Curriculum for Grade 3

Students build upon their knowledge of addition to identify factors (how many groups, how many objects in each group) and to compose and solve simple multiplication equations. They work with groups of 2-5 identical objects, beginning with models of identical concrete objects, such as bunches of bananas and fingers on a hand. As students progress, they work with more abstract objects (identical beads) and objects in an array.

Students work with models of real-world objects to solve equal sharing problems. They are introduced to the division symbol. They use the "dealing" method to create groups of a given size. Based on these models, they answer the questions, "How many groups?" and "How many in each group?" They compose and solve division equations.

Students deepen and expand their understanding of multiplication by 2 and 3 with new ways of visualizing the concept. The topic focuses on skip counting and arrays which helps students begin to see patterns as they multiply and solve equations. Students also discover and explore the commutative and distributive properties of multiplication.

Students use concrete and abstract objects to understand the concept of division. They then relate division to multiplication to help build understanding and fact fluency. Students begin by solving simple division equations (quotients to 5) and then advance to solving equations with quotients to 10.

Building upon previous learning about multiplication and division, students apply their understanding to facts using 4 as a product or divisor. They work with familiar manipulatives and progression of skills to build understanding and fluency.

Building upon previous learning about multiplication and division, students apply their understanding to facts using 5 as a product or divisor and 10 as a product. They also develop understanding of the distributive property of multiplication and division. Students build connections between equations, arrays, tape diagrams, and word problems.

Students review telling time on an analog clock and learn to write time as hours and minutes. They also learn how to use addition and subtraction skills to calculate start and end times and time intervals and apply this to word problems.

Students use a scale and a pan balance with weights to determine the mass of objects. They learn to read a scale between labeled increments and to add and subtract mass measurements to solve problems. To learn how to measure capacity, students pour liquid into labeled containers. They learn the relationship between kilograms and grams and between liters and milliliters.

Using a number line to provide context, they learn the rule for rounding up or down to the nearest ten and hundred. Finally, students round 2-, and 3-digit numbers to any given place value.

Students review the standard algorithm for addition with regrouping and then use it to solve word problems involving measurements. As they progress, they receive fewer prompts to complete the standard algorithm.

Students review the standard algorithm for subtraction with regrouping and then use it to solve word problems involving measurements. As they progress, they receive fewer prompts to complete the standard algorithm.

Students enrich their understanding of multiplication and division by introducing the multiplication chart and the commutative property (or 'turnaround facts') of multiplication. They continue to build fact fluency, adding factors 6-9 to their repertoire.

Students begin with familiar tasks taken to a more challenging level with higher factors. They deepen their understanding of the relationship between multiplication and division as well as their fact fluency.

In addition to extending students' mastery of multiplication and division to include 8, they are also introduced to multi-step equations that use parentheses. Using illustrations and step-by-step instruction, students learn that parentheses and order of operations do not affect multiplication-only equations. They also continue to build their mastery of the break apart and distribute strategy.

Students apply and extend previous understanding to include 9 as a factor or divisor. We also introduce a strategy specifically for multiplying by 9.

Students dig deeper into concepts of multiplication and division as they work with 1 and 0. In addition to working with these numbers as factors, dividends, and divisors, students use a letter to represent an unknown number in an equation and are introduced to let statements regarding such letters.

Building upon students' fact fluency with single-digit factors, we introduce multiplying a single-digit factor by a multiple of ten. Students relate word-based multiplication (e.g., 4 x 3 tens = 12 tens) to numeric equations (e.g., 4 x 30 = 120).

Students are introduced to the very basics of area using tiling. They learn to use square units, measure sides of a rectangle, skip count rows of tiles, and rearrange tiles to form a different rectangle with the same area.

Building upon the previous module, students start by skip counting tiles in a rectangle to determine its area. They then progress to multiplication using a tiled rectangle and one with only labeled measurements. Students rearrange tiles to determine the measurements of a different rectangle that has the same area. They also solve for an unknown side represented by a letter.

Students dig deeper into their understanding of multiplication and area by using area models of rectangles. They compare parts to the whole, find missing parts, and manipulate equations to demonstrate properties. Exercises begin by using rectangles with gridlines and then advance to using those without.

Students learn two different approaches to finding the area of a composite shape based on side lengths. In the first, they break the shape into smaller rectangles and add those areas together. In the second, they "complete" the shape to find the total area and then subtract the area of the "missing piece". Students begin by using shapes with unit squares shown and then progress to those without.

Students establish a foundation for understanding fractions by working with equal parts of a whole. They use halves, thirds, fourths, fifths, sixths, sevenths, and eighths of shapes including circles, rectangles, line segments, and other shapes. Students partition shapes, label sections, shade fractions, and even solve word problems involving equal sharing. Throughout the topic, they do not use fraction notation (e.g., 2 thirds).

Students build upon their knowledge from Topic 5A to transition from word form to standard form in identifying fractions. They begin with unit fractions and advance to more complex fractions, including complements of a whole and improper fractions. Throughout the topic, students are presented with a variety of shapes, sizes, and colors of figures. While they do not use the term "improper fractions," they learn the underlying concept of fractional parts that form more than one whole.

Based on visual models, students learn that the more parts in a whole, the smaller each unit fraction. They then compare unit fractions using both words and symbols, and they relate the unit fraction to the whole.

Students apply their understanding of fractions to numbers on a number line. They learn that there are numbers between the whole numbers on a number line and how to identify them. Using this tool, students are able to name equivalent whole number/fraction pairs, label fractions greater than 1, and compare fractions with unlike denominators.

Using familiar shaded models and the number line, students focus on concepts of equivalent fractions. They extend this understanding to include whole numbers and fractions greater than 1.

Based on visual models, students learn to compare two fractions with the same numerator or two fractions with the same denominator. To do so, they apply their understanding of creating and naming fractions, as well as using the <, =, and > symbols.

Students learn to create picture graphs and bar graphs, both scaled and unscaled. They learn to interpret data from these graphs and use them to solve word problems about the number of objects in categories.

Students learn that polygons are made of equal numbers of line segments and angles. They learn the names and attributes of common polygons and instances where the attributes intersect (i.e., squares and rhombuses).

Students find the perimeter of a polygon by adding the lengths of its sides. They solve for the length of an unknown side and find the perimeters of equal-sided polygons.