the appropriate column. Always Sometimes Never Statement A negative number plus a positive number is a negative number. The product of two integers will have the same sign as the quotient of the two integers. The difference between two positive numbers is The quotient of a number and its opposite is one. The product of two positive numbers is positive. The difference of two negative numbers is The sum of two positive numbers is positive. The product of a positive number and a negative number is positive. The sum of a number and its absolute value is zero. The product of a number and its absolute value is positive. Communicating about Mathematics Select one of the sometimes true statements from above. Provide an example to illustrate when the statement is true and an example to illustrate when the statement is false. 05 Region 4 Education Service Center
Rational Number Operations, Activity 8 7()(A) Activity Objective I can use a number line to model multiplication of rational numbers. Materials Multiplication Models: Round Robin I can explain my multiplication model and compare it to others models. Answer Key. 5 x 6. 4 4 x 6. 5( 0.6) =. Possible open number line model shown: 0.6.4 0.6.8 0.6. 0.6 0.6 0.6 0 4. 8. 4 Possible open number line model shown: 4 8 4 7 5 0 Debriefing Questions What do you notice about the length of each arrow, its direction, and the number of arrows in problem? Problem? How are each of those reflected in the numerical representation? How did you show a part of a group? In problems and 4, what is the size of the group being repeated? How many groups are needed? Explain your thinking. Listen For... Appropriate understanding of how to use an open number line to model multiplication of rational numbers as repeated groups of a given size. Understanding the connections among the two rational factors, the length and direction of the repeated arrow, and the number of times the arrow is repeated on the number line. Communicating about Mathematics Students may respond by talking to a partner and recording a written response in the space provided. Possible sentence frame: My model and my partner s model are similar. They are different. Listen/Look For... Appropriately representing -.5 on the number line as the size of a group that repeats three complete times and then half of a fourth time. 05 Region 4 Education Service Center
Student Name: Date: Multiplication Models: Round Robin Pass your paper to the person seated at your right. Determine the process you will use, and solve the first problem on the paper you have received. You may work with your group to solve the problem. Upon completing the first problem, pass the papers to the right again. Determine the process you will use, and solve the second problem. Continue this process for the two remaining problems.. Complete the number sentence so that it matches the representation modeled on the number line.. Complete the number sentence so that it matches the representation modeled on the number line. 0 4 5 6 7 7 6 5 4 0 X X. Use the open number line below to model the problem, 5( 0.6) =. 4. Use the open number line below to model the problem,. What value goes in the blank? What value goes in the blank? Communicating about Mathematics Explain your model in problem 4 to your partner. Compare and contrast your model with your partner s model. 05 Region 4 Education Service Center