Find a place to display a large monthly calendar for students to see and write on. As a daily routine, students will record their thinking on this calendar as they explore patterns in factors and multiples. See Unit 3 Lesson 5.
Display the class number line (0–130) where students can see and reach it with a pointer.
Attach a desk number line (0–100) to each student's desk to use throughout the year.
Display the Math Practices page where all students can see it.
Provide each student copies of the Small Multiplication Tables
Master. See Unit 8 Lesson 5.
Gather a collection of small, medium and large containers. See Lesson 7 and 8 Materials Preparation.
Gather a collection of small objects. See Lesson 9 Materials Preparation.
Gather graduated cylinders, eyedroppers, containers of water, and paper towels. See Lessons 7, 8, and 9 Materials Preparation.
Have the following tools readily available for the Daily Practice and Problems items in this unit:
- number lines
- monthly calendar
- centimeter rulers
- individual clocks
- calculators
- counters
- fraction circle pieces
- Fractions on Number Lines (Student Guide) Reference
- Fraction Chart (Student Guide) Reference
- Addition Strategies Menu (Student Guide) Reference
- Subtraction Strategies Menu (Student Guide) Reference
- Triangle Flash Cards: Last Six Facts (stored in an envelope)
- Multiplication Facts I Know chart (from Unit 8 or Master in Lesson 1)
| LESSON | SESSIONS | DESCRIPTION | SUPPLIES |
|---|---|---|---|
LESSON 1Break-Apart Products with Larger Numbers |
1 | Students break products, such as 6 x 12, into the sum of simpler products, e.g., 6 x 10 + 6 x 2. To do this, they divide a rectangular array representing a product into two smaller arrays that represent easier products. Then they add the easier products to get their answers. Students begin with a review of this method with one-digit by one-digit problems and move to two-digit by one-digit problems. In doing this activity, students develop an understanding of the distributive property of multiplication over addition although they do not study it formally. |
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LESSON 2More Multiplication Stories |
2 | Students solve two-digit by one-digit multiplication problems. After exploring and discussing their own methods for solving these problems, they focus on the method of breaking apart products into the sum of simpler products. They pay particular attention to partitioning numbers into tens and ones. Then they write stories to represent the multiplication problems and refine the stories to reflect their partitions. This work leads to the development of a paper-and-pencil algorithm for multiplication. |
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LESSON 3Multiplication Models and Strategies |
2 | Students are introduced to the all-partials algorithm for multiplication. They show connections between rectangle models and this new partial-product strategy to strengthen understanding of the meaning behind the notations they make. Students practice using the method to multiply and to check whether their answers are reasonable. |
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LESSON 4Solving Problems with Multiplication and Division |
2 | Using numbers between 25 and 50, students explore the number of groups of equal size that can be made from various numbers of objects. Students represent remainders in drawings and number sentences. Then they use strategies to solve multiplication and division word problems, including division problems in which remainders must be interpreted. |
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LESSON 5Earning Money |
2 | Students use models and strategies to divide $5.00 among three children. They devise, carry out, and communicate their problem-solving strategies. Students also review each other's work to provide feedback that informs revision of their written explanations. |
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LESSON 6Elixir of Youth |
1 | Sam V. and Tess V. Shovel, ace volume investigators, are on a case for the Ancient History Museum. Someone has stolen the liquid contents of an ancient jar in the museum's collection and Tess and Sam must find the thief. Through some clever detective work (more than once involving volume measurement), the youthful heroes track the thief to a suspicious dairy barn. This story sets the context for explorations with volume in Lessons 7–10. |
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LESSON 7Measuring Volume of Containers |
2–3 | Students find the volume of containers by first using U.S. Customary Units of Measurement: cup, pint, quart, and gallon. They fill containers to find the relationships among these units. Students then explore metric measures of volume: cubic centimeters, milliliters, and liters. Students use square centimeter cubes to estimate the volume of containers before using a graduated cylinder to find actual volume. |
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LESSON 8Fill It Up |
3 | In this lab, students develop a plan for accurately finding the volume of large containers. They find the volumes of at least three containers of various sizes and shapes. Students use addition, subtraction, multiplication, and division to solve problems involving volume. In working with containers of different shapes, the students are reminded that the tallest container may not always have the largest volume. |
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LESSON 9Measuring Volume of Solid Objects |
2–3 | Working in groups, students estimate the volume of small solid objects based on models they made from centimeter connecting cubes. Then they measure the actual volume of the objects by determining the amount of water displaced in a graduated cylinder when an object is placed in the cylinder. Students record the estimates and the actual volumes in a data table and analyze the data they collected. |
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LESSON 10End-of-Year Test |
1–2 | Students take a paper-and-pencil test that assesses skills and concepts studied in the last five units. |
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