2015­2016 NCPS Mathematics Unit Map – Grade 5 Parent Guide These ​
mathematical practices​
are developed in each unit throughout the year: ● Make sense of problems and persevere in solving them. ● Reason abstractly and quantitatively. ● Construct viable arguments and critique the reasoning of others. ● Model with mathematics. ● Use appropriate tools strategically. ● Attend to precision. ● Look for and make use of structure. ● Look for and express regularity in repeated reasoning. Mathematical Unit Student Learning Expectations Unit 1 is intended to build upon place value understandings and the use of the base ten system. Students will use previous understandings and strategies when computing to apply the standard algorithm when multiplying. Furthermore, students will work on building efficient strategies when dividing. The relationship between multiplication and division will continue to be examined. Powers of ten will be explored in this unit and put into context of expanded form and exponents. By the end of this unit students will gain an understandings of how to apply orders of operations appropriately when writing, expressing and interpreting. Unit 1 Numbers and Operations in Students will : Base 10 ­ Whole Numbers ● understand how to multiply multiple digit numbers using the standard algorithm. ● divide using an efficient strategy. ● understand the relationship between multiplication and division. ● understand the relationship between powers of ten and exponents. ● apply the order of operations to solve problems with more than one operation. ● use efficient multiplication and division strategies to solve real world problems. ● understand the relationship between number place value and expanded form with powers and ten and exponents. ● write simple expressions that record calculations with numbers, and interpret them. 1 Unit 2 Volume Unit 3 Numbers and Operations ­ Fractions Unit 2 is intended to build conceptual understanding of volume. Students will be given opportunities to understand the meaning of volume, use the formula to solve, label and interpret the volume of irregular rectangular prisms. Students will use this learning to solve real world problems. Students will: ● understand that volume is measured in cubic units. ● understand that volume is a measure of the capacity or space inside a solid figure. ● use appropriately the formula length times width times height to find the volume of a rectangular prism and label correctly ● apply the formula for volume to solve real world problems. ● find the volume of an irregular rectangular prism. In unit 3, students will extend their previous understandings of fractions. They will demonstrate learning through the use of number lines, visual representations, symbolic representations and clear rationales for their choices. Students will use this knowledge to solve real world problems with all four operations. This work will also extend to the use of whole numbers, fractions and mixed numbers. Students will: ● understand how to use equivalent fractions to solve problems ● use number lines to demonstrate the placement of fractions ● add and subtract fractions and mixed numbers with unlike denominators. ● apply their understanding of adding and subtracting fractions to solve real world problems. ● demonstrate all four operations using visual models when working with fractions. ● multiply and divide fractions, whole numbers, and mixed numbers using an efficient strategy. ● apply their understanding of multiplying and dividing fractions to solve real world problems. ● understand that multiplying a number by a fraction greater than one results in a larger product and multiplying by a fraction less than one results in a smaller product. 2 Unit 4 Geometry Unit 5 Numbers and Operations in Base 10 ­ Decimals In unit 4, students will extend their understanding of geometry by making connections, inferences and applying properties of geometric figures to draw conclusions. Students will be able to understand the relationship between squares and rectangles and how attributes of shapes can be classified. They will use these understandings to plot and identify points on a coordinate plane on the first quadrant. Students will: ● describe the relationship between square and rectangles ● understand that attributes of two dimensional shapes can belong to more than one category of shapes. ● understand the meaning of a coordinate plane ● plot points on a coordinate plane in the first quadrant. ● understand how to use plotted points on a coordinate plane to represent real world problems. ● identify parallel and perpendicular lines on a coordinate plane. In Unit 5, students will continue to study place value. Students will extend their understanding of decimals to read, write and compare decimals to the thousandths place. In addition to this, students will express numbers with decimals in expanded form using fractions. They will analyze the properties of rounding and understand how to compute using decimals in all four operations. Students will apply this knowledge to solve measurement problems containing decimals and use to solve real world applications. Students will: ● understand that a digit increases by ten each time and moves to the right and decreases by 1/10 when moved to the left. ● read, write, and compare decimals to the thousandths place. ● write a decimal in expanded form using fractions. ● compare two decimals based on place value using the <,>,= symbols and justify ● understand how place value applies to rounding decimals. ● add, subtract, multiply, and divide decimals to the hundredths using models or drawings. ● add, subtract, multiply, and divide decimals using computational strategies. 3 Unit 6 Algebraic Thinking & Interpreting and Representing Data ● understand the relationship between multiplication and division of decimals. ● apply their knowledge of decimals to convert among different sized measurement units to solve real world problems. In unit 6, students begin to extend their understanding of operations and algebraic thinking by understanding what a variable is, how it is used in an expression and understand that an unknown can be represented by a variable. Students will also understand and apply orders of operations with a variable. This learning will be the foundation for understanding more complex expressions and equations, which will be studied in sixth grade. Real world problem solving will be present throughout the unit Students will: ● use parenthesis in numerical expressions to evaluate patterns ● understand what a variable is and what it represents. ● write rules using a variable to describe growth patterns. ● understand that an unknown can be represented by a variable to solve a problem for any given number. ● make a line plot using fractions to display data sets in order to interpret the data and solve problems. 4