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| In this unit, children are introduced to the basic principles of multi-digit multiplication by focusing on extending multiplication skills and exploring the partial products method. They use their knowledge of multiplication to find the areas of rectangles and to convert units of measurement.The following big ideas will be covered in this unit: -Fact extensions can be used to compute mental math strategies for all operations involving larger numbers.
-Flexible methods of computation for multiplication involve taking apart and combining numbers in a variety of ways, which require deep understanding of the operations and the properties of the operations.
-Multi-digit numbers can be built up or taken apart in a variety of ways. These parts can be used to create estimates in calculations rather than using the exact numbers involved.
-Multi-digit multiplication can be illustrated and explained by using equations (partial products) and area models.
-When finding the area of a rectangle, the dimensions represent the factors in a multiplication problem.
- A two-column chart can be used to convert from larger to smaller units and record equivalent measurements. (mass, capacity, time) |
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| Operations & Algebraic Thinking 4.OA.A. Use the four operations with whole numbers to solve problems. 4.OA.A.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 4.OA.A.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Number & Operations in Base Ten 4.NBT.A. Generalize place value understanding for multi-digit whole numbers. 4.NBT.A.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.A.3. Use place value understanding to round multi-digit whole numbers to any place. 4.NBT.B. Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.B.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.NBT.B.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.MD.A. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), … 4.MD.A.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. | Students will have opportunities to: - Make sense of their problems (MP.1)
- Reflect on their thinking as they solve the problem (MP.1)
- Keep trying when the problem is hard (MP.1)
- Check whether their answer makes sense (MP.1)
- Solve problems in more than one way (MP.1)
- Compare strategies with others (MP.1)
- Look for mathematical structures such as categories, patterns and properties (MP.7)
- Use structures to solve problems and answer questions (MP.7)
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| - In multiplicative comparison problems there are two different sets. The comparison is based on one group being a particular multiple of the other (multiple copies). -Multi-digit numbers can be built up or taken apart in a variety of ways. These parts can be used to create estimates in calculations rather than using the exact numbers involved. -Using rounding is an appropriate estimation strategy for solving problems and estimating. Rounded numbers are approximate and not exact. -The larger the unit, the smaller the number you obtain as you measure. - A two-column chart can be used to convert from larger to smaller units and record equivalent measurements. (length) - Formulas such as, P = 2l + 2w or P = 2(l + w) or P= l + l + w + w can be used to find the sum of the side lengths of a rectangle. | - Flexible methods of computation for division involve taking apart and combining numbers in a variety of ways, which require deep understanding of the operations and the properties of the operations. -The meanings of the operations on fractions are the same as the meanings for the operations on whole numbers. (whole number times a fraction) - A two-column chart can be used to convert from larger to smaller units and record equivalent measurements. (Customary system) |
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| commutative property, decompose, distributive property, gram(g), kilogram (kg), liter(L), mass, milliliter (mL), partial-products multiplication, partition, ream, rectilinear figure, ones , tens, hundreds, thousands, double, digit, strategy, area, perimeter, patterns, place value, estimate, rows, length, width, factor, product, unit, compare, minutes, hours Bold Font: Listed in teacher's EDM4 edition Normal Font: not listed in teacher’s edition as a vocabulary word but will be helpful for students in explanations |
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| The following lesson plan sequence is obtained from Everyday Mathematics 4. Each lesson is aligned with a learning objective to inform the teachers on what students should be able to at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day. |
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| The following language supports are for English Language Learners but could also be used to support any struggling learner in mathematics. The strategies are obtained from the SIOP model. The language objectives will support students' academic language development. The sentence stems and starters provides the support many students need to be able to participate in discussions and writing about mathematics. |
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