Grade 3 

Mathematics Curriculum

 Decomposition:  How do breaking numbers and whole units into parts help build number sense and fluency? 

Large Numbers and their Parts - How does the strategic use of numbers facilitate computation?

Students will begin with graphing, using their knowledge of whole numbers to interpret and analyze bar graphs and line plots.  Students will then review the place value they learned in second grade and expand upon it by learning about rounding and its uses.  Addition and subtraction will be reviewed next, with instruction coming not just from Math In Focus (and traditional algorithms) but with Number Talks as well, so that students become flexible with their procedural computation.  Students were introduced to the bar model as a visual (pictorial) problem solving strategy in second grade and its use will be continued and encouraged with higher difficulty problems in third grade.  Lastly students will apply their knowledge of addition and subtraction to solving problems involving money.  Students will understand that strategic use of numbers facilitates computation.

Common Core State Standards:  3.NBT.1     3.NBT.2     3.NBT.3

 Multiplication - What is multiplication?

Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.

Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. 

Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole. (CCSS Grade 3 Introduction)  Students will understand that repeatedly addition groups of equal size can be an efficient way to calculate.

Common Core State Standards:  3.OA.1     3.OA.2     3.OA.3     3.OA.4     3.OA.5    3.OA.5     3.OA.6     3.OA.7   3.OA.8     3.OA.9     3.MD.5     3.MD.6     3.MD.7     3.MD.8

Fractions as Numbers - What are fractions?

Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.  Students will understand that fractions represent values and are numbers.

Common Core State Standards:  3.NF.1     3.NF.2    3.NF.3   3.MD.1     3.MD.2    3.MD.3     3.MD.4