Our 5th grade math content will be taught in the following order. Though we do not have a textbook for math, we will have many resources in our binders that will help us visually with the strategies and concepts we will learn and use. Parents/guardians, I encourage you to use the resources in your student's binder as a first resource for providing assistance when needed. See also the Strategy and Concept Videos section of my webpage for a helpful video library.
These first standards will be spiraled throughout the year, often in the context of problem solving and homework, rather than taught and assessed within in a single unit.
-Fluently multiply multi-digit whole numbers using a standard algorithm.
-Apply and extend understanding of division to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
-Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems.
-Understand and describe a coordinate system as perpendicular number lines, called axes, that intersect at the origin (0 , 0). Identify a given point in the first quadrant of the coordinate plane using an ordered pair of numbers, called coordinates. Understand that the first number (x) indicates the distance traveled on the horizontal axis, and the second number (y) indicates the distance traveled on the vertical axis.
-Generate two numerical patterns using two given rules (e.g., generate terms in the resulting sequences). Identify and explain the apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
-Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
-Understand primes have only two factors and decompose numbers into prime factors.
Unit 1: Write and interpret numerical expressions
-Use parenthese and brackets in numerical expression, and evaluate expressions with these symbols (Order of Operations).
-Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g., express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product).
Unit 2: Decimal place value and operations
-Apply concepts of place value, multiplication, and division to understand that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
-Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
-Read, write, and compare decimals to thousandths.
-Use place value understanding to round decimals to any place.
-Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations. Relate the strategy to a written form.
Unit 3: Add and subtract fractions
-Add and subtract fractions with unlike denominators (including mixed numbers).
-Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Unit 4: Multiply and divide fractions
-Interpret a fraction as the number that results from dividing the whole number numerator by the whole number denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
-Apply and extend previous understandings of multiplication to multiply a fraction by a whole number and a fraction by a fraction.
-Interpret multiplication as scaling (resizing).
-Solve problems in real-world contexts involving multiplication of fractions, including mixed numbers, by using a variety of representations including equations and models.
-Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
-Make a line plot to display a data set of measurements in fractions of a unit (1/8, 1/2, 3/4). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Unit 5: Measure volume
-Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
-Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
-Relate volume to the operations of multiplication and addition and solve mathematical problems and problems in real-world contexts involving volume.
Unit 6: Classify two-dimensional figures
-Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
-Classify two-dimensional figures in a hierarchy based on properties.
TERC's Investigations is a research-based resource that I often use for planning our 5th grade math lessons and units. Additional information can be found at https://investigations.terc.edu/the-curriculum/?et_open_tab=et_pb_tab_6#my-tabs|6