Fourth Grade Math: Concepts and Targets
Month / Concepts & TargetsAugust/
September
24 days / Fraction Concepts Review: Unit, Non-unit Fractions
(approx. 4 days)
1. Using fraction circles and paper strips, identify, model, and name unit and non-unit fractions orally, with words, and with symbols.
(3.NF.1; 3.G.2)
2. Explain how to know if a unit fraction or non-unit fraction has been
correctly identified. (3.NF.1; 3.G.2)
3. Understand that the unit can change. (3.NF.1; 3.G.2)
4. Using models or drawings reconstruct the unit if given a fractional
part of it. (3.NF.1; 3.G.2)
5. Use models or drawings to show and explain how a given fraction
represents a single quantity in which the denominator represents
the number of equal parts the whole is divided into and the
numerator represents the number of equal parts that are being
counted in a situation. (3.NF.2)
Place Value of Multi-Digit Whole Numbers (approx. 7 days)
1. Understand that a digit in one place represents 10 times as much as it would in the place to the right. (4.NBT.2)
2. Read and write multi-digit numbers through millions using base ten numerals, number names, and expanded form. (4.NBT.1; 4.OA.1)
3. Compare two multi-digit numbers through millions based on meanings of the digits in each place and use the symbols >,<, and = to record the comparisons. (4.NBT.2)
4. Round multi-digit numbers to any place using a vertical number line. (4.NBT.3)
5. Identify the least and greatest numbers that can be rounded to a given whole number. (4.NBT.3)
6. Use place value understanding to round multi-digit numbers to any value. (4.NBT.3)
7. Use place value understanding to round multi-digit numbers to any value using real world applications. (4.NBT.3)
September cont. / Addition & Subtraction: Problem Solving & Algorithms (approx. 10 days)
1. Use the problem solving process and “Draw a Picture” strategy to analyze, represent, and solve single–step addition and subtraction word problems. (4.OA.3)
2. Represent and solve word problems using equations with a letter standing for the unknown quantity. (4.OA.3)
3. Use mental computation strategies based on place value understanding and properties of operations to estimate, find exact sums and differences, and determine reasonableness of answers. (4.OA.3)
4. Use the problem solving process and “Draw a Picture” strategy to analyze, represent, and solve multi-step addition and subtraction word problems. (4.OA.3)
5. Use place value understanding and properties of operations to explain and use the standard addition and subtraction algorithms. (4.NBT.4)
6. Apply the standard addition and subtraction algorithms to solve word problems. (4.NBT.4)
October
23 days / Equivalent Fractions: Extending Understanding
(approx. 4 days)
1. Use models (cutting, folding, or drawing) to create and explain equivalent fractions, paying close attention to how the number and size of the parts differ even though the two fractions themselves are the same size. (4.NF.1)
2. Understand that in addition to being the same size, equivalent fractions also name the same point on a number line, noting that the number and size of the intervals have changed. (4.NF.1)
2. Create symbolic representations of equivalent fractions ab=nxanxb from physical representations of equivalent fractions. (4.NF.1)
October cont. / Ordering Fraction Between 0 & 1: Extending Understanding (approx. 5 days)
1. Compare two fractions with unlike numerators and unlike denominators using a benchmark fraction (0,12, 1) and record using <, >, =. (4.NF.2)
2. Compare two fractions with different numerators and different
denominators by comparing both fractions to ½ when both fractions
are close to ½ . Example: 4912 and 5812 so 4958 (4.NF.2)
3. Compare two fractions with different numerators and different denominators by comparing the residual space of each fraction. (4.NF.2)
4. Compare two fractions with different numerators and different denominators finding equivalent fractions with the same denominator. (4.NF.2)
Review Multiplication Fact Strategies & Problem Types (approx. 7 days)
1. Multiples of 10, Facts with Factors ≤5. (3.OA.5; 3.OA.7, 3.OA.9)
2. Strategies: More Area Compare, Less Area Compare, Splitting (3.OA.5, 3.OA.7)
3. Multiplication Patterns (3.OA.9)
4. Analyze a multiplication word problem to identify the problem
type (area, array, like-size groups, or repeated addition) and
explain how the numbers for the factors and product are related.
(3.OA.1; 3.OA.3; 3.MD.7; 4.OA.3; 4.MD.3)
5. Use objects to act out and drawings to represent multiplication
word problems. (3.OA.1; 3.OA.3; 4.OA.4)
6. Represent multiplication word problems using equations with a
letter standing for the unknown product. (3.OA.3; 4.OA.3)
7. Create and solve multiplication word problems. (3.OA.3; 4.OA.3)
October cont. / Multiplicative Comparison (approx. 1 day)
1. Represent verbal statements of Multiplicative Comparisons as multiplication equations. (4.OA.1)
2. Use objects to act out and drawings to represent Multiplicative Comparison word problems where the greater amount is unknown. (4.OA.1)
3. Represent Multiplicative Comparison word problems using equations with a letter standing for the unknown greater amount. (4.OA.2)
4. Create and solve Multiplicative Comparison word problems where the
greater amount is unknown. (4.OA.2)
Multi-Step Multiplication Word Problems Within 100
(approx. 2 days)
1. Analyze and solve two-step multiplication word problems (for multiplication within 100. )(3.OA.8)
2. Analyze and solve multi-step word problems (where only one step involves multiplication within 100.) (4.OA.3)
3. Represent word problems using equations with a letter standing for the unknown quantity. (4.OA.3)
4. Use drawings and equations to represent each step of a word problem. (4.OA.3)
5. Assess the reasonableness of answers using estimation and mental computation strategies. (4.OA.3)
November
18 days / Factors and Multiples, Prime and Composite Numbers (approx. 3 days)
1. Use area model strategies to find factor pairs for whole numbers 1 to 100. (4.OA.4)
2. Recognize whether a number from 0 to 100 is a multiple of a given 1-digit number. (4.OA.4)
3. Determine whether a whole number from 1 to 100 is prime or composite. (4.OA.4)
4. Generate a number pattern that follows a rule. (4.OA.5)
November cont. / Review: Division Fact Strategies & Problem Types
(approx. 9 days)
1. Use multiplication to find division facts. (3.OA.5; 3.OA.7; 3.OA.9)
2. Change a multiplication equation with an unknown factor to a division equation with the quotient as the unknown. (3.OA.6)
3. Use the area model to connect multiplication to division. (3.OA.7)
4. Analyze a division word problem to identify the problem type (area, array, fair share, or repeated subtraction) and explain how the missing factor (quotient) is related to the known numbers (dividend and divisor). (3.OA.2; 3.OA.3; 3.OA.4, 3.MD.7; 4.OA.3; 4.OA.4)
5. Use objects to act out and drawings to represent division word problems. (3.OA.2; 3.OA.3; 4.OA.3; 4.MD.3)
6. Represent division word problems using equations with a letter standing for the unknown quotient. (3.OA.3; 3.OA.4; 4.OA.3)
7. Create and solve division word problems. (3.OA.3; 4.OA.3)
Multiplicative Comparison as Division (approx. 5 days)
1. Use objects to act out and drawings to represent Multiplicative Comparison word problems where the unknown is either the multiplier or the lesser amount. (4.OA.1)
2. Represent and solve Multiplicative Comparison word problems using equations with a letter standing for the unknown multiplier or lesser amount. (4.OA.2)
3. Create and solve Multiplicative Comparison word problems where the unknown is either the multiplier or the lesser amount. (4.OA.2)
December 15 days / Fractional Parts of a Set Review (approx. 9 days)
1. Represent a given fraction using different sets of chips as a unit. (3.NF.1; 3.NF.2; 4.NF.1)
2. Using chips for the units, determine what units can be
used to model a given fraction and what units cannot be used to model
it. (3.NF.1; 3.NF.2; 4.NF.1)
3. Given a set of chips as the unit, determine possible
fractions that can be shown using that unit. (3.NF.1; 3.NF.2; 4.NF.1)
4. Use chips to model equivalent fractions. (3.NF.1; 3.NF.2; 4.NF.1)
January 20 days / Conversion of Measurement Units and Problem Solving (approx. 7 days)
1. Know relative sizes of measurement units within one system of units
including km, m, cm; kg, g; lb, oz, ml, l; hr, min, sec. (4.MD.1)
2. Within a single system of measurement express larger units in terms of
smaller units. (1 foot is 12 times as long as 1 inch. A 4 foot snake is 48
inches long.) (4.MD.1)
3. Record measurement equivalents in a two-column table. (4.MD.1)
4. Use addition and subtraction to solve word problems involving
distance, intervals of time, liquid volume, masses of objects, and
money, including problems with that involve conversion of larger units
to smaller units. (4.MD.2)
Composing and Decomposing Fractions (approx. 4 days)
1. Given 1 or more equal size parts, reconstruct the unit. (4.NF.3b)
2. Use models to build fractions greater than 1 and name them using
both fraction and mixed number names. (4.NF.3b)
3. Use a number line to decompose a fraction into a sum of unit
fractions and write a matching equation. (4.NF.3b)
4. Use a number line to decompose a fraction into a sum of fractions
with the same denominator in more than one way, write matching
equations, and justify the results. (4.NF.3b)
5. Decompose a fraction into a sum of fractions with the same
denominator in more than one way, write equations, and justify the
results. (4.NF.3b)
January cont. / Ordering Fractions > 1 and Mixed Numbers (approx. 2 days)
1. Name a fraction or mixed number for a given point on a number line. (4.NF.2)
2. Find the point on a number line for a given fraction or mixed number.
(4.NF.2)
3. Find and use benchmarks to order fractions and mixed numbers on a
number line. (4.NF.2)
4. Use equivalence strategies to order fractions and mixed numbers on a
number line. (4.NF.2)
Exploring Points, Lines, Rays, and Angles (approx. 4 days)
1. Identify points, lines, line segments, rays, and angles in figures and in
real world contexts. (4.G.1)
2. Recognize angles as shapes formed whenever two rays share
a common endpoint. (4.G.1)
3. Draw and label points, lines, line segments, rays, and angles. (4.G.1)
4. Recognize parallel and perpendicular lines in figures and in
real world contexts. (4.G.1)
5. Identify acute and obtuse angles by comparing them to right angles.
(4.G.1)
February
15 days
February cont. / Angle Measurement (approx. 6 days)
1. Understand that an angle is measured with reference to a circle with its center at the common endpoints of the rays forming the angle. (4.MD.5)
2. Understand angle measure as different from length measure. (4.MD.5)
3. Understand a 1-degree angle as 1360 of a turn. (4.MD.5)
4. Recognize angles as sums of 1° angles whose rays share a common endpoint at the center of a circle. (4.MD.5)
5. Identify acute and obtuse angles by comparing them to right
angles. (4.MD.5)
6. Measure angles in whole-number degrees using a protractor. (4.MD.6)
7. Draw angles of a given measure using a protractor and straight edge.
(4.MD.6)
8. Decompose an angle into a sum of the angle measurements of its parts.
(4.MD.7)
9. Solve addition and subtraction problems to find unknown angles on a
diagram in real world and mathematical problems by using an equation
with a symbol for the unknown angle measurement. (4.MD.7)
Multiplication Area Model and Algorithm (approx. 14 days)
1. Apply place value understanding and properties of operations to multiply 1-digit numbers by multiples of 10 up to 90. (3.NBT.)
2. Apply place value understanding and properties of operations to multiply 1-digit numbers by multiples of 10, 100, 1000.
3. Use an area model rectangular grid to identify the partial products for multiplying 1-digit by up to 4-digit whole numbers. (4.NBT.5)
4. Use an area model rectangular grid to identify the partial products for multiplying 2-digit by 2-digit whole numbers. (4.NBT.5)
5. Apply the Commutative and Associative Properties of Multiplication to simplify the multiplication of 3 factors. (4.NBT.5)
6. Solve area word problems with multi-digit factors by applying the formula length x width = area. (4.MD.3)
7. Use place value understanding and the standard algorithm to multiply 1-digit whole numbers by up to 4-digit whole numbers with and without regrouping. (4.NBT.5)
8. Use place value understanding and the standard algorithm to multiply two 2-digit whole numbers with and without regrouping.
(4.NBT.5)
March
22 days / Multi-Step Multiplication Word Problems
With Multi-digit Numbers (approx. 1 day)
1. Analyze and solve multi-step word problems (where only one step involves multiplication) posed with multi-digit whole numbers. (4.OA.3)
2. Represent word problems using equations with a letter standing for the unknown quantity. (4.OA.3)
3. Use drawings and equations to represent each step of a multi-step word problem. (4.OA.3)
4. Assess the reasonableness of answers using estimation and mental computation strategies. (4.OA.3)
Measurement Problem Solving
Including Area, Perimeter, and Multi-step (approx. 5 days)
1. Use the four operations to solve word problems involving distance,
intervals of time, liquid volume, masses of objects, and money,
including problems with simple fractions or decimals that involve
conversion of larger units to smaller units. (4.MD.2)
2. Represent measurement quantities using diagrams with a
measurement scale, such as a number line. (4.MD.2)
3. Apply the area formula for rectangles in real world and mathematical
problems with the unknown measurement in any position of an
equation. (Area=length x width) (4.MD.3)
4. Apply the perimeter formula for rectangles in real world and
mathematical problems. (Perimeter=2 length + 2 width) (4.MD.3)
Add and Subtract Fractions with Like Denominators
(approx. 6 days)
1. Understand addition and model addition and subtraction of fractions as joining and separating parts referring to the same whole and made from the same unit fraction. (4.NF.3a)
2. Replace a mixed number with an equivalent fraction having the same
denominator in order to add or subtract fractions with like
denominators. (4.NF.3c)
3. Estimate the sum or difference of two fractions by comparing them to
benchmarks. (4.NF.3a)
4. Use concrete or picture models to find exact sums or differences of
fractions. (4.NF.3a)
5. Represent and solve one-step word problems involving addition and
subtraction of fractions and mixed numbers with like denominators.
(4.NF.3d)
6. Use objects and drawings to represent and solve two- or three-step
word problems that involve addition and subtraction of fractions and