Standards in this Framework
Standard | Lessons |
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4.1(A)
Apply mathematics to problems arising in everyday life, society, and the workplace. |
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4.1(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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4.1(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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4.1(D)
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. |
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4.1(E)
Create and use representations to organize, record, and communicate mathematical ideas. |
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4.1(F)
Analyze mathematical relationships to connect and communicate mathematical ideas. |
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4.1(G)
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. |
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4.2(A)
Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left. |
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4.2(B)
Represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals. |
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4.2(C)
Compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =. |
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4.2(D)
Round whole numbers to a given place value through the hundred thousands place. |
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4.2(E)
Represent decimals, including tenths and hundredths, using concrete and visual models and money. |
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4.2(F)
Compare and order decimals using concrete and visual models to the hundredths. |
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4.2(G)
Relate decimals to fractions that name tenths and hundredths. |
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4.2(H)
Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line. |
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4.3(A)
Represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b. |
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4.3(B)
Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations. |
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4.3(C)
Determine if two given fractions are equivalent using a variety of methods. |
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4.3(D)
Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <. |
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4.3(E)
Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. |
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4.3(F)
Evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole. |
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4.3(G)
Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. |
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4.4(A)
Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. |
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4.4(B)
Determine products of a number and 10 or 100 using properties of operations and place value understandings. |
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4.4(C)
Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15. |
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4.4(D)
Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. |
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4.4(E)
Represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations. |
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4.4(F)
Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. |
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4.4(G)
Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. |
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4.4(H)
Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders. |
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4.5(A)
Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity. |
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4.5(B)
Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. |
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4.5(C)
Use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w). |
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4.5(D)
Solve problems related to perimeter and area of rectangles where dimensions are whole numbers. |
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4.6(A)
Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. |
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4.6(B)
Identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure. |
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4.6(C)
Apply knowledge of right angles to identify acute, right, and obtuse triangles. |
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4.6(D)
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. |
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4.7(A)
Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. |
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4.7(B)
Illustrate degrees as the units used to measure an angle and determine approximate measures using a protractor. |
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4.7(C)
Determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures. |
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4.8(A)
Identify relative sizes of measurement units within the customary and metric systems. |
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4.8(B)
Convert measurements within the same measurement system. |
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4.8(C)
Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division. |
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4.9(A)
Represent data on a frequency table, dot plot, or stem-and-leaf plot. |
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4.9(B)
Solve one- and two-step problems using data in whole number, decimal, and fraction form. |
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4.10(A)
Distinguish between fixed and variable expenses. |
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4.10(B)
Calculate profit in a given situation. |
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4.10(C)
Compare the advantages and disadvantages of various savings options. |
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4.10(D)
Describe how to allocate a weekly allowance among spending, saving, and sharing. |
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4.10(E)
Describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending. |
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