Standards in this Framework
Standard | Lessons |
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5.1(A)
Apply mathematics to problems arising in everyday life, society, and the workplace. |
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5.1(B)
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. |
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5.1(C)
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. |
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5.1(D)
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. |
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5.1(E)
Create and use representations to organize, record, and communicate mathematical ideas. |
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5.1(F)
Analyze mathematical relationships to connect and communicate mathematical ideas. |
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5.1(G)
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. |
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5.2(A)
Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. |
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5.2(B)
Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =. |
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5.2(C)
Round decimals to tenths or hundredths. |
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5.3(A)
Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. |
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5.3(B)
Multiply with fluency a three-digit number by a two-digit number using the standard algorithm. |
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5.3(C)
Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. |
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5.3(D)
Represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models. |
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5.3(E)
Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers. |
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5.3(F)
Represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models. |
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5.3(G)
Solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm. |
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5.3(H)
Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. |
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5.3(I)
Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. |
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5.3(J)
Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction using objects and pictorial models, including area models. |
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5.3(K)
Add and subtract positive rational numbers fluently. |
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5.3(L)
Divide whole numbers by unit fractions and unit fractions by whole numbers. |
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5.4(A)
Identify prime and composite numbers. |
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5.4(B)
Represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity. |
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5.4(C)
Generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph. |
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5.4(D)
Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. |
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5.4(E)
Describe the meaning of parentheses and brackets in a numeric expression. |
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5.4(F)
Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. |
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5.4(G)
Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism. |
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5.4(H)
Represent and solve problems related to perimeter, area, and volume. |
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5.5(A)
Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. |
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5.6(A)
Recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes. |
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5.6(B)
Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. |
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5.7(A)
Solve problems by calculating conversions within a measurement system, customary or metric. |
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5.8(A)
Describe the key attributes of the coordinate plane, including perpendicular number lines where the intersection (origin) coincides with zero on each number line. |
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5.8(B)
Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. |
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5.8(C)
Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table. |
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5.9(A)
Represent categorical data with bar graphs or frequency tables and numerical data with dot plots or stem-and-leaf plots. |
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5.9(B)
Represent discrete paired data on a scatterplot. |
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5.9(C)
Solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot. |
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5.10(A)
Define income tax, payroll tax, sales tax, and property tax. |
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5.10(B)
Explain the difference between gross income and net income. |
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5.10(C)
Identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments. |
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5.10(D)
Develop a system for keeping and using financial records. |
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5.10(E)
Describe actions that might be taken to balance a budget when expenses exceed income. |
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5.10(F)
Balance a simple budget. |
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