Course Content
A. Numbers and Counting
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A.01. Recognize and identify place values in whole numbers
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A.02. Read and write word names for numbers up to millions
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A.03. Interpret and convert Roman numerals to Arabic numerals and vice versa
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A.04. Understand the concept of prime and composite numbers
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A.05. Identify factors of a given number
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A.06. Determine the prime factorization of a number
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A.07. Express prime factorization using exponents
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A.08. Apply divisibility rules to determine if a number is divisible by another
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A.09. Solve real-world problems involving whole numbers and basic operations
B. Addition and Subtraction
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B.01. Add and subtract whole numbers accurately
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B.02. Solve word problems involving addition and subtraction of whole numbers
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B.03. Apply estimation strategies to check the reasonableness of answers in addition and subtraction problems
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B.04. Add and subtract decimal numbers accurately
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B.05. Solve word problems involving addition and subtraction of decimals
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B.06. Estimate sums and differences of decimals to approximate solutions
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B.07. Add and subtract money amounts in practical contexts
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B.08. Solve word problems involving addition and subtraction of money
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B.09. Add and subtract fractions with like denominators
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B.10. Solve word problems involving addition and subtraction of fractions with like denominators
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B.11. Add and subtract fractions with unlike denominators
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B.12. Solve word problems involving addition and subtraction of fractions with unlike denominators
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B.13. Solve inequalities with addition and subtraction of like and unlike fractions
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B.14. Add and subtract mixed numbers accurately
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B.15. Solve word problems involving addition and subtraction of mixed numbers
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B.16. Estimate sums and differences of mixed numbers
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B.17. Solve real-world problems that involve multiple steps and require estimation
C. Multiplication
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C.01. Multiply whole numbers accurately using various methods
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C.02. Solve word problems involving multiplication of whole numbers
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C.03. Multiply numbers ending in zeroes efficiently
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C.04. Solve word problems involving multiplication of numbers ending in zeroes
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C.05. Multiply three or more numbers together
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C.06. Solve word problems involving multiplication of three or more numbers
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C.07. Estimate products to approximate solutions in multiplication problems
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C.08. Multiply money in word problems
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C.09. Apply multiplication to solve real-world problems involving rates and scaling
D. Division
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D.01. Apply divisibility rules to simplify division problems
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D.02. Recognize and utilize division patterns with zeroes
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D.03. Solve word problems involving division of numbers ending in zeroes
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D.04. Estimate quotients to approximate solutions in division problems
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D.05. Divide whole numbers accurately using two-digit divisors
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D.06. Divide money amounts accurately
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D.07. Solve word problems involving division of money
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D.08. Apply division to solve real-world problems involving sharing and grouping
E. Number Theory
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E.01. Identify whether a number is prime or composite
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E.02. List all the factors of a given number
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E.03. Determine the prime factorization of a number
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E.04. Express the prime factorization using exponents
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E.05. Find the highest common factor (HCF) of two or more numbers
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E.06. Find the lowest common multiple (LCM) of two or more numbers
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E.07. Solve word problems involving HCF and LCM
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E.08. Apply number theory concepts to solve problems related to patterns and relationships between numbers
F. Fractions and Mixed Numbers
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F.01. Identify and represent fractions and mixed numbers
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F.02. Solve word problems involving understanding fractions
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F.03. Identify and generate equivalent fractions
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F.04. Write fractions in their lowest terms (simplify fractions)
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F.05. Solve word problems involving fractions in various contexts
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F.06. Determine the lowest common denominator (LCD) for a set of fractions
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F.07. Compare fractions with like and unlike denominators
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F.08. Solve word problems involving comparison of fractions
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F.09. Convert between improper fractions and mixed numbers
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F.10. Convert between decimals and fractions or mixed numbers
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F.11. Place a mix of decimals, fractions, and mixed numbers in order from least to greatest
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F.12. Apply knowledge of fractions to solve real-world problems involving proportions and sharing
G. Decimals
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G.01. Identify the decimal number illustrated by a model
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G.02. Recognize and understand decimal place values
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G.03. Read and write word names for decimal numbers
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G.04. Convert decimals to mixed numbers
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G.05. Put decimal numbers in order from least to greatest
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G.06. Compare decimals using inequalities
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G.07. Round decimals to a specified place value
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G.08. Round whole numbers and decimals, finding the missing digit to achieve a desired rounded value
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G.09. Locate and represent decimals on a number line
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G.10. Apply decimals to solve real-world problems involving measurement and money
H. Integers
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H.01. Understand the concept of integers and their representation
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H.02. Represent integers on number lines
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H.03. Graph integers on horizontal and vertical number lines
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H.04. Compare and order integers
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H.05. Add integers using counters and number lines
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H.06. Add integers accurately
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H.07. Subtract integers using counters and number lines
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H.08. Subtract integers accurately
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H.09. Determine the sign of the result when adding and subtracting integers
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H.10. Complete input/output tables involving addition and subtraction of integers
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H.11. Add three or more integers
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H.12. Apply integers to represent real-world situations like temperature and elevation
I. Ratios and Rates
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I.01. Write a ratio to compare two quantities
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I.02. Solve word problems involving writing ratios
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I.03. Identify equivalent ratios
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I.04. Write an equivalent ratio for a given ratio
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I.05. Complete ratio tables to find missing values
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I.06. Calculate unit rates and identify equivalent rates
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I.07. Solve word problems involving comparison of ratios
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I.08. Determine if two ratios form a proportion
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I.09. Solve proportions for a missing value
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I.10. Solve word problems involving scale drawings
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I.11. Use ratios and rates to solve problems involving proportions and scaling
J. Expressions and Properties
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J.01. Write variable expressions to represent mathematical relationships
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J.02. Evaluate variable expressions by substituting given values
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J.03. Understand and apply properties of addition and multiplication (commutative, associative, distributive, identity)
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J.04. Multiply using the distributive property
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J.05. Write equivalent expressions using properties
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J.06. Understand and apply properties of addition (commutative, associative, identity)
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J.07. Understand and apply properties of multiplication (commutative, associative, identity, distributive)
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J.08. Solve for a variable using properties of multiplication
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J.09. Identify equivalent expressions
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J.10. Use variables and expressions to generalize patterns and relationships
K. One-Variable Equations
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K.01. Write variable equations to represent word problems
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K.02. Solve equations using properties of equality
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K.03. Solve one-variable equations using inverse operations
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K.04. Solve equations by isolating the variable
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K.05. Check solutions to equations by substituting back into the original equation
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K.06. Apply equations to solve real-world problems
L. Units of Measurement
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L.01. Estimate metric measurements (length, mass, volume)
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L.02. Convert and compare metric units (e.g., meters to centimeters)
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L.03. Work with metric mixed units (e.g., 1 m 25 cm)
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L.04. Convert square and cubic units of length
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L.05. Convert between cubic meters and liters
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L.06. Compare temperatures above and below zero using Celsius scale
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L.07. Apply unit conversions to solve practical measurement problems
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L.08. Solve problems involving time units, elapsed time, and schedules
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L.09. Convert between 12-hour and 24-hour time formats
M. Two-Dimensional Figures
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M.01. Identify polygons and distinguish them from non-polygons
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M.02. Recognize and classify different types of angles (acute, obtuse, right, straight)
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M.03. Measure angles using a protractor
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M.04. Distinguish between regular and irregular polygons
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M.05. Identify the number of sides in polygons
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M.06. Classify triangles based on their sides and angles
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M.07. Identify trapeziums
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M.08. Classify quadrilaterals (square, rectangle, parallelogram, rhombus)
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M.09. Graph triangles and quadrilaterals on a coordinate plane
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M.10. Find the unknown angle in triangles and quadrilaterals using angle properties
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M.11. Identify and differentiate between lines, line segments, and rays
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M.12. Recognize and identify parallel, perpendicular, and intersecting lines
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M.13. Identify and describe parts of a circle (center, radius, diameter, chord)
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M.14. Solve problems involving perimeter, area, and angle measures of geometric figures
N. Three-Dimensional Figures
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N.01. Identify common three-dimensional figures (cube, sphere, cone, cylinder, pyramid, prism)
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N.02. Count vertices, edges, and faces of three-dimensional figures
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N.03. Describe three-dimensional figures based on their properties
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N.04. Identify the nets of three-dimensional figures
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N.05. Visualize three-dimensional figures from different perspectives
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N.06. Relate two-dimensional shapes to the faces of three-dimensional objects
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N.07. Apply geometric concepts to solve problems involving spatial reasoning
O. Symmetry and Transformations
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O.01. Identify lines of symmetry in two-dimensional figures
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O.02. Determine if a figure has rotational symmetry
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O.03. Identify and describe transformations (reflection, rotation, translation)
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O.04. Determine if figures are congruent or similar
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O.05. Apply transformations to create symmetrical designs
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O.06. Explore tessellations and patterns using transformations
P. Geometric Measurement
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P.01. Calculate the perimeter of polygons
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P.02. Calculate the area of squares and rectangles
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P.03. Calculate the area of compound figures (composed of squares and rectangles)
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P.04. Calculate the area between two rectangles
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P.05. Determine area and perimeter of figures on grids
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P.06. Solve word problems involving area and perimeter
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P.07. Use area and perimeter to determine cost in real-world scenarios
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P.08. Calculate the volume of figures made of unit cubes
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P.09. Explore the relationship between perimeter and area
Q. Data and Graphs
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Q.01. Interpret information presented in pictographs
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Q.02. Create pictographs to represent data
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Q.03. Interpret data presented in stem-and-leaf plots
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Q.04. Create stem-and-leaf plots to organize data
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Q.05. Interpret data presented in line plots
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Q.06. Create line plots to represent data
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Q.07. Create frequency tables to summarize data
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Q.08. Interpret data presented in bar graphs
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Q.09. Create bar graphs to represent data
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Q.10. Interpret data presented in histograms
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Q.11. Create histograms to represent data
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Q.12. Interpret data presented in line graphs
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Q.13. Create line graphs to represent data
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Q.14. Analyze and compare different types of graphs
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Q.15. Draw conclusions and make predictions based on data presented in graphs
R. Probability
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R.01. Determine possible combinations of items
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R.02. Make predictions based on probability
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R.03. Calculate the number of outcomes for compound events by counting
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R.04. Understand the concept of likelihood and chance
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R.05. Use probability to make informed decisions and predictions
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R.06. Explore real-world applications of probability in games and experiments
S. Problem Solving and Estimation
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S.01. Use estimation to solve word problems
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S.02. Solve multi-step word problems involving various operations
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S.03. Identify and solve word problems with extra or missing information
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S.04. Use the guess-and-check strategy to solve word problems
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S.05. Determine distance and direction to a starting point based on given movements
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S.06. Use logical reasoning to determine the order of events or items
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S.07. Formulate and solve problems using a variety of strategies
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S.08. Check the reasonableness of solutions and interpret results in context
T. Money
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T.01. Find the number of each type of coin to make a given amount
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T.02. Add and subtract money amounts accurately
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T.03. Solve word problems involving addition and subtraction of money amounts
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T.04. Multiply money in word problems
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T.05. Divide money amounts accurately
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T.06. Solve word problems involving division of money amounts
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T.07. Apply money concepts to solve problems related to budgeting and spending
U. Time
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U.02. Understand and use different time units (seconds, minutes, hours, days, weeks, months, years)
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U.03. Find start and end times given elapsed time
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U.04. Convert between 12-hour and 24-hour time formats
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U.05. Interpret transportation schedules
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U.06. Apply time concepts to solve problems involving scheduling and planning
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U.01. Calculate elapsed time
V. Constructions
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V.01. Construct the midpoint or perpendicular bisector of a line segment using compass and straightedge
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V.02. Construct an angle bisector using compass and straightedge
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V.03. Construct a perpendicular line to a given line using compass and straightedge
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V.04. Construct an equilateral triangle or regular hexagon using compass and straightedge
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V.05. Develop spatial reasoning skills through geometric constructions
