Standards

###
### PA Core Standards - CC.2: PA Core: Mathematics
Standard - CC.2.1.4.B.1: Apply place value concepts to show an understanding of multi-digit whole numbers.

### Eligible Content

**M04.A-T.1.1.1:** Demonstrate
an understanding that in a multi-digit whole number (through
1,000,000), a digit in one place represents ten times what it represents
in the place to its right. Example: Recognize that in the number 770,
the 7 in the hundreds place is ten times the 7 in the tens place.
**M04.A-T.1.1.2:** Read and write whole numbers in expanded, standard, and word form through 1,000,000.
**M04.A-T.1.1.3:** Compare
two multi-digit numbers through 1,000,000 based on meanings of the
digits in each place, using >, =, and < symbols.
**M04.A-T.1.1.4:** Round multi-digit whole numbers (through 1,000,000) to any place.
### Eligible Content

**M04.A-T.2.1.1:** Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000).
**M04.A-T.2.1.2:** Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers.
**M04.A-T.2.1.3:** Divide up to four-digit dividends by one-digit divisors with answers written as whole-number quotients and remainders.
**M04.A-T.2.1.4:** Estimate
the answer to addition, subtraction, and multiplication problems using
whole numbers through six digits (for multiplication, no more than 2
digits × 1 digit, excluding powers of 10).
### Eligible Content

**M04.A-F.1.1.1:** Recognize and generate equivalent fractions.
**M04.A-F.1.1.2:** Compare
two fractions with different numerators and different denominators
(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the
symbols >, =, or < and justify the conclusions.
### Eligible Content

**M04.A-F.2.1.1:** Add
and subtract fractions with a common denominator (denominators limited
to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be
simplified; and no improper fractions as the final answer).
**M04.A-F.2.1.2:** Decompose
a fraction or a mixed number into a sum of fractions with the same
denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100),
recording the decomposition by an equation. Justify decompositions
(e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 +
1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 +
1/12
**M04.A-F.2.1.3:** Add
and subtract mixed numbers with a common denominator (denominators
limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with
subtraction; fractions do not need to be simplified; and no improper
fractions as the final answers).
**M04.A-F.2.1.4:** Solve
word problems involving addition and subtraction of fractions referring
to the same whole or set and having like denominators (denominators
limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
**M04.A-F.2.1.5:** Multiply
a whole number by a unit fraction (denominators limited to 2, 3, 4, 5,
6, 8, 10, 12, and 100 and final answers do not need to be simplified or
written as a mixed number). Example: 5 × (1/4) = 5/4
**M04.A-F.2.1.6:** Multiply
a whole number by a non-unit fraction (denominators limited to 2, 3, 4,
5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified
or written as a mixed number). Example: 3 × (5/6) = 15/6
**M04.A-F.2.1.7:** Solve
word problems involving multiplication of a whole number by a fraction
(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
### Eligible Content

**M04.A-F.3.1.1:** Add
two fractions with respective denominators 10 and 100. Example: Express
3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100.
**M04.A-F.3.1.2:** Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.
**M04.A-F.3.1.3:** Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions.Standard Area - CC.2.2: Algebraic Concepts
### Eligible Content

**M04.B-O.1.1.1:** Interpret
a multiplication equation as a comparison. Represent verbal statements
of multiplicative comparisons as multiplication equations. Example 1:
Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7
times as many as 5. Example 2: Know that the statement 24 is 3 times as
many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3.
**M04.B-O.1.1.2:** Multiply
or divide to solve word problems involving multiplicative comparison,
distinguishing multiplicative comparison from additive comparison.
Example: Know that 3 × 4 can be used to represent that Student A has 4
objects and Student B has 3 times as many objects not just 3 more
objects.
**M04.B-O.1.1.3:** Solve
multi-step word problems posed with whole numbers using the four
operations. Answers will be either whole numbers or have remainders that
must be interpreted yielding a final answer that is a whole number.
Represent these problems using equations with a symbol or letter
standing for the unknown quantity.
**M04.B-O.1.1.4:** Identify the missing symbol (+, –, ×, ÷, =, <, and >) that makes a number sentence true (single-digit divisor only).
### Eligible Content

**M04.B-O.2.1.1:** Find
all factor pairs for a whole number in the interval 1 through 100.
Recognize that a whole number is a multiple of each of its factors.
Determine whether a given whole number in the interval 1 through 100 is a
multiple of a given onedigit number. Determine whether a given whole
number in the interval 1 through 100 is prime or composite.
### Eligible Content

**M04.B-O.3.1.1:** 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.
Example 1: Given the rule “Add 3” and the starting number 1, generate
terms in the resulting sequence and observe that the terms alternate
between odd and even numbers. Example 2: Given the rule “increase the
number of sides by 1” and starting with a triangle, observe that the
tops of the shapes alternate between a side and a vertex.
**M04.B-O.3.1.2:** Determine the missing elements in a function table (limit to +, –, or × and to whole numbers or money).
**M04.B-O.3.1.3:** Determine the rule for a function given a table (limit to +, –, or × and to whole numbers).
### Eligible Content

**M04.C-G.1.1.1:** Draw
points, lines, line segments, rays, angles (right, acute, and obtuse),
and perpendicular and parallel lines. Identify these in twodimensional
figures.
**M04.C-G.1.1.2:** 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.
**M04.C-G.1.1.3:** Recognize
a line of symmetry for a twodimensional figure as a line across the
figure such that the figure can be folded along the line into mirroring
parts. Identify line-symmetric figures and draw lines of symmetry (up to
two lines of symmetry).
### Eligible Content

**M04.C-G.1.1.1:** Draw
points, lines, line segments, rays, angles (right, acute, and obtuse),
and perpendicular and parallel lines. Identify these in twodimensional
figures.
**M04.C-G.1.1.2:** 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.
**M04.C-G.1.1.3:** Recognize
a line of symmetry for a twodimensional figure as a line across the
figure such that the figure can be folded along the line into mirroring
parts. Identify line-symmetric figures and draw lines of symmetry (up to
two lines of symmetry).
### Eligible Content

**M04.C-G.1.1.1:** Draw
points, lines, line segments, rays, angles (right, acute, and obtuse),
and perpendicular and parallel lines. Identify these in twodimensional
figures.
**M04.C-G.1.1.2:** 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.
**M04.C-G.1.1.3:** Recognize
a line of symmetry for a twodimensional figure as a line across the
figure such that the figure can be folded along the line into mirroring
parts. Identify line-symmetric figures and draw lines of symmetry (up to
two lines of symmetry).
### Eligible Content

**M04.D-M.1.1.1:** Know
relative sizes of measurement units within one system of units
including standard units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal),
metric units (cm, m, km; g, kg; and mL, L), and time (sec, min, hr,
day, wk, mo, and yr). Within a single system of measurement, express
measurements in a larger unit in terms ofa smaller unit. A table of
equivalencies will be provided. Example 1: Know that 1 kg is 1,000 times
as heavy as 1 g. Example 2: Express the length of a 4-foot snake as 48
in.
**M04.D-M.1.1.2:** Use
the four operations to solve word problems involving distances,
intervals of time (such as elapsed time), liquid volumes, masses of
objects; 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.
**M04.D-M.1.1.3:** Apply
the area and perimeter formulas for rectangles in real-world and
mathematical problems (may include finding a missing side length). Whole
numbers only. The formulas will be provided.
**M04.D-M.1.1.4:** Identify
time (analog or digital) as the amount of minutes before or after the
hour. Example 1: 2:50 is the same as 10 minutes before 3:00. Example 2:
Quarter past six is the same as 6:15.
### Eligible Content

**M04.D-M.2.1.1:** Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8).
**M04.D-M.2.1.2:** Solve
problems involving addition and subtraction of fractions by using
information presented in line plots (line plots must be labeled with
common denominators, such as 1/4, 2/4, 3/4).
**M04.D-M.2.1.3:** Translate information from one type of display to another (table, chart, bar graph, or pictograph).
### Eligible Content

**M04.D-M.2.1.1:** Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8).
**M04.D-M.2.1.2:** Solve
problems involving addition and subtraction of fractions by using
information presented in line plots (line plots must be labeled with
common denominators, such as 1/4, 2/4, 3/4).
**M04.D-M.2.1.3:** Translate information from one type of display to another (table, chart, bar graph, or pictograph).
### Eligible Content

**M04.D-M.3.1.1:** Measure angles in whole-number degrees using a protractor. With the aid of a protractor, sketch angles of specified measure.
**M04.D-M.3.1.2:** Solve
addition and subtraction problems to find unknown angles on a diagram
in real-world and mathematical problems. (Angles must be adjacent and
non-overlapping.)

### PA Core Standards - CC.2: PA Core: Mathematics Standard - CC.2.1.4.B.1: Apply place value concepts to show an understanding of multi-digit whole numbers.

### Eligible Content

**M04.A-T.1.1.1:**Demonstrate an understanding that in a multi-digit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right. Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens place.

**M04.A-T.1.1.2:**Read and write whole numbers in expanded, standard, and word form through 1,000,000.

**M04.A-T.1.1.3:**Compare two multi-digit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols.

**M04.A-T.1.1.4:**Round multi-digit whole numbers (through 1,000,000) to any place.

### Eligible Content

**M04.A-T.2.1.1:**Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000).

**M04.A-T.2.1.2:**Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers.

**M04.A-T.2.1.3:**Divide up to four-digit dividends by one-digit divisors with answers written as whole-number quotients and remainders.

**M04.A-T.2.1.4:**Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding powers of 10).

### Eligible Content

**M04.A-F.1.1.1:**Recognize and generate equivalent fractions.

**M04.A-F.1.1.2:**Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the conclusions.

### Eligible Content

**M04.A-F.2.1.1:**Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).

**M04.A-F.2.1.2:**Decompose a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 + 1/12

**M04.A-F.2.1.3:**Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).

**M04.A-F.2.1.4:**Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).

**M04.A-F.2.1.5:**Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 × (1/4) = 5/4

**M04.A-F.2.1.6:**Multiply a whole number by a non-unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 × (5/6) = 15/6

**M04.A-F.2.1.7:**Solve word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).

### Eligible Content

**M04.A-F.3.1.1:**Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100.

**M04.A-F.3.1.2:**Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.

**M04.A-F.3.1.3:**Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions.Standard Area - CC.2.2: Algebraic Concepts

### Eligible Content

**M04.B-O.1.1.1:**Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3.

**M04.B-O.1.1.2:**Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects.

**M04.B-O.1.1.3:**Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity.

**M04.B-O.1.1.4:**Identify the missing symbol (+, –, ×, ÷, =, <, and >) that makes a number sentence true (single-digit divisor only).

### Eligible Content

**M04.B-O.2.1.1:**Find all factor pairs for a whole number in the interval 1 through 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the interval 1 through 100 is a multiple of a given onedigit number. Determine whether a given whole number in the interval 1 through 100 is prime or composite.

### Eligible Content

**M04.B-O.3.1.1:**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. Example 1: Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule “increase the number of sides by 1” and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex.

**M04.B-O.3.1.2:**Determine the missing elements in a function table (limit to +, –, or × and to whole numbers or money).

**M04.B-O.3.1.3:**Determine the rule for a function given a table (limit to +, –, or × and to whole numbers).

### Eligible Content

**M04.C-G.1.1.1:**Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

**M04.C-G.1.1.2:**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.

**M04.C-G.1.1.3:**Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).

### Eligible Content

**M04.C-G.1.1.1:**Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

**M04.C-G.1.1.2:**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.

**M04.C-G.1.1.3:**Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).

### Eligible Content

**M04.C-G.1.1.1:**Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

**M04.C-G.1.1.2:**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.

**M04.C-G.1.1.3:**Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).

### Eligible Content

**M04.D-M.1.1.1:**Know relative sizes of measurement units within one system of units including standard units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units (cm, m, km; g, kg; and mL, L), and time (sec, min, hr, day, wk, mo, and yr). Within a single system of measurement, express measurements in a larger unit in terms ofa smaller unit. A table of equivalencies will be provided. Example 1: Know that 1 kg is 1,000 times as heavy as 1 g. Example 2: Express the length of a 4-foot snake as 48 in.

**M04.D-M.1.1.2:**Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; 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.

**M04.D-M.1.1.3:**Apply the area and perimeter formulas for rectangles in real-world and mathematical problems (may include finding a missing side length). Whole numbers only. The formulas will be provided.

**M04.D-M.1.1.4:**Identify time (analog or digital) as the amount of minutes before or after the hour. Example 1: 2:50 is the same as 10 minutes before 3:00. Example 2: Quarter past six is the same as 6:15.

### Eligible Content

**M04.D-M.2.1.1:**Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8).

**M04.D-M.2.1.2:**Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4).

**M04.D-M.2.1.3:**Translate information from one type of display to another (table, chart, bar graph, or pictograph).

### Eligible Content

**M04.D-M.2.1.1:**Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8).

**M04.D-M.2.1.2:**Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4).

**M04.D-M.2.1.3:**Translate information from one type of display to another (table, chart, bar graph, or pictograph).

### Eligible Content

**M04.D-M.3.1.1:**Measure angles in whole-number degrees using a protractor. With the aid of a protractor, sketch angles of specified measure.

**M04.D-M.3.1.2:**Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (Angles must be adjacent and non-overlapping.)