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Place Value Concepts for Decimal Operations
Place Value Concepts for Decimal Operations
Understanding Decimal Numbers with Place Value and Fraction Thinking
Students represent decimal numbers to thousandths by using a variety of concrete and pictorial models and name the numbers in different forms. Students describe relationships between adjacent decimal place value units as 10 times as much as the next smaller unit and 1/10. as much as the next larger unit. Students compare two decimal numbers to thousandths and round decimal numbers to any place value.
Addition and Subtraction of Decimal Numbers
Students apply the methods they use to add and subtract whole numbers to add and subtract decimal numbers. By the end of the topic, they apply place value understanding and use concrete and pictorial models, recording the work in vertical form, to support the transition to the standard algorithm.
Multiplication of Decimal Numbers
Students apply the methods they use to multiply whole numbers to multiply decimal numbers to hundredths. They rely on unit form and their understanding of multiplication as equal groups to make sense of products of decimal numbers and whole numbers. Then students transition to multiplying two decimal numbers by using fraction multiplication to determine the product and make sense of its units.
Division of Decimal Numbers
Students apply the methods they use to divide whole numbers to divide decimal numbers to hundredths. With a continued emphasis on unit thinking, students rename decimal numbers in unit form, use whole-number division methods to divide, and then rename the quotient in decimal form. Students also connect dividing whole numbers by unit fractions to dividing numbers by 0.1 and 0.01.
Applications of Decimals
Students apply their understanding of decimal place value, relationships between decimals and fractions, and computation with decimals, fractions, and whole numbers to convert measurements in both the metric and customary measurement systems. They use tape diagrams to interpret and evaluate numerical expressions, and they create word problems that can be represented by a given expression or tape diagram.
Common Core State Standards covered in Module 4
5.NBT.A: Understand the place value system.
5.NBT.A.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.A.3: Read, write, and compare decimals to thousandths.
5.NBT.A.4: Use place value understanding to round decimals to any place.
5.NBT.A.3.a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
5.NBT.A.3.b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.NBT.B:Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.A.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Mathematical Practices
Mathematical Practices
Students can:
1. Solve problems without giving up.
2. Think about numbers in many ways
3. explain their thinking and try to understand others.
4. Show their work in many ways.
5. Use math tools and explain why they used them.
6. Work carefully and check their work.
7. Use what they know to solve new problems.
8. Solve problems by looking for rules and patterns.
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