Topic: Operations and Algebraic Thinking |
Common Core Mathematics 3-5 |
| Cluster Represent and solve problems involving multiplication and division. |
| | Grade 3 |
| | | 3.OA.1. | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total
number of objects in 5 groups of 7 objects each. For example, describe
a context in which a total number of objects can be expressed as 5 × 7. |
| | | 3.OA.2. | Interpret whole-number quotients of whole numbers, e.g., interpret
56 ÷ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when
56 objects are partitioned into equal shares of 8 objects each. For
example, describe a context in which a number of shares or a number of
groups can be expressed as 56 ÷ 8. |
| | | 3.OA.3. | Use multiplication and division within 100 to solve word problems in
situations involving equal groups, arrays, and measurement quantities,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem |
| | | 3.OA.4. | Determine the unknown whole number in a multiplication or division
equation relating three whole numbers. For example, determine the
unknown number that makes the equation true in each of the equations 8
× ? = 48, 5 = █ ÷ 3, 6 × 6 = ?. |
| Cluster Understand properties of multiplication and the relationship
between multiplication and division. |
| | Grade 3 |
| | | 3.OA.6. | Understand division as an unknown-factor problem. For example, find
32 ÷ 8 by finding the number that makes 32 when multiplied by 8. |
| Cluster Solve problems involving the four operations, and identify and
explain patterns in arithmetic. |
| | Grade 3 |
| | | 3.OA.8. | Solve two-step word problems using the four operations. 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.[Note:This standard is limited to problems posed with whole numbers and having wholenumber
answers; students should know how to perform operations in the conventional
order when there are no parentheses to specify a particular order (Order of
Operations]. |
| Cluster Use place value understanding and properties of operations to
perform multi-digit arithmetic.[A range of algorithms may be used] |
| | Grade 3 |
| | | 3.NBT.1. | Use place value understanding to round whole numbers to the nearest
10 or 100. |
| | | 3.NBT.2. | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. |
| Cluster Use the four operations with whole numbers to solve problems. |
| | Grade 4 |
| | | 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. |
| | | 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. |
| | | 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. |
| Cluster Gain familiarity with factors and multiples. |
| | Grade 4 |
| | | 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. |
| Cluster Generate and analyze patterns. |
| | Grade 4 |
| | | 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. |
| Cluster Write and interpret numerical expressions. |
| | Grade 5 |
| | | 5.OA.1. | Use parentheses, brackets, or braces in numerical expressions, and
evaluate expressions with these symbols. |
| | | 5.OA.2. | Write simple expressions that record calculations with numbers, and
interpret numerical expressions without evaluating them. For example,
express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7).
Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921,
without having to calculate the indicated sum or product. |
| Cluster Analyze patterns and relationships. |
| | Grade 5 |
| | | 5.OA.3. | Generate two numerical patterns using two given rules. Identify
apparent relationships between corresponding terms. Form ordered
pairs consisting of corresponding terms from the two patterns, and
graph the ordered pairs on a coordinate plane. For example, given the
rule “Add 3” and the starting number 0, and given the rule “Add 6” and the
starting number 0, generate terms in the resulting sequences, and observe
that the terms in one sequence are twice the corresponding terms in the
other sequence. Explain informally why this is so. |