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Elementary

Grade 5

12 chapters46 lessons
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1

Decimal place value and powers of ten

6 lessons

Place value to thousandths, each place ten times the one to its right, written with powers of ten.

Review first: Tenths and hundredths Comparing and ordering decimals Multiplying and dividing by ten, one hundred and one thousand Rounding to any place, including decimals
1.1Thousandths: reading, writing and expanded form
1.2Rounding decimals
1.3Powers of ten
1.4Multiplying a decimal by ten, one hundred or one thousand
1.5Dividing a decimal by ten, one hundred or one thousand
1.6Numbers in other bases
2

Multi-digit multiplication and division

4 lessons

Fluency with the standard multiplication algorithm and long division by two-digit divisors, with estimates to check.

Review first: Partial products Partial quotients Dividing by a single digit Estimating by rounding
2.1The standard multiplication algorithm
2.2Friendly numbers and deliberate over and under estimates
2.3The standard long division algorithm
2.4Dividing by a two-digit number
3

Adding and subtracting decimals

2 lessons

Adding and subtracting decimals to hundredths by lining up place values, including money.

Review first: Comparing and ordering decimals Thousandths: reading, writing and expanded form
3.1Adding and subtracting decimals
3.2Money written as decimals
4

Multiplying and dividing decimals

5 lessons

Converting fractions to decimals by division, and multiplying and dividing decimals with place-value reasoning.

Review first: Powers of ten The standard long division algorithm
4.1Converting between fractions and decimals
4.2Multiplying decimals
4.3Where the point goes in a product
4.4Dividing decimals
4.5Dividing by a decimal
5

Adding and subtracting fractions with unlike denominators

6 lessons

Renaming fractions to a common denominator so they can be compared, added and subtracted, including mixed numbers.

Review first: Common denominators and the least common denominator Adding and subtracting fractions with like denominators Mixed numbers and improper fractions: rewriting and comparing
5.1Comparing by finding a common denominator
5.2Adding and subtracting fractions with unlike denominators
5.3Estimating with fractions
5.4Adding mixed numbers
5.5Subtracting mixed numbers
5.6Word problems that add or subtract fractions
6

Multiplying fractions

5 lessons

A fraction times a fraction, a fraction of a fraction of an amount, and multiplying as scaling.

Review first: A fraction times a whole number A fraction of a whole number
6.1A fraction as division
6.2A fraction times a fraction
6.3A fraction of a fraction of an amount
6.4Multiplying as scaling
6.5Multiplying mixed numbers
7

Dividing with unit fractions

2 lessons

Dividing a unit fraction by a whole number as sharing, and a whole number by a unit fraction as how many fit.

Review first: A fraction as division Multiplication and division undo each other
7.1Dividing fractions: sharing into equal parts
7.2Dividing fractions: how many fit
8

Volume

4 lessons

Volume as filling with unit cubes, then as length times width times height, adding volumes of joined boxes.

Review first: Area of rectangles and squares Liquid volume: liters and milliliters
8.1Volume as filling
8.2Volume with unit cubes
8.3Volume of a box
8.4Volume of a solid made of boxes
9

Expressions and the order of operations

3 lessons

Writing and reading numerical expressions, and evaluating them with parentheses and the order of operations.

9.1Numerical expressions
9.2Grouping symbols
9.3Writing and reading numerical expressions from words
10

The coordinate plane and number patterns

3 lessons

Plotting ordered pairs in the first quadrant and reading graphs of real situations.

10.1Ordered pairs and the first quadrant
10.2Two number patterns side by side and graphing their pairs
10.3Line graphs
11

Measurement conversions and line plots with fractions

4 lessons

Multi-step conversions within one system, and line plots of fractional data used to share amounts out evenly.

Review first: Customary conversions Converting metric units by powers of ten Twenty four hour time and crossing midnight
11.1Multi-step problems with unit conversions
11.2Line plots with fractions
11.3Time zones
11.4Mean as fair share: computing the mean
12

The hierarchy of two-dimensional shapes

2 lessons

Classifying triangles and quadrilaterals into categories and subcategories by their properties.

Review first: Classifying triangles Naming and classifying polygons Perpendicular lines
12.1Parallelograms, rectangles, rhombuses and squares: what each one guarantees
12.2Classifying shapes in a hierarchy