## The big ideas in Grade 5 include •  place value and operations with multi-digit whole numbers and decimals to hundredths; •  multiplication and division with fractions; •  understanding volume and how it relates to multiplication.

Students begin the year by studying volume, which is used to support and deepen their understanding of multiplication and place-value structure. There are three other units that could come first as they have no pre-requisite units: 5.4 Multiplication by Fractions, 5.6 Addition and Subtraction of Fractions, and 5.7 Classifying Two-Dimensional Figures.

Next, students revisit and deepen their understanding of place-value structure, culminating in understanding the general principle that the value of any digit is 10 times the value of the same digit on place to the right and 1/10 the value of the same digit one place to the left. Students use this understanding to read, write, round, and compare decimals. This work supports students’ developing fluency with the standard algorithm for multiplying multi-digit whole numbers.

Students then turn to work with fractions, revisiting their work in fourth grade with multiplying fractions by whole numbers and extending it to multiplying fractions by fractions. They see the relationship between division and fractions and divide unit fractions by whole numbers and vice versa. Students apply their understanding of fractions in order to solve real-world problems involving multiplication and division of fractions and mixed numbers. Following up on their work with multiplying and dividing fractions, students add and subtract them. Traditionally, many curricula begin fraction arithmetic by adding and subtracting fractions. This blueprint suggests beginning with multiplication and division because fractions are the solution to the problem that the quotient of two whole numbers is not always a whole number. Fractions feel at home with multiplication and division; they submit to addition and subtraction more reluctantly.

Finally, students finish the work they started in earlier grades on classifying two-dimensional figures based on their attributes and learn how to graph points in the first quadrant in the coordinate plane and use that knowledge to solve real-world and mathematical problems.

Note that this course blueprint is only one of many possible ways of arranging a sequence of topics designed to achieve the standards. It is a continually evolving document and we welcome your comments here.

## Units

5.1 Volume

#### Summary

In this unit students

•  measure volume by counting cubes;
•  understand and explain the relationship between multiplication and volume of right rectangular prisms.

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5.2 Ten Times and One-tenth of

#### Summary

In this unit students

•  understand the relationship between the value of adjacent digits in a number;
•  relate volume to multiplication and addition
•  read, write, compare, and round decimals to thousandths.

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5.3 Multi-Digit Operations

#### Summary

In this unit students

•  cement understanding of the standard algorithm for multiplication of multi-digit whole numbers;
•  solve division problems with whole number quotients;
•  add, subtract, multiply, and divide decimals to hundredths;
•  write and interpret numerical expressions.

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5.4 Multiplication by Fractions

#### Summary

In this unit students

•  multiply whole numbers and fractions by fractions;
•  interpret multiplication as scaling (resizing);
•  solve real world problems involving fraction multiplication.

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5.5 Fractions and Division

#### Summary

In this unit students

•  understand that when you divide two whole numbers $a$ and $b$, the quotient is $\frac{a}{b}$;
•  divide unit fractions by whole numbers and whole numbers by unit fractions;
•  solve real world problems involving fractions.

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5.6 Addition and Subtraction of Fractions

#### Summary

In this unit students

•  find equivalent fractions as a strategy to add and subtract fractions with unlike denominators;
•  solve fraction word problems.

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5.7 Classifying Two-Dimensional Figures

#### Summary

In this unit students

•  understand attributes of and classify two-dimensional figures;
•  graph points on the coordinate plane to solve real-world problems.

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