Grade 5

 Mathematics Curriculum

Part/Whole:  Why are there multiple ways to represent parts of a whole? 

The Base 10 Number System - How do mathematicians use the base 10 number system to facilitate computation?                                                 

Students’ understandings of the patterns in the Base Ten System are extended from Grade 4’s work with place value to include decimals to the thousandths place.  In Grade 5 students deepen their knowledge through a more generalized understanding of the relationship between and among adjacent places on the place value chart.  For example students will understand that in a multi-digit number, a digit in one place represents10 times as much as the digit in the place to its right and 1/10th of the digit in the place to its left.    Students learn to multiply and divide using patterns and conventional algorithms, simplify numeric expressions using the order of operations and solve real-world problems involving multiplication and division.  Students will make reasonable estimates of decimal sums, differences, products, and quotients.  Students apply these new understandings as they reason about and perform whole number and decimal operations, including multi-step problems and problems involving measurement.   Students will understand that The Base 10 Number System enables students to recognize patterns and relationships between whole numbers and decimals and flexibly perform operations.

Common Core State Standards:  5.OA.1,  5.OA.3,   5.NBT.1,   5.NBT.2,   5.NBT.3.a,   5.NBT.3.b,  5.NBT.4,  5.NBT.5,  5.NBT.6,  5.NBT.7,   5.MD.1

Fractions - How do multiple representations facilitate fluency with fractions and decimals?   

Students will develop and solidify their previous understanding of adding and subtracting fractions with unlike denominators in order to build an understanding of adding and subtracting mixed numbers. Students will learn about the relationship between fractions, mixed numbers, and will express division expressions as fractions and mixed numbers.  Students will apply this understanding to solve real world problems. Students will use visual models to develop an understanding of abstract concepts of multiplication and division of fractions. Students will learn how to multiply and divide whole numbers, proper fractions, improper fractions, and mixed numbers in any combination. Students will apply this understanding to solve area problems with fractional sides. Students will understand that decimals are another way of writing fractional parts of a whole. Students will apply this understanding to convert fractions to decimals and decimals to fractions. And understand that multiple representations of the same value facilitates the understanding of relationships, patterns, and computation of fractions and decimals.

Common Core State Standards:  5.NBT.3.a,  5.NBT.3.b,  5.NF.1,  5.NF.2,  5.NF.3,   5.NF.4.a,  5.NF.4.b,  5.NF.5.a,  5.NF.5.b,  5.NF.6,  5.NF.7.a, 5.NF.7.b,  5.NF.7.c,  5.MD.1,   5.MD.2

Geometry and Measurement - How do we use representations to make sense of our world?               

Students will learn to read and plot individual points and sets of points that create 2-D shapes on a coordinate grid. Points or vertices of 2-D shapes are attributes used to classify shapes. Students will then use their understanding of angles and other attributes to classify 2-D shapes into a hierarchy. Students will develop an understanding of volume by using the concrete to visual to abstract approach in order to solve real-world problems, including composing and decomposing complex 3-D shapes. Students will apply their understanding of volume to develop a formula.  Students will build the understanding that Geometry and Measurement are pictorial and physical representations of mathematical relationships. 

Common Core State Standards:  5.G.1,   5.G.2,  5.G.3,  5.G.4,   5.MD.4,  5.MD.5.a,  5.MD.5.b,  5.MD.5.c