Mathematics

In Grade 5, students build on and extend the work they did in Grade 4 with multi-digit multiplication and division, making connections between different kinds of representations.

In Grade 4, students were introduced to decimals to the hundredths as numbers that we use to show money, and as fractions with denominators 10 and 100. In fifth grade, students work with decimals to the thousandths place. What is true of computation with whole numbers is also true for computation with decimals, so students practice many of the same skills and concepts they have worked with in earlier grades, such as rounding and comparing.

Fifth graders continue to work with the structure of our base ten number system, noting that the value represented by each place is always 10 times the value represented by the place to its immediate right, and 1/10th the value represented by the place to its immediate left. Very large and very small numbers are harder to imagine and are less frequent in our everyday world.

The rules for adding and subtracting whole numbers, decimals, and fractions are all the same. In this unit, fifth graders practice many strategies to add and subtract decimals and fractions.

In this unit, fifth graders continue to work with the structure of our base-10 number system. The value represented by each place is always 10 times the value represented by the place to its immediate right, which is true for both whole numbers and decimals. We often refer to the size of a number by its magnitude​, which is helpful for comparing and ordering. A number in the hundreds place, for example, is ten times the magnitude​ of a number in the tens place.

In this unit, fifth graders continue to work with the structure of our base-10 number system. In Unit 4, fifth graders multiplied and divided whole numbers by decimals. In this unit, they extend that work to multiplying and dividing decimals by decimals.

The ideas that apply to multiplying whole numbers and decimals also apply to multiplying fractions. In this unit, fifth graders continue to work with multiplication, extending their understandings to fractions.

The ideas that apply to dividing whole numbers and decimals also apply to dividing fractions. In this unit, fifth graders continue to work with division, extending their understanding to fractions, and building on work done in Unit 5.6: Multiplying Fractions.

In this unit, students will work with volume, which is the major emphasis for geometric measurement in Grade 5. Students will also work on other aspects of measurement, including conversion, building on ideas from earlier grades and units, especially the work with measurement and area in Grade 4.

Patterns can be made of numbers or shapes. Since kindergarten, students have described these patterns using words, charts, and numbers. In this unit, Grade 5 students continue to describe these patterns and connect them to their work with expressions and equations.

In this unit students also learn about and start to use the coordinate plane, which helps us to specify locations in space. Number patterns can be graphed on the coordinate plane and analyzed. A final topic in this unit is graphing data on line plots.

Students have worked with 2-D and 3-D figures since pre-school and kindergarten. In Grade 2, they learned the formal definition of a polygon, which is a closed plane figure in which every edge is straight. In Grade 4, students classified and categorized polygons by their sides and angles. They formalized the distinctions between the different kinds of polygons.

In Grade 5, students categorize polygons based on their properties, focusing especially on the nested (hierarchical) groups of quadrilaterals (trapezoids, parallelograms, rectangles, rhombuses, squares).