Scope and Sequence
Units:
September - 1st week of November
- Place Value
- Writing decimals in word form, decimal form, and expanded form.
- Value of digits from the ten millions to the millionths place.
- equivalent decimals (12 tenths is equivalent to 1.2; or .220 is equivalent to .2200).
- Subtracting money in real life story problems
- .1 less than and .01 less than
- ordering decimals
- comparing decimals
- rounding decimals
November - December
- Decimals and fractions
- Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
- Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.
- Model addition and subtraction of fractions and decimals using a variety of representations.
- Add and subtract decimals and fractions using efficient and generalizable procedures, including standard algorithms.
- Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
- Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.
January
- Multiplication and Order of Operations
- Estimate solutions to multiplication problems in order to assess the reasonableness of results.
- Solve real-world and mathematical problems requiring addition, subtraction, and multiplication.
- Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Example 2 + 10 x 3 / 2 = . or
- Mean, Median, Mode
January - February
- Division
- Divide multi-digit numbers using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number or a decimal.
- Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately.
February - March
- Geometry
- Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.
- Recognize and draw a net for a three-dimensional figure.
- Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.
- Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms.
- Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements.
April - May
- Algebra and Data and Measurement
- Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
- Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities.
- Evaluate expressions and solve equations involving variables when values for the variables are given.
- Develop and use the formulas V = â„“wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.
- Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.
- Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.
- Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.