4th grade Reference Guide for Investigations

2010 Arizona Standards
Common Core Reference Guide for
Investigations
4th Grade
Domain Cluster Standard Unit Unit Unit Unit Unit Unit Unit Unit Unit
1 2 3 4 5 6 7 8 9
Use the four operations 4.OA.1. Interpret a multiplication equation as a comparison, e.g., X X
interpret 35 = 5  7 as a statement that 35 is 5 times as many as 7 and
with whole numbers to 7 times as many as 5. Represent verbal statements of multiplicative
solve problems. comparisons as multiplication equations. X X
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,
Operations and Algebraic Thinking (OA)

distinguishing multiplicative comparison from additive comparison.
4.OA.3. Solve multistep word problems posed with whole numbers and X X X
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.
AZ.4.OA.3.1 Solve a variety of problems based on the multiplication X X X
principle of counting.
a. Represent a variety of counting problems using arrays,
charts, and systematic lists, e.g., tree diagram.
b. Analyze relationships among representations and make
connections to the multiplication principle of counting.

Gain familiarity with 4.OA.4. Find all factor pairs for a whole number in the X
range 1–100. Recognize that a whole number is a multiple
factors and multiples. 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.

Generate and analyze 4.OA.5. Generate a number or shape pattern that follows a given rule. X X
Identify apparent features of the pattern that were not explicit in the rule
patterns. 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.

4th Grade Reference Guide
Created on 2/4/2012 9:07 PM -1-

Investigations
4th Grade
Generalize place value 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one X
place represents ten times what it represents in the place to its right.
understanding for
Number and Operations in Base Ten

For example, recognize that 700  70 = 10 by applying concepts of
multidigit whole numbers. place value and division.
4.NBT.2. Read and write multi-digit whole numbers using base-ten
numerals, number names, and expanded form. Compare two multi-digit X X X
numbers based on meanings of the digits in each place, using >, =, and
< symbols to record the results of comparisons.
4.NBT.3. Use place value understanding to round multi-digit whole
numbers to any place. X
(NBT)

Use place value 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the X X X
standard algorithm.
understanding and 4.NBT.5. Multiply a whole number of up to four digits by a one-digit
properties of operations to whole number, and multiply two two-digit numbers, using strategies X X X
based on place value and the properties of operations. Illustrate and
perform multi-digit explain the calculation by using equations, rectangular arrays, and/or
arithmetic. area models.
4.NBT.6. Find whole-number quotients and remainders with up to four-
digit dividends and one-digit divisors, using strategies based on place X X X
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.

Extend understanding of 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x X
Operations—Fractions

fraction equivalence and b) by using visual fraction models, with attention to how the number
and size of the parts differ even though the two fractions themselves
ordering. are the same size. Use this principle to recognize and generate
Number and

equivalent fractions.
4.NF.2. Compare two fractions with different numerators and different
(NF)

denominators, e.g., by creating common denominators or numerators, X
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.

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Investigations
4th Grade
Build fractions from unit 4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. X
fractions by applying and a. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
extending previous b. Decompose a fraction into a sum of fractions with the same
understandings of denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by
operations on whole using a visual fraction model.
numbers. 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.
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.
4.NF.4. Apply and extend previous understandings of multiplication to X
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.)
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?

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Investigations
4th Grade
Understand decimal 4.NF.5. Express a fraction with denominator 10 as an equivalent X
fraction with denominator 100, and use this technique to add two
notation for fractions, and fractions with respective denominators 10 and 100. For example,
Number and Operations—

compare decimal express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (Students who
fractions. can generate equivalent fractions can develop strategies for adding
fractions with unlike denominators in general. But addition and
Fractions (NF)

subtraction with unlike denominators in general is not a requirement at
Continued

this grade.)
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; X
locate 0.62 on a number line diagram
4.NF.7. Compare two decimals to hundredths by reasoning about their
size. Recognize that comparisons are valid only when the two decimals X X
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.

Solve problems involving 4.MD.1. Know relative sizes of measurement units within one system of X X X
units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a
measurement and
Measurement and Data (MD)

single system of measurement, express measurements in a larger unit
conversion of 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.
measurements from a Express the length of a 4 ft snake as 48 in. Generate a conversion
larger unit to a smaller table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),
unit. 4.MD.2. Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects, and X X X X X X
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.
4.MD.3. Apply the area and perimeter formulas for rectangles in real
world and mathematical problems. For example, find the width of a X
rectangular room given the area of the flooring and the length, by
viewing the area formula as a multiplication equation with an unknown
factor

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Investigations
4th Grade
Represent and interpret 4.MD.4. Make a line plot to display a data set of measurements in X X
fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and
data.
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.
Measurement and Data (MD)

Geometric measurement: 4.MD.5. Recognize angles as geometric shapes that are formed X
wherever two rays share a common endpoint, and understand
understand concepts of concepts of angle measurement:
angle and measure 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
angles. 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
4.MD.6. Measure angles in whole-number degrees using a protractor.
Sketch angles of specified measure.
4.MD.7. Recognize angle measure as additive. When an angle is
X
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
X
world and mathematical problems, e.g., by using an equation with a
symbol for the unknown angle measure.
Draw and identify 4.G.1. Draw points, lines, line segments, rays, angles (right, acute, X
obtuse), and perpendicular and parallel lines. Identify these in two-
lines and angles, and dimensional figures.
Geometry (G)

classify shapes by 4.G.2. Classify two-dimensional figures based on the presence or X
absence of parallel or perpendicular lines, or the presence or absence
properties of their of angles of a specified size. Recognize right triangles as a category,
lines and angles. and identify right triangles.
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 X
into matching parts. Identify line-symmetric figures and draw lines of
symmetry.

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Investigations
4th Grade
4.MP.1. Make sense of problems and persevere in solving them.
In fourth grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem
and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking
themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.

4.MP.2. Reason abstractly and quantitatively.
Fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at
hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals.
Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.

4.MP.3. Construct viable arguments and critique the reasoning of others.
In fourth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain their thinking and make connections between
models and equations. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and
“Why is that true?” They explain their thinking to others and respond to others’ thinking.

4.MP.4. Model with mathematics.
Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart,
list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these
representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense.

4.MP.5. Use appropriate tools strategically.
Fourth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may
use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size of
units within a system and express measurements given in larger units in terms of smaller units.

4.MP.6. Attend to precision.
As fourth graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are
careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line plot.

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Investigations
4th Grade
4.MP.7. Look for and make use of structure.
In fourth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations to explain calculations (partial products model). They
relate representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting. They generate number or shape patterns that follow a
given rule.

4.MP.8. Look for and express regularity in repeated reasoning.
Students in fourth grade should notice repetitive actions in computation to make generalizations Students use models to explain calculations and understand how algorithms work.
They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent fractions

Created on 2/4/2012 9:07 PM -7-

4th grade Reference Guide for Investigations

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4th grade Reference Guide for Investigations