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The compelling questions are designed to support learning connections and an inquiry based approach to math learning. Teachers and students should work through the questions in sequenceΒ and with the intent to develop a growth mindset that supports the belief that everyone can learn math at high levels.
Big ideas in fourth grade:
(1) fluency with multi-digit multiplication & division using strategies based on place value
(2) understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers
(3) classifying skills and analyze geometric figures based on their properties.
Students must develop mathematical practices that will allow them to achieve the three critical areas stated above.
Instructional Time Guidance for Fourth Grade:
Printables:Β
Printables:Β
learning targets, year at a glance, report card correlation, & resource list
learning targets, year at a glance, report card correlation, & resource list
4th grade learning targets printable list click here.
Year at a Glance printable version click hereΒ
4th gr Number talk guide click here
Report Card Standards Correlation click here Β Β
Standards Based Report Cards 4th gradeΒ Β ENGLISHΒ Β SPANISH Β ARABIC Β Β Β parent information Β Β
K-5 Math Framework click hereΒ Β Β &Β Β Vertical Coherency overview click here
4th grade Classroom Inventory list click here
Ready Teacher Toolbox math templates printables
Fourth Grade Fluency
Fourth Grade Fluency
4.NBT.B.4Β Fluently add and subtract multi-digit whole numbers using the standard algorithm (connecting the algorithm to strategies learned in second and third grades). Β Addition strategiesΒ Β Β Β Β Subtraction strategiesΒ Β Β Β Β Β
4.NBT.B.4Β Fluently add and subtract multi-digit whole numbers using the standard algorithm (connecting the algorithm to strategies learned in second and third grades). Β Addition strategiesΒ Β Β Β Β Subtraction strategiesΒ Β Β Β Β Β
Begin developing proficiency with multiplying and dividing multi-digit numbers, using strategies based on place value and the properties of operations. Β Β Β Multiplication strategiesΒ Β (**standard multiplication algorithm is a 5th grade standard) Β Β Β Β Β Β Division strategies Β Β Β (**standard division algorithm is a 6th grade standard)
More information and Resources on the fluency tab.Β
All Print Resources from Mastering the Basic Facts Multiplication and Division: xΓ·facts
Essential Questions
Essential Questions
Year at a Glance
Year at a Glance
Click here for a printable version of Year at a Glance.Β Β
You will find that content in our curriculum maps have been given a priority designation; however, lower priority is not meant to imply exclusion. These priorities are meant to help guide the focus of teachers as they allocate their limited time for planning and instruction. Teachers should always use their best judgment for what works for them and their students.
π© Major content identifies those areas where students should spend the large majority (65-85%) of instructional time and focus on the major work of the grade.
π· Supporting content is designed to strengthen the areas of major emphasis, as these pieces are closely connected to the major clusters of the grade.
π‘ Additional content covers material that does not connect tightly or explicitly to the major work of the grade, but still engages students in grade-level conceptual learning.
Starting out the year
Starting out the year
Growth Mindset Lessons, Activities and Videos to use as you lay the groundwork for a Mathematical Mindset connected to The 8 Standards for Mathematical Practice. Β Good Group Work-setting norms
Begin launching Guided Math:
For assistance on structuring guided math, click here. Guide to the first 20 days here.
T1
1 week
How are patterns recognized and explained?
How are patterns recognized and explained?
π‘ 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
T1
1 week
How does place value relate to addition and subtraction?
How does place value relate to addition and subtraction?
π© 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.Β For example, recognize that 700 Γ· 70 = 10 by applying concepts of place value and division.
π© 4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
π© 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.
π© 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. (the ability to borrow and carry is an end of year expectation and can be taught throughout the year, after place value strategies are well established)
T1
4-5 weeks
How does addition relate to multiplication?Β Β
How does addition relate to multiplication?Β Β
π© 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 Γ 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
π© 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
π· 4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
T1
2-3 weeks
How do addition and multiplication strategies relate to the concepts of area and perimeter?
π· 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
π© 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
T1
3 weeks
π© 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models (Standard long division is not an expectation of 4th grade)
π© 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
T2
3 weeks
How does place value relate to decimals?
π© 4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
π© 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
π© 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
T2
2-3 weeks
How do fractional parts apply to creating, comparing, and decomposing fractions?
How do fractional parts apply to creating, comparing, and decomposing fractions?
π© 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n Γ a)/(n Γ b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
π© 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
π© 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (with the same denominator)
4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 =Β 8/8 + 8/8 + 1/8.
T2
2 weeks
How do the operations of addition, subtraction and multiplication apply to fractions?
How do the operations of addition, subtraction and multiplication apply to fractions?
π© 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
π© 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 Γ (1/4), recording the conclusion by the equation 5/4 = 5 Γ (1/4).
4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 Γ (2/5) as 6 Γ (1/5), recognizing this product as 6/5. (In general, n Γ (a/b) = (n Γ a)/b.)
4.NF.4cΒ Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?Β (Fraction multiplied by fraction is not necessary in 4th grade)
π· 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
T2/3
3-4 weeks
How are shapes defined by properties?
How are shapes defined by properties?
π‘ 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
π‘ 4.G.2 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. Recognize right triangles as a category, and identify right triangles.Β
π‘ 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
T3
3 weeks
How are angles classified and measured?
How are angles classified and measured?
π‘ 4.MD.5 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
4.MD.5a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a βone-degree angle,β and can be used to measure angles.
4.MD.5b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
π‘ 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
π‘ 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
T3
2 weeks
How are measurements converted and displayed?Β
How are measurements converted and displayed?Β
π· 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ....
π· 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
T3
2-3 weeks
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