Place Value, Multiplication and Division with Whole Numbers, and Expressions
Students will build on their place value understandings from fourth grade, and begin to compare digits that are to the left of other digits, in addition to the right, multiply three and four digit numbers, and divide with two digit divisors.
Essential Outcomes
Number in Operations in Base Ten
- 5.NBT.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.2: Use whole-number exponents to denote powers of 10. 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.
- 5.NBT.5: Fluently multiply multi-digit whole numbers using a standard algorithm.
- 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Operations and Algebraic Thinking
- 5.OA.1: post-test – Apply the order of operations to evaluate numerical expressions, e.g.:
- 6+8÷2
- (6 + 8) ÷ 2
- Note: Exponents and nested grouping symbols are not included.
- 5.OA.2: post-test – Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. e.g., Express the calculation “add 8 and 7, then multiply by 2” as (8 + 7) × 2. Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product
Essential Questions and Big Ideas
- What is the base ten number system and how can I use it to represent numbers?
- Numbers are based on powers of 10.
- A digit in one place represents 10 times as much as it represents in the place to its right.
- A digit in one place represents 1/10 of what it represents in the place to its left.
- Exponents can be used to represent powers of ten.
- An exponent is used to indicate how many times to multiply a number (base) by itself. Ex: a^3 = a x a x a
- Powers of 10 are the values of 10 with different exponents.
- Powers of 10 represent different place values.
- Numbers can be written in numeral form, word form, and expanded form.
- Numbers can be written in expanded form with powers of ten.
- How can I fluently multiply whole numbers?
- Multiplication represents repeated addition.
- Multiplication represents finding a total made from equal groups.
- The distributive property can be used to multiply larger numbers by breaking them up based on place value and multiplying each part.
- How can I fluently divide with whole numbers?
- Division represents breaking a total into equal groups.
- When dividing you take away multiples of the divisor until you’ve completed the dividend.
- When dividing by two-digit divisors, it can help to write out multiples of the divisor.
- What are expressions, and how do I solve them?
- Expressions are number sentences without an equal sign.
- Expressions can be written with words or with numbers.
- The order of operations represents the sequence to complete to solve an expression.
- Parentheses in an expression can note which steps to complete first in an expression.
Download the complete Grade 5 Math Unit 1 framework to customize for your own planning.