Intro to Order of Operations
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Practice Order of Operations
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Order of Operations
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Words to Numbers
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Patterns from Ordered Pairs
Generate two numerical patterns using two given rules. Identify 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.
Understand Patterns
Generate two numerical patterns using two given rules. Identify 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.
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. Use whole-number exponents to denote powers of 10.
Read/Write Decimals: Thousandths
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
Compare Decimals to Thousandths
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Round Decimals to Any Place
Use place value understanding to round decimals to any place.
Multiply Multi-Digit Numbers
Fluently multiply multi-digit whole numbers using the standard algorithm.
Find Whole-Number Quotients
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Operations with Decimals
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Add and Subtract Fractions
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Word Problems: Basic Fractions
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
Word Problems: Divide Fractions
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Multiplying Fractions
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
Word Problems: Mixed Numbers
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Dividing Fractions and Numbers
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
Dividing Fractions and Numbers
Interpret division of a whole number by a unit fraction, and compute such quotients.
Converting Measurements
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Concepts of Volume
A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
Concepts of Volume
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
Counting Units to Find Volume
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Volume of Rectangular Prisms
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
Volume of Rectangular Prisms
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
Define the Coordinate System
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
Graph Points on 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.
Classifying Triangles & Quadrilaterals
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Classifying Triangles & Quadrilaterals
Classify two-dimensional figures in a hierarchy based on properties.
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