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Count objects from 1 to 10

Count by fives using number lines with answers ranging from 5 to 40.

Count by twos using pictographs of paired objects

Addition facts with sums up to 5

Addition facts with sums from 11 to 14

Subtraction facts subtracting from 5 or less

Subtraction facts subtracting from 11 to 14

Count pennies only

Practice adding a two-digit number and a one-digit number, and a two-digit number and a multiple of 10, using place value strategies.

Find the missing number in addition and subtraction equations.

Subtract multiples of 10 from two-digit numbers in the range 10–90, using place value understanding.

Subtract numbers within 10.

Add numbers within 10.

Solve addition and subtraction word problems within 20, including problems with three addends, using objects, drawings, and equations.

Compare and order numbers.

Count to 100 and identify missing numbers in sequences.

Read and interpret pictographs.

Skip count by 2s, 5s, and 10s.

Mentally find 10 more or 10 less than any two-digit number, explaining the reasoning using place value.

Understand place value by breaking numbers into tens and ones.

Learn to read clocks showing time to the half hour

Read time on analog clocks to the hour and half hour.

Count collections of pennies.

Identify coins and their values.

Measure and compare lengths.

Compare and order objects by length.

Partition circles and rectangles into two and four equal shares, and describe the shares using the words halves, fourths, and quarters.

Identify and describe 2D shapes by their attributes.

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Practice adding single-digit numbers fluently using strategies including counting on, making ten, and doubles.

Add three-digit numbers within 1,000 using place value understanding and regrouping strategies.

Add two-digit numbers within 100 using place value strategies and regrouping when needed.

Use number lines to add and subtract within 100 by identifying the starting point and counting forward or backward.

Solve mixed addition and subtraction problems within 1,000 to build fluency and flexible problem-solving skills.

Practice subtracting single-digit numbers fluently using strategies including counting back, counting up, and making ten.

Subtraction of 3-digit numbers within 1,000 with regrouping

Subtract two-digit numbers within 100 using place value strategies and regrouping when needed.

Add and subtract numbers within 100 and 1,000 using efficient place value strategies.

Use rectangular arrays to find the total number of objects and write repeated addition equations.

Explore multiplication as equal groups and repeated addition using arrays and single-digit factors.

Learn to identify even and odd numbers with visual support

Learn to skip count by 2s, 5s, and 10s with visual support

Mentally add and subtract 10 or 100 from three-digit numbers by identifying which place value digit changes.

Compare and order three-digit numbers using the symbols >, <, and = by examining hundreds, tens, and ones place values.

Identify digits in the hundreds, tens, and ones places

Learn place value concepts with ones and tens

Partition shapes into equal shares and identify halves, thirds, and fourths using fraction names and visual models.

Read analog clocks and determine AM or PM using real-world scenarios at 15-minute intervals

Read analog clocks to the hour and half hour

Review reading and setting analog clocks at 5 and 15-minute intervals

Set analog clock hands to show a given time to the nearest hour and half hour.

Set analog clock hands to show a given time to the nearest 5 minutes.

Learn to read analog clocks at 5-minute intervals

Learn to read analog clocks showing time to the hour

Count collections of coins and bills to find their total value and solve money word problems.

Count collections of coins (pennies, nickels, dimes, and quarters) to find their total value.

Solve addition and subtraction word problems involving lengths in inches and centimeters.

Identify measurement tools and measure and compare the lengths of objects using standard units.

Measure the length of objects using rulers in inches and centimeters.

Learn to identify basic 2D shapes with descriptions

Learn to identify shapes by sides, vertices, and angles

Read and interpret bar graphs and picture graphs to answer questions about data, comparisons, and totals.

Reading and interpreting line plots (dot plots) with whole-number data. Simple reading of dot counts from small data sets.

Practice adding and subtracting three-digit numbers within 1,000 using place value strategies.

Learn division as equal sharing using visual models

Learn multiplication using visual arrays

Practice multiplying single-digit numbers by multiples of 10 using place value strategies.

Practice identifying, extending, and explaining patterns in multiplication and division sequences.

Computational fluency for multiplication facts with 2, 5, and 10. Skip counting and repeated addition strategies.

Practice reading and interpreting place value charts showing hundreds, tens, and ones.

Practice rounding two- and three-digit numbers to the nearest 10 and 100.

Practice comparing fractions with the same numerator or same denominator using <, =, and >.

Understanding fraction equivalence using visual models. Side-by-side partitioned rectangles show equal amounts. Simple pairs like 1/2 = 2/4.

Learn to locate fractions on a number line from 0 to 1

Understanding and working with fractions using visual models and word problems, including halves, thirds, fourths, sixths, and eighths

Learn to read clocks showing time to 5 minutes using visual models

Calculating elapsed time between two clock readings. Whole hour intervals only. Both start and end clocks visible.

Practice measuring, estimating, and solving problems involving liquid volume in liters and mass in grams and kilograms.

Learn to find the perimeter of rectangles using visual models

Learn to find the area of rectangles using visual models

Learn to identify 2D shapes including triangles and polygons

Learn to classify quadrilaterals by their properties

Reading and interpreting bar charts and pictographs. Direct reading questions: how many, identify values from charts. Pictographs with scale of 1.

Adding and subtracting multi-digit numbers without regrouping. Introduction level.

Learn long division with single-digit divisors using visual models

Learn to multiply multi-digit numbers using visual models and the standard algorithm

Interpret multiplication equations as comparisons, and solve word problems involving multiplicative comparison using multiplication and division.

Understand the value of digits in multi-digit numbers, read and write numbers in multiple forms, and compare multi-digit numbers up to the millions.

Round multi-digit whole numbers to any place using place value understanding and the standard rounding algorithm.

Locating, comparing, and ordering decimal numbers on a number line

Understanding and working with decimal numbers in tenths and hundredths

Adding fractions with the same denominator using visual models. Introduction level.

Learn to compare and order fractions using visual models

Learn to identify and generate equivalent fractions

Multiply a fraction by a whole number and solve word problems involving fraction multiplication.

Convert between customary units of length, weight, and capacity, and solve word problems involving unit conversions within the same measurement system.

Measuring objects to the nearest whole and half inch using a ruler. Introduction level.

Apply formulas for area and perimeter of rectangles to solve real-world and mathematical problems involving unknown side lengths.

Learn to identify and draw lines of symmetry

Identifying points, lines, line segments, rays, and classifying angles

Reading angle measurements from a protractor. Classifying angles as acute, right, or obtuse. Introduction level with common angles.

Find all factor pairs for whole numbers up to 100 and recognize multiples of given numbers.

Determine whether a whole number in the range 1–100 is prime or composite by finding its factor pairs.

Generate and analyze number patterns that follow a given rule, identify features of patterns not explicit in the rule, and explain how a rule produces a pattern.

Standard long division algorithm with 2-digit divisors. Introduction level with 3-digit dividends, no remainders.

Explore how multiplying and dividing by powers of 10 shifts digits in the place value system, and use exponent notation to express powers of 10.

Estimate unit prices using rounding and mental math

Divide decimals by whole numbers using place value strategies

Apply decimal operations including addition, subtraction, multiplication, and division.

Practice rounding decimals to a specified place value, from whole numbers to hundredths, using place value understanding and number line reasoning.

Solve word problems involving decimal division

Add and subtract fractions with unlike denominators

Understand fractions as division and solve sharing problems by dividing whole numbers

Add and subtract mixed numbers with like denominators

Add and subtract mixed numbers with regrouping (same denominators)

Practice all four fraction operations: addition, subtraction, multiplication, and division.

Understand multiplication as scaling — compare the size of a product to its factors without computing, and explain why multiplying by a fraction greater than or less than 1 makes a number larger or smaller.

Multiply fractions by whole numbers. Answers are expressed as improper fractions — no simplification required.

Multiplying fractions by other fractions. No simplification required.

Multiplying with mixed fractions using area models. Simplification required.

Multiplying with mixed fractions by converting to improper fractions. Simplification required.

Multiply fractions by whole numbers and simplify the product. Express answers as mixed numbers or whole numbers in simplest form.

Divide unit fractions by whole numbers using models and reasoning

Divide whole numbers by unit fractions using models and reasoning

Solve multi-step word problems by converting between units using fractions, multiplication, and division

Find the area of rectangles using visual models and the length × width formula, including missing dimension problems and real-world applications.

Find area and perimeter of rectangles using formulas

Practice reading and locating points on a Quadrant 1 grid — identify labeled points, read coordinates, and interpret real-world data sets plotted on a coordinate plane.

Learn to plot and identify points on a coordinate plane

Learn the basics of the coordinate plane — the origin, x and y axes, and how to read and write ordered pairs in Quadrant 1.

Practice plotting and identifying points in Quadrant 1 — given an ordered pair, identify the correct grid location; given a plotted point, write its ordered pair; and interpret plotted data sets.

Apply coordinate plane skills to real-world situations including reading maps, interpreting data sets, and solving problems using ordered pairs in Quadrant 1.

Learn how quadrilaterals are classified in shape hierarchies

Learn to find the volume of rectangular prisms using visual models

Learn to calculate volume using the formula V = l x w x h

Reading and interpreting dot plots (line plots) where the x-axis uses fractional values. Introduction level with simple counting.

Learn PEMDAS with simple expressions

Learn to generate number patterns and graph ordered pairs

Divide fractions by whole numbers and fractions by fractions using the keep-change-flip method, and apply fraction division to real-world problems.

Add, subtract, multiply, and divide multi-digit decimals using standard algorithms, and solve multi-step real-world problems involving decimals.

Plot and identify points in all four quadrants of the coordinate plane

Calculate area of triangles, parallelograms, and trapezoids using formulas

Calculate area of triangles and polygons by decomposing into familiar shapes

Find the surface area of rectangular and triangular prisms by identifying faces, using nets, and calculating the total area of all faces.

Find the volume of rectangular prisms with fractional edge lengths by applying the formula V = l × w × h.

Identify independent and dependent variables in equations and real-world situations, and use tables and graphs to show how they relate.

Evaluate algebraic expressions by substituting values for variables

Evaluate and compare expressions using exponent notation

Solve one-step equations using inverse operations

Simplify algebraic expressions by combining like terms and applying the distributive property

Translate words and real-world situations into algebraic expressions

Find the greatest common factor (GCF) and least common multiple (LCM) of pairs of whole numbers, and apply them in real-world contexts.

Write, solve, and graph inequalities on a number line

Understand, compare, and order integers and negative numbers on the number line

Plot and compare negative numbers and rational numbers on the number line

Use ratio reasoning to convert between metric and customary measurement systems and transform compound units

Understand and calculate percentages in real-world contexts

Write and interpret ratios, and find equivalent ratios

Find and compare unit rates to solve real-world problems

Read, interpret, and analyze data displayed in histograms

Calculate and interpret mean, median, and mode as measures of center

Add and subtract rational numbers, including negative integers, fractions, and decimals. Use properties of operations and number lines to solve real-world and mathematical problems involving signed numbers.

Apply and extend understanding of multiplication and division to all rational numbers, including negative integers, fractions, and decimals. Understand sign rules for products and quotients, and solve real-world problems using all four operations with rational numbers.

Use facts about supplementary angles (sum to 180°), complementary angles (sum to 90°), vertical angles (equal measure), and adjacent angles to find unknown angle measures. Write and solve equations when angles are expressed algebraically.

Apply the formulas for the area and circumference of a circle. Use C = 2πr = πd and A = πr² to find measurements, and work backwards from circumference or area to find radius or diameter. Use π ≈ 3.14 for all calculations unless the problem asks for an exact answer in terms of π.

Solve problems using scale drawings. Convert between drawing measurements and actual measurements using the scale ratio, compute actual areas and perimeters, and reproduce scale drawings at a different scale.

Simplify, expand, and factor linear expressions with rational coefficients. Apply the distributive property, combine like terms, and rewrite expressions in equivalent forms to reveal structure and solve problems.

Solve two-step linear equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Apply inverse operations in sequence to isolate the variable, and use equations to model and solve real-world word problems.

Solve two-step inequalities of the form px + q > r and p(x + q) < r, where p, q, and r are rational numbers. Apply inverse operations to isolate the variable, flip the inequality sign when multiplying or dividing by a negative number, and interpret solution sets in real-world contexts.

Solve real-world percent problems: find a percent of a quantity, find the whole from a part and percent, calculate percent increase and decrease, apply percents to tax, tip, discount, markup, simple interest, and percent error.

Identify and represent proportional relationships between quantities. Find the constant of proportionality in tables, graphs, and equations. Write equations of the form y = kx and interpret key points on proportional graphs. Aligned to CCSS 7.RP.A.2.

Compare two populations using measures of center (mean, median) and variability (range, mean absolute deviation, interquartile range). Use random sampling to draw inferences about populations and determine which population has greater spread or a higher center.

Find probabilities of compound events. Use organized lists, tables, and tree diagrams to identify sample spaces. Calculate P(A and B) by multiplying branch probabilities for independent events.

Understand and apply probability. Find the theoretical probability of simple events as a fraction, decimal, or percent. Compare theoretical and experimental probability, and use probability models to make predictions.

Identify rational and irrational numbers, convert repeating decimals to fractions, and approximate irrational numbers on a number line. Aligned to CCSS 8.NS.A.1 and 8.NS.A.2.

Apply the Pythagorean Theorem to find missing sides in right triangles, solve real-world and 3D problems, and find distance between points in the coordinate plane. Recognize Pythagorean triples and the converse. Aligned to CCSS 8.G.B.6, 8.G.B.7, 8.G.B.8.

Apply triangle angle-sum and exterior angle theorems, parallel-line/transversal angle relationships, and the AA similarity criterion. Identify similar figures and find missing side lengths or angle measures. Aligned to CCSS 8.G.A.4 and 8.G.A.5.

Apply translations, reflections, rotations, and dilations to figures using coordinates. Recognize congruence as a sequence of rigid motions. Describe the effect of each transformation type. Aligned to CCSS 8.G.A.1, 8.G.A.2, 8.G.A.3.

Apply volume formulas for cylinders, cones, and spheres to solve real-world and mathematical problems. Compare volumes and find missing dimensions. Aligned to CCSS 8.G.C.9.

Calculate slope from two points, recognize unit rate as slope, derive y=mx and y=mx+b, and compare proportional relationships across tables, graphs, and equations. Aligned to CCSS 8.EE.B.5 and 8.EE.B.6.

Solve multi-step linear equations in one variable, including those with the distributive property and like terms. Identify equations with one solution, infinitely many solutions, or no solutions. Aligned to CCSS 8.EE.C.7.

Solve systems of two linear equations using graphing, substitution, and elimination. Recognize systems with one solution, no solution, or infinitely many solutions. Apply to real-world problems. Aligned to CCSS 8.EE.C.8.

Apply properties of integer exponents — product, quotient, power, zero, and negative exponents — to generate equivalent expressions. Aligned to CCSS 8.EE.A.1.

Express very large and very small numbers in scientific notation, compare orders of magnitude, and perform multiplication, division, addition, and subtraction with numbers in scientific notation. Aligned to CCSS 8.EE.A.3 and 8.EE.A.4.

Evaluate square roots of perfect squares and cube roots of perfect cubes. Solve equations of the form x²=p and x³=p, and recognize when roots are irrational. Aligned to CCSS 8.EE.A.2.

Recognize when a relation is a function (each input → exactly one output). Compare functions across multiple representations (table, graph, equation, verbal). Identify linear vs nonlinear. Aligned to CCSS 8.F.A.1, 8.F.A.2, 8.F.A.3.

Construct linear functions from real-world situations, tables, graphs, or two points. Interpret slope and y-intercept in context. Describe qualitative features of graphs. Aligned to CCSS 8.F.B.4 and 8.F.B.5.

Construct and interpret scatter plots, describe association patterns, fit a line of best fit, and use linear-model equations to interpret slope and intercept in real-world contexts. Aligned to CCSS 8.SP.A.1, 8.SP.A.2, 8.SP.A.3.

Construct and interpret two-way frequency tables for categorical bivariate data. Compute joint, marginal, and relative frequencies, and use them to describe association between variables. Aligned to CCSS 8.SP.A.4.