1) Number Sense & Place Value
- Understanding place value to the millions and to the thousandths
- Reading, writing, and comparing whole numbers, decimals, and fractions
- Rounding and estimating with whole numbers and decimals
- Addition, subtraction, multiplication, and division of multi-digit numbers
- Order of operations (including parentheses, exponents, multiplication/division, addition/subtraction - PEMDAS)
- Prime and composite numbers; least common multiple (LCM) and greatest common factor (GCF)
- Divisibility rules (2, 3, 5, 9, 10)
- Representing fractions on number lines
- Equivalent fractions and simplest form
- Comparing and ordering fractions
- Addition and subtraction of like and unlike fractions and mixed numbers
- Multiplication of a fraction by a whole number
- Writing fractions as decimals and vice versa
- Comparing and ordering decimals (to at least thousandths)
- Addition and subtraction of decimals
- Multiplication of a decimal by a whole number
- Addition and subtraction of positive and negative integers
- Understanding the number line for integers and decimals
- Introduction to multiplication and division of positive and negative integers
- Ratio concepts and notation (a:b, “a to b”)
- Unit rates (e.g., miles per hour)
- Solving ratio and rate problems (including scaling up and down)
- Understanding and solving simple proportion equations
- Converting between fractions, decimals, and percents
- Finding a percent of a quantity (e.g., 25% of 80)
- Solving basic percent-increase and percent-decrease problems
- Understanding variables and algebraic expressions
- Writing expressions for real-world situations (e.g., “n × 5” for “five times a number n”)
- Evaluating expressions by substituting values for variables
- Using the distributive property
9) Equations & Inequalities
- Writing and solving one-step equations (addition/subtraction, multiplication/division)
- Writing and solving two-step equations
- Understanding and graphing simple inequalities on a number line
- Perimeter and area of rectangles, squares, triangles, parallelograms, and compound shapes
- Surface area and volume of right rectangular prisms
- Finding missing dimensions given area or volume
- Classifying triangles (by side: equilateral, isosceles, scalene; by angle: acute, right, obtuse)
- Classifying quadrilaterals (parallelogram, rectangle, square, trapezoid)
- Understanding angles: measure, sum of interior angles, supplementary and complementary
- Plotting and identifying points (x,y)(x,y) in all four quadrants
- Understanding horizontal and vertical distances
- Converting within measurement systems (e.g., mm↔cm↔m, in↔ft↔yd)
- Understanding and using customary units (inch, foot, yard, mile; ounce, pound; cup, pint, quart, gallon)
- Time (reading clocks, elapsed time calculations)
- Perimeter and area units vs. volume units
- Collecting data and organizing into tables
- Displaying data: bar graphs, line plots, histograms, and circle graphs (pie charts)
- Calculating measures of central tendency: mean, median, mode, and range
- Interpreting data sets and drawing conclusions
- Simple probability models (e.g., rolling a die, drawing colored counters)
- Expressing probability as a fraction, decimal, or percent
- Experimental vs. theoretical probability
- Understanding exponents as repeated multiplication
- Evaluating expressions with whole-number exponents
- Problem-solving strategies (draw a picture, make a table, guess and check)
- Reasoning and proof (explaining why an answer makes sense)
- Precision in calculation and terminology
- Looking for and making use of structure (patterns, relationships)
- Using tools (ruler, protractor, calculator) appropriately
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