# Mathematics

## What Do Students Learn in 3rd Grade Math?

3rd Grade Math focuses on four key advancements from previous years: (1) developing understanding of and fluency with multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions; (3) developing understanding of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

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## Units

Unit 1

14 Lessons

Students estimate quantities using rounding and develop fluency with the standard algorithm of addition and subtraction. Students focus on the precision of their calculations, and use them to solve real-world problems.

Unit 2

21 Lessons

### Multiplication and Division, Part 1

Students begin to explore the concepts of multiplication and division, beginning in the context of equal group and array problems, moving to skip-counting and repeated addition, and ending with more complex and/or abstract problems.

Unit 3

23 Lessons

### Multiplication and Division, Part 2

Students deepen their understanding of multiplication and division, including their properties and extending their study of factors to include all units from 0 to 10, as well as multiples of 10 within 100.

Unit 4

14 Lessons

### Area

Students develop an understanding of areas as how much two-dimensional space a figure takes up, and relate it to their work with multiplication from Units 2 and 3.

Unit 5

16 Lessons

### Shapes and Their Perimeter

Students explore attributes of shapes in different categories, then learn to measure at least one of these attributes, their perimeter. They come to differentiate between perimeter and area as different measurements.

Unit 6

24 Lessons

### Fractions

Students understand fractions as numbers on the number line and explore fraction equivalence and comparison in simple cases, then apply this fractional understanding to measure fractional lengths and represent them on a number line plot.

Unit 7

12 Lessons

### Measurement

Students explore measurement using kilograms, grams, liters, milliliters, and intervals of time in minutes.

## How Do Students Build 3rd Grade Math Skills Across Units?

In Unit 1, Rounding, Addition, and Subtraction, students rely on their substantial work in 2nd grade on place value to develop an understanding of rounding. They then develop fluency with addition and subtraction within 1,000. Finally, they use both aforementioned skills to solve one-and two-step word problems involving addition and subtraction, using rounding to assess the reasonableness of their answers. While the content taught in this unit is not major work of 3rd grade as determined by the Common Core State Standards, it serves as a foundation for later work, such as assessing the reasonableness of all types of two-step word problems and multiplying one-digit numbers by multiples of ten, making it a useful introduction to 3rd grade math.

In Unit 2, Multiplication and Division Part I and Unit 3, Multiplication and Division Part II, students are introduced to the other two major operations, multiplication and division. They come to understand multiplication as finding the total number of objects in a certain number of equal-sized groups, and division as finding either the size of the group or the number of groups. Students work towards fluency of all multiplication and division facts within 100, relying on the properties and patterns to help in particular with the difficult facts of 6, 7, 8, 9. Students solve one-step multiplication and division word problems involving equal groups and arrays, and solve two-step word problems involving all four operations. They also explore myriad connections to multiplication and division, including exploring patterns, including patterns in the skip-counting sequence, and scaled picture and bar graphs.

In Unit 4, Area, students define area to be the number of square units needed to cover a two-dimensional space. They initially find the area of rectangles by counting unit squares or skip-counting by rows and columns. Then, seeing the connection between skip-counting and multiplication that was built in the prior two units, students apply their recently acquired skills with multiplication and division to calculate the area of a rectangle and solve real-world problems involving area. Finally, they find the area of composite rectilinear shapes, by decomposing them into rectangles, finding the area of those rectangles, and adding those areas together.

In Unit 5, Shapes and their Perimeter, students start by exploring two-dimensional shapes in different categories, seeing that shapes in those categories share attributes. They then explore the attribute of perimeter, and come to differentiate between perimeter and area as different measurements.

In Unit 6, Fractions, students build on their work partitioning circles and rectangles in 2nd grade to study fractions. They build more complex fractions from unit fractions, and start to understand fractions as numbers, rather than portions of shapes. To do so, students do extensive work with placing fractions on a number line, a helpful representation for comparing and finding equivalent fractions. Students also explore line plots with fractional measurements, a key advancement from 2nd grade work with line plots that connects to their work with fractions.

In Unit 7, Measurement, students study time as well as liquid volumes and masses. Students learn to read time to the nearest minute and use their work with number lines in Unit 1 (with rounding) and Unit 5 (with fractions) to solve problems involving elapsed time. They also rely on their work with number lines to read measurement scales, and use those measurements to solve one-step word problems in all four operations with liquid volumes and masses.

### What math skills do students learn in 3rd grade?

Students in third grade math focus on 4 key math skills: Fluently multiplying and dividing within 100, comparing and finding equivalent fractions, defining and computing areas, and analyzing two-dimensional shapes.

### What Common Core Math Standards do students focus on in 3rd grade?

The major work of the course focuses on the following Common Core State Standards:

• 3.OA.A Represent and solve problems involving multiplication and division.
• 3.OA.B Understand properties of multiplication and the relationship between multiplication and division.
• 3.OA.C Multiply and divide within 100.
• 3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic.
• 3.NF.A Develop understanding of fractions as numbers.
• 3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
• 3.MD.D Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

### What are the expectations for 3rd grade math fluency?

3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

3.NBT.2: Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Learn how to develop students' procedural skill and fluency within Fishtank Math curriculum with our Procedural Skill and Fluency Teacher Tool.

### What kind of word problems do students solve in 3rd grade math?

In third grade, students are introduced to multiplication and division situations involving equal groups and arrays, solving one-step word problems of these types. They will also solve two-step problems involving all four operations with whole numbers. Learn how to develop students' word problem solving skills in the Fishtank Math curriculum with our Word Problem Teacher Tool

Math Worksheets

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