Grade 4 - Fractions
Essential Questions:
1. Why do we use numbers, what are their properties, and how does our number system function?
2. Why do we use estimation and when is it appropriate?
3. What makes a strategy effective and efficient and the solution reasonable?
4. How do numbers relate and compare to one another?
Essential Vocabulary - partition(ed), fraction, unit fraction, equivalent, multiple, reason, denominator, numerator, comparison/compare, ‹, ›, =, benchmark fraction,
partition(ed), whole, tenth, hundredth
We want students to understand that all numbers have parts, values, uses, types, and we use operations and reasonableness to work with them.
4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The definition of a numerator and denominator. 1. That fractions are comprised of equal sized
1. Draw models using fractions.
2. The definition of equivalent.
pieces.
2. Draw models to show equivalent fractions with
unlike denominators.
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.
Students will know…
1. The benchmark fractions of 0, ¼, ½, and ¾ and
1.
2. How to draw visual representation of fractions
using a variety of methods using their
knowledge of fractional parts.
3. That the denominator tells how many parts in
the whole.
4. That the numerator tells how many parts are
being used/taken.
5. The symbols >,<, and = are used for comparison
Grade 4 Enduring Understandings
Students will understand…
1. That they must consider the size of the whole
when comparing fractions.
2. That benchmark fractions can help them
compare and order fractions.
Students will be able to…
1. Compare fractions by creating visual fraction
models or by finding common denominators or
numerators (the focus is on visual fraction
models rather than algorithms).
2. Draw fraction models to help them compare and
order fractions.
3. Use area models, number lines, verbal
justification and benchmark numbers to
compare fractional parts.
4. Use the symbols of <,>, and = to compare and
order fractions.
4.NF.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the
same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify
decompositions, e.g., by using a visual fraction
model.
Examples: 3/8 = 1/8 + 1/8 + 1/8 ;
3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 +
1/8 = 8/8 + 8/8 + 1/8.
c. 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.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction
models and equations to represent the problem.
Students will know…
1. How to draw visual representation of fractions
using a variety of methods using their
knowledge of fractional parts.
2. That the denominator tells how many parts in
the whole.
3. That the numerator tells how many parts are
being used/taken.
4. A unit fraction is defined as a fraction with a
numerator of one.
5. That Montana American Indians are an integral
part of Montana’s culture.
Grade 4 Enduring Understandings
Students will understand…
1. That numbers, including fractions, can be
written in a variety of ways (decomposing and
composing of number)
2. That wholes can be divided into different and
equivalent fractional parts that will allow ease of
addition and subtraction of fractions.
3. Using visual models helps us understand and
compare the relative size and equivalent parts of
a whole.
Students will be able to…
1. Investigate fractions other than unit fractions
and join (compose) or separate (decompose) the
fractions of the same whole.
2. Justify their breaking apart (decomposing) of
fractions using visual fraction models.
3. Turn mixed numbers into improper fractions
using visual fraction models.
4. Solve real world problems involving addition
and subtraction of fractions with cultural
context.
4.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. 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 × (1/4), recording the conclusion by
the equation 5/4 = 5 × (1/4).
b. 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 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
c. 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?
Students will know…
1. How to draw visual
representation of fractions using a variety of
methods using their knowledge of fractional
parts.
2. That the denominator tells how many parts in
the whole.
3. That the numerator tells how many parts are
being used/taken.
4. Another way to read the multiplication symbol
is “of”.
Grade 4 Enduring Understandings
Students will understand…
1. That visual models (number lines, area models
and repeated addition) can be used to help
interpret fractional equations.
2. That improper fractions can be shown visually
to show relationships between numerator and
denominator.
3. That multiplication is repeated addition, and
visual models of fractions help model this
concept.
Students will be able to…
1. Use repeated addition to create visual fraction
models to multiply a whole number by a
fraction.
2. Use and create visual fraction models to
multiply a whole number by a fraction.
3. Use visual fraction models to solve word
problems related to multiplying a whole number
by a fraction.
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. For example, express 3/10 as 30/100, and add 3/10 +
4/100 = 34/100.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. Place values of tenths and hundredths.
1. A fraction expressed in tenths can be written as
1. Change fractions with a 10 in the
2. Place value block representations of fractions.
an equivalent fraction expressed in hundredths.
denominator into equivalent fractions that
2. A number can be written as decimal or as
have a 100 in the denominator.
equivalent fractions that have the same value.
2. Use decimal grids to show stated amounts in
3. Fractions can be added or subtracted using like
tenths and hundredths.
size parts (equivalent fractions).
3. Use base ten blocks to show the value of a
given number.
4. Add and subtract fractions using their
knowledge of place value to create
equivalencies.
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
1. Place values of tenths and hundredths.
1. Place value determines the value of a decimal.
2. Place value block representations of decimals
2. A decimal in the tenth’s place can be written as
an equivalent decimal expressed in hundredths.
3. A number can be written as a decimal or as
equivalent fractions.
Students will be able to…
1. Read, write and say decimal and fractional
numbers to the hundredths place.
2. Use and draw visual models such as area model,
decimal grids, circles and meter sticks to
represent decimal and fractional numbers to the
hundredths place.
3. Write decimals in fractional form and word
form.
4. Decompose fractional and decimal numbers.
5. Compare and order decimals using a number
line.
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, e.g., by using a visual model.
Students will know…
1. Symbols for comparing and ordering (<,>,=).
Grade 4 Enduring Understandings
Students will understand…
1. Those comparisons are valid only when the two
Students will be able to…
1. Justify comparisons using visual models such as
2. Place values of tenths and hundredths.
3. Place value block representations of decimals
decimals refer to the same whole.
2. Fractional and decimal parts can be compared
and ordered according to size of parts.
pictures or place value representations.
2. Use the compare and order symbols with
fractional and decimal numbers.
Grade 4 - Geometry
Essential Questions:
1. Why are geometry and geometric figures relevant and important?
2. How can geometric ideas be communicated using a variety of representations?
******(i.e maps, grids, charts, spreadsheets)
3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning?
Essential Vocabulary – Geometry, Point, Line, Line Segment, Ray, Angles (Right, Acute, Obtuse), Degree, Perpendicular Lines, Parallel Lines, Attributes, TwoDimensional, Space, Plane, Vertex, Intersecting, Protractor, Triangle, Square, Rectangle, Parallelogram, Quadrilateral, Rhombus, Trapezoid, Pentagon, Hexagon,
Octagon, Polygon, Line of Symmetry, Symmetry, Polygon, Regular Polygon, Irregular,
We want students to understand that geometry is all around us in 2D or 3D figures. Geometric figures have certain properties and can be transformed,
compared, measured, and constructed.
4.G.1.: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The definition of the following:
1. That a precise geometrical vocabulary is
1. Illustrate and Identify the following in isolation
important for mathematical communication.
and within two-dimensional figures:
 a point
2. That shapes are comprised of different
 a point
 line
geometrical
components
which
allow
us
to
 line
 line segment
classify
and
identify
them.
 line segment
 ray
 ray
 right angle
 right angle
 acute angle
 acute angle
 obtuse angle
 obtuse angle
 perpendicular lines
 perpendicular lines
 parallel lines
 parallel lines
2. The names and attributes of two-dimensional
figures.
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.
Students will know…
1. The definition of parallel and perpendicular
lines.
2. The definition of right, acute, and obtuse angles.
3. The definition of right, acute, and obtuse
triangles.
4. The definition of scalene, isosceles, and
equilateral triangles.
5. How to use appropriate tools to measure angles.
Grade 4 Enduring Understandings
Students will understand…
1. That a precise geometrical vocabulary is
important for mathematical communication.
2. That shapes are comprised of different
geometrical components which allow us to
classify and identify them.
Students will be able to…
1. Classify two-dimensional shapes based on
specific attributes.
2. Identify and classify triangles by their angles
and sides.
4.G.3.: Recognize a line of symmetry for a two-dimensional figure, including those found in Montana American Indian design, 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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The definition of symmetry.
1. That some geometrical figures can be divided
1. Divide a regular and irregular polygon using
into equal parts using a line of symmetry.
lines of symmetry.
Grade 4 - Measurement
Essential Questions:
1. How does estimation help you find a reasonable measurement?
2. How do you determine the tool and unit to help you accurately measure?
3. When do you need to measure?
Essential Vocabulary - measure, metric, customary, convert/conversion, relative size, liquid
volume, mass, length, distance, kilometer (km), meter (m), centimeter (cm), kilogram (kg), gram (g), liter (L), milliliter (mL), inch (in), foot (ft), yard (yd), mile
(mi), ounce (oz), pound (lb), cup (c), pint (pt), quart (qt), gallon (gal), time, hour, minute, second, equivalent, operations, add,
subtract, multiply, divide, fractions, decimals, area, perimeter, measure, customary, convert/conversion, relative size, length, distance, inch (in), foot (ft),
equivalent, operations, add, subtract, fractions, data, line plot, center, measure, point, end point, geometric shapes, ray, angle, circle, fraction, intersect, one-degree
angle, protractor, decomposed, addition, subtraction, unknown, acute, right, obtuse, straight
We want students to understand when to measure, what tool and unit to use, and how to use estimation to find a reasonable measurement.
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), ...
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. That conversions can be made within the
1. That larger units can be subdivided into
1. Choose appropriate measurement.
metric/standard system.
equivalent units (partition).
2. Convert measurements within a system using a
2. That what is being measured determines the unit 2. That the same unit can be repeated to determine
two-column table.
of measure used.
the measure (iteration).
3. List numbered pairs to show measurement
3. The essential vocabulary as noted above.
3. That the smaller the unit used to measure the
equivalency.
distance, the more of those units that will be
needed. (compensatory principal).
4.MD.2: Use the four operations to solve word problems within cultural contexts, including those of Montana American Indians, 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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. That Montana American Indians are an integral
1. That knowledge of units of measure can be used 1. Solve multi-step word problems involving
part of Montana culture.
to solve multi-step problems.
measurement. (Some of which may include
2. That conversions can be made within the
2. That problems can be solved in a variety of
cultural context)
metric/standard system.
ways using the four operations as well pictorial
2. Use diagrams such as number lines to justify
models.
their solutions.
3. That what is being measured determines the unit 3. That larger units can be subdivided into
of measure used.
equivalent units (partition).
4. The essential vocabulary as noted below.
4. That the same unit can be repeated to determine
the measure (iteration).
5. That the smaller the unit used to measure the
distance, the more of those units that will be
needed. (compensatory principal).
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The formula for area is I x w and the answer will 1. That their previous knowledge of area and
1. Use formulas to calculate area and perimeter of
always be in square units.
perimeter can be connected to a formula.
rectangles.
2. The formula for perimeter can be 2 l + 2 w or 2
2. That these formulas should be developed
2. To communicate their understanding of why the
(l + w) and the answer will be in linear units.
through experience not just memorization.
formulas work.
3. That a formula can be used to find an unknown
3. That area and perimeter formulas may be used
3. Solve real world problems using area and
factor. Ex. (8 x w) = 24 sq. units
to solve real world problems.
perimeter.
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. How to use a ruler to measure objects within an 1. That larger units can be subdivided into
1. To reason using appropriate mathematical
eighth of an inch.
equivalent units (partition).
language while interpreting data on a line plot.
2. That a line plot is a visual way to display data.
2. That the smaller the unit used the more precise
2. To work with fractions by measuring objects to
3. That a ruler contains equivalent fractions using
the measurement.
an eighth of an inch.
eighths, fourths, and halves.
3. That a line plot can be used to analyze data.
3. Make a line plot of data and then add or subtract
4. How to add and subtract equivalent fractions.
4. That fractions can be added or subtracted to
fractions based on the data in the line plot.
solve a real world problem.
4.MD.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
a. 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 “one-degree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have
an angle measure of n degrees.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. That a circle is comprised of 360 degrees.
2. Angles are comprised of two rays sharing a
common end point.
1. That angles are made up of one degree turns
within a 360 degree circle.
2. A degree measurement does not relate to area
but rather the distance between two rays.
4.MD.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
1. The terms acute, obtuse, straight, and right
1. That they can use benchmark angle
angles.
measurements (45, 90, 180, 270, 360) to
2. That a protractor is a tool used to measure
estimate angle measure.
angles.
2. That a protractor can be used to identify, draw,
and measure angles.
1. Communicate using appropriate language how
an angle is formed in relation to a circle.
2. Tell how these angles can be measured within
the context of a circle using degrees.
Students will be able to…
1. Estimate an angle measure using benchmark
angle measurements.
2. Measure a give angle in degrees using a
protractor.
3. Use a protractor to draw and label an angle.
4. Identify the type of a given angle. (Right, Acute,
Obtuse, Straight)
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The terms acute, obtuse, straight, and right
1. That angles can be broken into smaller parts.
1. Solve real world problems using benchmark
angles.
(decompose)
angle measurements.
2. That a protractor is a tool used to measure
2. That they can use benchmark angle
2. Solve real world problems using addition and
angles.
measurements (45, 90, 180, 270, 360) to find
subtraction of angles to find an unknown
3. That a symbol/variable can be used to represent
unknown angle measurements.
measurement.
an unknown value.
3. The perpendicular and parallel lines form
3. Evaluate a diagram that uses angle
distinct angle measurements.
measurements and a symbol/variable to find an
unknown angle measurement.
Grade 4 – Numbers & Operations Base Ten
Essential Questions:
5. Why do we use numbers, what are their properties, and how does our number system function?
6. Why do we use estimation and when is it appropriate?
7. What makes a strategy effective and efficient and the solution reasonable?
8. How do numbers relate and compare to one another?
Essential Vocabulary – Value, Digit, Multiply, Divide, Place Value, Rounding, and Estimation, Addition, Subtraction, Regrouping, Borrowing, Algorithm, Place
Value, Factor, Product, Multiplication, Array, Distributive Property, Partial Product, Equation, Compensation, Quotient, Dividend, Divisor, Remainder, Inverse
Operations, Division, Multiplication
We want students to understand that all numbers have value, uses, values, types, and we use operations and reasonableness to work with them.
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. For example,
recognize that 700 ÷ 70 =10 by applying concepts of place value and division.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. Place value positions for 7 – 9 digit numbers
1. The relationships/ magnitude of digits
3. Multiply and divide by multiples of ten to change
(millions.)
within the base-ten number system.
the value of a digit.
2. Multiplication and Division facts to ten.
2. That multiplying/ dividing by 10 increases/
3. The value of a digit within a multi-digit number
decreases the value of the digit.
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The symbols <, >, =
1. The placement of a digit dictates its value, 1. To use appropriate tools when comparing numbers
2. The value of a digit in any given place to the
how it is read, written, and compared.
to 1,000,000-999,999,999.
hundred millions places.
2. Read and write numbers using standard form,
word from, and expanded notation using 1 – 9
digits.
3. Compare and order two 1 – 9 digit numbers using
comparative symbols.
4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The value of a digit in any given place of a multi1. That they must use place value and number 1. Round multi-digit numbers, explain the process,
digit number.
sense in order to evaluate their answers
and apply to real world situations.
2. To use appropriate tools to evaluate/compare
when they round or estimate solutions.
numbers. For example, place value mats, number
lines, and hundred charts.
4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.4 – Numbers & Operations Base Ten
Students will know…
Students will understand…
1. Basic addition and subtraction facts to 10.
1. That the standard algorithm for addition
2. How to set up an addition/subtraction problem.
and subtraction is based on the
understanding of place value.
Students will be able to…
1. Accurately and efficiently use the standard
algorithm to add or subtract multi-digit numbers.
2. Justify the steps in the algorithm using the
knowledge of place value to explain why the
procedure works.
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. Multiplication and addition facts to 10.
1. There are a variety of methods to solve
1. Multiply 4 digit by 1 digit and 2 digit by 2 digit
2. There are multiple ways to solve any given
multi-digit multiplications problems based
numbers (model in variety of ways).
problem.
on the properties of place value and the
2. Explain/Justify their solutions and the method they
distributive property. For example: partial
used to find a product.
products, area models, compensation
strategies, and equations.
2. That multiplication is repeated addition.
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.
Grade 4 Enduring Understandings
We want students to understand that all numbers have value, uses, values, types, and we use operations and reasonableness to work with them.
Students will know…
Students will understand…
Students will be able to…
1. Basic facts to 10 using all operations.
1. There are a variety of methods to solve
1. Divides using a four-digit dividend and 1 digit
2. There are multiple ways to solve any given
division problems based on the properties
divisors. (Model in variety of ways).
problem.
of place value, operations, and inverse
2. Explain/Justify their solutions and the method they
operations. For example: base ten blocks,
used to find a quotient.
place value, open array models, area
models, and multiplication.
2. That division is repeated subtraction.
3. Multiplication and division are related
operations.
Grade 4 – Algebraic Thinking
Essential Questions:
1. How do you use patterns to understand mathematics and model situations?
2. What is algebra?
3. How are the horizontal and vertical axes related?
4. How do algebraic representations relate and compare to one another?
5. How can we communicate and generalize algebraic relationships?
Essential Vocabulary - multiplication/multiply, equations, unknown , reasonableness, mental computation, factor, product, equation, variable, equality,
division/divide, equations, remainders, addition/add, subtraction/subtract, estimation, rounding, benchmark numbers, pattern
We want students to understand how we use patterns and relationships of algebraic representations to generalize, communicate, and model situations in
mathematics.
4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. How to write a multiplication sentence.
1. That any given word problems can be
1. Write and identify equations and statements for
2. That a multiplication sentence can be comprised of
represented using an equation.
multiplicative comparisons.
factors, product, and variables.
2. That a multiplicative comparison is a
2. Identify and verbalize which quantity is being
3. That an equal sign within an equation shows that
situation in which one quantity is
multiplied and which number tells how many
both sides are equivalent.
multiplied by a specified number to get
times in a given word problem.
another quantity (e.g., “a is n times as
much as b”).
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. How to write a multiplication and division
1. That comparative situations can be solved
1. Use drawings, equations, and symbols to solve
sentence.
by writing equations with an unknown
multiplication and division problems.
2. That a multiplication sentence can be comprised of
variable.
2. Solve problems with an unknown product,
factors, product, and variables.
unknown group size, and unknown number of
3. That a division sentence can be comprised of
groups.
divisor, dividend, quotient, and variables.
4. That an equal sign within an equation shows that
both sides are equivalent
5. That the multiplicative comparison uses the key
words, “how many times more…”
6. The additive comparison uses the key words, “how
many more…”
4.OA.3: Solve multistep word problems within cultural contexts, including those of Montana American Indians, posed with whole numbers and having wholenumber 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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. How to compute using the four basic operations.
1. That a remainder needs to be appropriately 1. To use and discuss various strategies for solving
2. That some problems require multiple steps.
interpreted within the context of a word
multistep word problems.
3. That Montana American Indians are an integral
problem.
2. To use estimation strategies, including using
part of Montana’s culture.
2. That writing an equation will help solve
compatible numbers (numbers that sum to 10 or
4. That a remainder is a component of a division
word problem numerically.
100) or rounding to assess reasonableness.
problem.
3. That estimating (rounding, compatible
3. Solve multistep story problems using all four
5. Variables can be written in an equation to help
numbers, benchmark numbers should be
operations.
solve for an unknown quantity.
used to assess the reasonableness of an
answer.
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. The definition of …
1. That an array can be used to find factor pairs of
1. Name all the factors for a given number 1 -100.
a given number.
2. Name all the multiples for a given number 1 –
 Prime
2.
That
numbers
can
be
classified
according
to
100.
 Composite
their
factors.
3.
Classify a number as prime, composite, or
 Square
square based on its factors.
 Factor



Multiple
Factor Pair
Array
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.
Grade 4 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. That a pattern is a rule.
1. That patterns involving numbers or
1. Identify rules and features from patterns.
2. That rules can be written as equations using
symbols either repeat or grow.
2. Generate a numerical or shape pattern from a
variables.
2. That patterns and rules are related. A
given rule.
pattern is a sequence that repeats the same 3. Investigate different patterns to find rules, identify
process over and over. A rule dictates what
features in the patterns, and justify the reason for
that process will look like.
those features.
4. Use a t-chart as a tool to help students see number
patterns.