Big Numbers, Estimation, and Computation

Unit 5 Big Numbers, Estimation, and Computation

5.1 Extended Multiplication Facts Objective: To extend basic multiplication facts to products of ones and tens and products of tens and tens. Teacher’s Manual pages 214-218

Standards: M4.A.1.3.2 Find/list/identify multiples of a number; M4.A.2.1.1 Solve problems involving all operations with whole numbers.

Advanced Preparation/ Manipulatives Necessary: Make copies of math masters p. 69

Vocabulary: extended multiplication facts

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet. Review and discuss the Math Message focusing on how to multiply by tens.  Develop a rule for multiplying ones by tens. Demonstrate how to multiply by tens. Have students complete journal p. 112.  Develop a rule for multiplying tens by tens. Have students work with a partner to complete p. 113.  Students will then play Beat the Calculator in groups of three using extended facts. The rules are listed on S.R.B. p. 188.  Students will fill in the bottom of p. 100 with a partner.  Independently, students will complete math boxes 5.1.

Homework: Study Links 5.1

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.2 Multiplication Wrestling Objective: To practice the extended multiplication facts; and to introduce the basic principles of multiplication with multidigit numbers.

Teacher’s Manual pages 286-290

Anchors: M4.A.2.1.1- Solve problems involving all operations with whole numbers

Advanced Preparation/ Manipulatives Necessary: Copy math masters p. 72; Have Everyday Math Card Decks available for each partnership Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet. Review and discuss the Math Message emphasizing the possible combinations of numbers.  Introduce how to play Multiplication Wrestling on math journal p. 115. This is the first step in learning how to multiply 2-digits by 2- digits, so make sure students understand the rules of the game clearly.  Divide students into partners, and let them play the game. Watch carefully to ensure they are playing correctly.  Students will independently complete math journal p. 116 to review place value in decimals.  Students will complete math boxes 5.2 independently.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.3 Estimating Sums Objective: To examine situations in which it is appropriate to make an estimate; and to estimate sums. Teacher’s Manual pages 291-296

Anchors: M4.A.3.1.3 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through 6 digits.

Advanced Preparation/ Manipulatives Necessary: n/a

Vocabulary: estimation

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet. Review and discuss the Math Message emphasizing estimation.  Examine the travel map on journal p. 119. Discuss distances and travel times and how they are obtained. Focus on how estimation would be helpful in planning trips and creating travel maps.  Divide students into partners. They will plan a trip on math journal pp. 118 and 119.  Independently students will solve logic problems on math journal p. 120 and complete math boxes 5.3.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.4 Estimating Products Objective: To estimate whether a product is in the tens, hundreds, thousands or more. Teacher’s Manual pages 297-301

Anchors: M4.A.3.1.3 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers

Advanced Preparation/ Manipulatives Necessary: Copy math masters p. 77 for every 4 students; Have multiplication wrestling materials available.

Vocabulary: rough estimate

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet. Review and discuss the Math Message.  Read journal p. 122. Discuss what the book means by “average American.” Discuss how to make a rough estimate.  Practice making rough estimates using the information on journal p. 122.  Divide students into partnerships to complete journal p. 123 on which they will be estimating averages.  Complete math boxes 5.4.  Play multiplication wrestling with a partner.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.5 The Partial-Products Algorithm for Multiplication (Part 1) Objective: To learn and practice the partial-products algorithm for 1-digit multipliers.

Standards: M4.A.2.1.1 Solve problems involving all operation with whole numbers; M4.B.2.2.1 Make reasonable estimates of weights, lengths, and capacities.

Advanced Preparation/ Manipulatives Necessary: see optional activities in manual

Vocabulary: partial-products method, partial product

 Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet. Review and discuss the Math Message. Share solution strategies  Practice finding products mentally to 1-digit times 2-digit multiplication problems.  Demonstrate the partial products algorithm for 1-digit multipliers.  With a partner, students complete p. 125 of the math journal to practice the partial products method.  Independently, students will estimate the lengths of various objects in the classroom and then compare their estimates to the actual length on journal p. 126.  Independently, students complete math boxes 5.5.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.6 The Partial-Products Algorithm for Multiplication (Part 2) Objective: To learn and practice the partial-products algorithm for 2-digit multipliers. Teacher’s Manual pages 309- 314

Anchors: M4.A.2.1.1 Solve problems involving all operation with whole numbers

Advanced Preparation/ Manipulatives Necessary: Copy Math Masters page 80 to place near the Math Message. (Extra Practice: Math Masters p. 84)

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Using Math journal pp. 128 and 129, introduce step a and step b by completing problem 1 together. Then have students complete step a and b with a partner.  Using the students number models to provide exact answers, demonstrate how to use the partial-products method for 2-digit multipliers.  Complete the rest of the math journal problems using this algorithm.  Do several more problems until the students are able to use the algorithm without help. (This lesson may take more than 1 day.)  Students complete math boxes 5.6 on math journal p. 130 independently.  If time allows, use Judging a Multiplication Wrestling Competition for extra practice.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.7 Lattice Multiplication Objective: To learn and practice the lattice method for multiplication.

Advanced Preparation/ Manipulatives Necessary: Copy Math masters p. 85 for class

Vocabulary: lattice method; lattice

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Demonstrate how to use the lattice method using various examples of 1-digit multipliers.  Partners complete math journal p. 131 to practice the lattice method for 1-digit multipliers.  Demonstrate how to use the lattice method for 2-digit multipliers.  Partners complete math journal p. 131 to practice the lattice method for 2-digit multipliers.  Independently students complete math journal p. 132 to review place value in whole numbers and math boxes 5.7 on journal p. 133.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities Multiplication Algorithm/ 4Sight Practice To practice multiplication algorithms; to prepare for 4Sight testing objectives.

Advanced Preparation: Identify students’ goals for 4Sight testing. Prepare stations for each group of students.

Procedure:  Computation Drill  Review homework/previous lesson  Students will complete multiplication facts using both the partial- products and lattice method algorithms.  Students will work at a station to attend to 4Sight goals.

Assessment Possibilities: Observation of student work 5.8 Big Numbers Objective: To read, write, and compare large numbers using patterns in the base-ten place-value system.

Anchors: M4.A.1.2.2 Compare and order whole numbers through 6 digits

Advanced Preparation/ Manipulatives Necessary: Copy Math Masters p. 86 for each pair of students. Borrow a ream of paper and a box used to carry 10 reams if possible.

Vocabulary: million, billion

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Practice reading and writing numbers to the billions using dashes and commas first. Then use a place value chart. Assign journal p. 134.  Show students the ream of paper and the box. Explain how much paper they contain. Have pairs complete math journal p. 135 using math masters p. 86. Compare strategies and answers.  Independently complete Math boxes 5.8 on journal p. 136.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.9 Powers of 10 Objective: To introduce exponential notation for powers of ten to name values of places.

Anchors: M4.A.1.2.2 Compare and order whole numbers through 6 digits; M4.A.2.1.1 Solve problems involving all operation with whole numbers

Advanced Preparation/ Manipulatives Necessary: Draw a place value chart on the board.

Vocabulary: trillion, quadrillion, quintillion, sextillion, powers of ten, exponent

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Introduce exponential notation for powers of 10 by showing the relationship between the place value chart and exponents. Practice using math journal p. 137.  Practice multiplication algorithms on math journal p. 138.  Complete math boxes 5.9.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.10 Rounding and Reporting Large Numbers Objective: To discuss sensible ways of reporting a count when a large number of items has been counted.

Standards:

Advanced Preparation/ Manipulatives Necessary: buildings, dry erase markers

Vocabulary: rounding

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Review rounding by using numbered buildings. Students decide which building they would run to if there is an emergency.  In partners, have students complete math journal p. 140.  Independently, students complete math boxes 5.10.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.11 World Tour: Traveling to Europe Objective: To look up and compare numerical data, including geographical measurements.

Standards:

Advanced Preparation/ Manipulatives Necessary:

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Mental Math and Reflexes using slates  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Look up and compare data about the countries in Europe using math journal p. 143 and the Student Reference Book.  Students independently update their notes on the world tour using math journal pp. 179-181  Students independently complete math boxes 5.11.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities 5.12 Unit 5 Review and Assessment Objective: To review and assess students’ progress on the material covered in Unit 5

Standards:

Advanced Preparation/ Manipulatives Necessary: Copy Unit 5 Checking Progress for each student

Lesson Procedure:  Computation Drill  Review of homework/ previous lesson  Display Math Message on the chart tablet.  Review and discuss the Math Message.  Complete Oral and Slate Assessments.  Students independently complete Unit 5 Checking Progress.  After handing in their tests, students complete math boxes 5.12.

Assessment Possibilities: Observation of journal pages/ math boxes; slate activities; Unit 5 Checking Progress 5.1 Name: ______

4 * 6 = ______4 * 60 = ______40 * 60 = ______

5 * 7 = ______5* 70 = ______50 * 70 = ______

5.1 Name: ______

4 * 6 = ______4 * 60 = ______40 * 60 = ______

5 * 7 = ______5* 70 = ______50 * 70 = ______

5.1 Name: ______

4 * 6 = ______4 * 60 = ______40 * 60 = ______

5 * 7 = ______5* 70 = ______50 * 70 = ______

5.1 Name: ______

4 * 6 = ______4 * 60 = ______40 * 60 = ______

5 * 7 = ______5* 70 = ______50 * 70 = ______

5.1 Name: ______

4 * 6 = ______4 * 60 = ______40 * 60 = ______

5 * 7 = ______5* 70 = ______50 * 70 = ______5.2 Multiplication Wrestling Name: ______

Cards: 7 9 2 5

Numbers formed: ______* ______

Teams: (______+ ______) * (______+ ______)

Products: ______*______= ______

______*______= ______

Total (add 4 products) ______

5.2 Multiplication Wrestling Name: ______

Cards: 7 9 2 5

Numbers formed: ______* ______

Teams: (______+ ______) * (______+ ______)

Products: ______*______= ______

______*______= ______

Total (add 4 products) ______5.5 Partial- Products Name: ______Multiply. Show your work in the grid below.

7 * 1, 439 = ______

5.5 Partial- Products Name: ______Multiply. Show your work in the grid below.

7 * 1, 439 = ______