Grade 5 · Mathematics
5.10A
Taxes & Income
Define income, payroll, sales, and property taxes; explain gross vs. net income.
5.10B
Payment Methods
Identify advantages and disadvantages of checks, credit cards, debit cards, and electronic payments.
5.10C
Financial Records
Develop a system for keeping and using financial records.
5.10D
Balance a Budget
Describe actions to balance a budget when expenses exceed income; balance a simple budget.
5.1A
Apply Math to Real Life
Apply mathematics to problems in everyday life, society, and the workplace.
5.1B
Problem-Solving Model
Use a problem-solving model: analyze, plan, solve, justify, and evaluate.
5.1C
Select Tools & Techniques
Select appropriate tools and techniques (manipulatives, mental math, estimation).
5.1D
Communicate Math Ideas
Communicate ideas and reasoning using multiple representations.
5.1E
Use Representations
Create and use representations to organize, record, and communicate ideas.
5.1F
Analyze Relationships
Analyze mathematical relationships to connect and communicate ideas.
5.1G
Justify with Precise Language
Display, explain, and justify ideas using precise mathematical language.
5.2A
Place Value to Thousandths
Represent the value of a digit in decimals through the thousandths using expanded notation and numerals.
5.2B
Compare & Order Decimals
Compare and order two decimals to thousandths using >, <, or =.
5.2C
Round Decimals
Round decimals to tenths or hundredths.
5.3A
Estimate Solutions
Estimate to determine solutions to problems using all four operations.
5.3B
Multiply Fluently (3-digit × 2-digit)
Multiply with fluency a three-digit number by a two-digit number using the standard algorithm.
5.3C
Divide (up to 4-digit ÷ 2-digit)
Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm.
5.3D
Multiply Decimals to Hundredths
Represent multiplication of decimals to the hundredths using objects and pictorial (area) models.
5.3E
Solve Products of Decimals (Money)
Solve for products of decimals to the hundredths, including money, using place value, properties, and relationships to whole-number multiplication.
5.3F
Quotients of Decimals (Models)
Represent quotients of decimals to the hundredths using objects and pictorial models, including area models.
5.3G
Quotients of Decimals (Algorithms)
Solve for quotients of decimals to the hundredths using strategies and algorithms, including the standard algorithm.
5.3H
Add/Subtract Fractions (Unlike Denominators)
Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole.
5.3I
Multiply Whole Number × Fraction
Represent and solve multiplication of a whole number and a fraction referring to the same whole using objects and pictorial models (area models).
5.3J
Divide Unit Fraction by Whole & Vice Versa
Represent division of a unit fraction by a whole number and a whole number by a unit fraction (e.g., 1/3 ÷ 7; 7 ÷ 1/3) using models.
5.3K
Add/Subtract Positive Rational Numbers
Add and subtract positive rational numbers fluently.
5.3L
Divide Whole Numbers by Fractions
Divide whole numbers by unit fractions and unit fractions by whole numbers.
5.4A
Prime & Composite Numbers
Identify prime and composite numbers.
5.4B
Equations with Letter for Unknown
Represent and solve multi-step problems with whole numbers using equations with a letter for the unknown.
5.4C
Generate Numerical Patterns
Generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph.
5.4D
Additive vs. Multiplicative
Recognize differences between additive and multiplicative patterns in tables/graphs.
5.4E
Parentheses & Brackets
Describe the meaning of parentheses and brackets in numeric expressions.
5.4F
Simplify Expressions
Simplify numerical expressions that do not involve exponents, including up to two levels of grouping.
5.4G
Volume Formulas (Cube & Rectangular Prism)
Use objects and models to develop formulas for volume of a rectangular and a cube (V = l × w × h; V = s × s × s).
5.4H
Perimeter & Area Word Problems
Represent and solve problems related to perimeter and/or area.
5.5
Classify 2‑D Figures
Classify two‑dimensional figures in hierarchies by attributes and properties.
5.6A
Unit Cubes & Volume as Cubic Units
Recognize a unit cube and volume as the number of unit cubes filling a figure (no gaps/overlaps).
5.6B
Volume of Rectangular Prisms
Determine volume of rectangular prisms with whole-number side lengths using layers and base area.
5.7
Convert Within a System
Solve problems by calculating conversions within a measurement system (customary or metric).
5.8A
Coordinate Plane Basics
Describe axes, origin (0,0), x- and y-coordinates and movement to plot points.
5.8B
Process to Graph Ordered Pairs
Describe the process for graphing ordered pairs in Quadrant I.
5.8C
Graph & Interpret Ordered Pairs
Graph ordered pairs in Quadrant I from patterns or input-output tables and real-world contexts.
5.9A
Represent Data
Represent categorical data with bar graphs or frequency tables and numerical data with dot plots or stem‑and‑leaf plots (including fractions/decimals).
5.9B
Scatterplots
Represent discrete paired data on a scatterplot.
5.9C
Solve Problems from Data
Solve one- and two-step problems using data from frequency tables, dot plots, bar graphs, stem‑and‑leaf plots, or scatterplots.