Fifth Grade

In fifth grade, students expand their place value practice to decimals to the thousandths place including rounding and comparing values. Additionally, they are introduced to whole-number exponents to the power of 10. In the area of computation, division is extended to two-digit divisors. Students will be adding, subtracting, multiplying, and dividing decimals to the hundredths place

Strategies include using a variety of manipulatives including money, base ten blocks, place value charts from thousands through thousandths, discover patterns, expanded form, number line, area model, distributive property, commutative property, associative property, partial products and quotients, grids (hundredths), accurate place value oral reading of decimal numbers, standard algorithm for adding and subtracting decimals, graph paper, pictorial representations, repeated subtraction, missing factor, and using a large variety of problem-solving strategies with an emphasis on mathematical discourse.

Common Core Standards

Understand the place value system.

CCSS.MATH.CONTENT.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.

CCSS.MATH.CONTENT.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.

CCSS.MATH.CONTENT.5.NBT.A.3
Read, write, and compare decimals to thousandths.

CCSS.MATH.CONTENT.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).

CCSS.MATH.CONTENT.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.

CCSS.MATH.CONTENT.5.NBT.A.4
Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths.

CCSS.MATH.CONTENT.5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.

CCSS.MATH.CONTENT.5.NBT.B.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.

CCSS.MATH.CONTENT.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.

Video Series of what the standard look like in the classroom with an overview of the progressions

Place value in base 10

Read, write and compare decimals to thousandths

Rounding

Multiplication

Division

Computation of decimals to hundredths

Multiplication and division with decimals

Concrete Level

In fifth grade, base ten expands from fourth grade's work with tenths and hundreds to thousandths. Students compare and round to the thousandths place. Additionally, students will be introduced to exponents for the power of ten. Base ten blocks or bundles of ten are concrete models that can be used for this work.

Arrays of blocks can be used as a concrete model for division and multiplication with decimals as well.

Represenational Level

Pictorial representations can assist with the base ten expansion to hundredths and exponents.

Area models can serve as representational level models for multiplication and division.

Abstract Level

By fifth grade, students should be able to fluently compute products of whole numbers and do all previously learned computations using equations. For division, 4th-grade techniques are expanded to two-digit divisors in fifth grade. Students should be able to estimate quotients abstractly.

Concrete Representation Abstract Examples