Grade 5

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.