Primary Standard:
MAFS.4.OA.1.3: 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.
MAFS.4.OA.3.5: 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.
MAFS.4.OA.1a: Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60 + 24 = 57 + 27 is true or false.
MAFS.OA.1b: Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example, solve 76 + 9 = n + 5 for n by arguing that 9 is 4 more than 5, so the unknown number must be greater than 76.
Content Knowledge:
A foundational problem-solving skill is knowing which operation makes sense to solve a problem, and not by relying on key words. Modeling the operations using drawings or diagrams and discussing the contexts, including the interpretation of remainders, and how they relate to each operation help students expand their understanding.
In this Unit, students will look for and make sense of both number and shape patterns. Students will explore number patterns that follow given rules, such as adding 3 or divide by 2 then subtract 3, allowing them to relate one number to the next on in the pattern and make predictions about terms further along in the pattern. Students should also generalize about the patterns they see, for example when the rule is adding 7, the numbers alternate between odd and even. The aim of comparative relational thinking is to begin making a transition from purely arithmetical thinking to algebraic thinking. Rather than adding or subtracting to determine if two sides of an equation are equal, students are asked to use comparative relational thinking to analyze the relationship between the terms on either side of the equation. Students will use the relationship between terms on either side of the equation to find an unknown number mentally. Scrutiny of students’ mistakes will provide valuable knowledge as to how the students see equivalency, as well as the extent of their development of number sense.
GCG 1 – Learning Goal: As a mathematician, I can Solve up to three step problems involving the four operations and including remainders
- Step 1: Represent multi-step problems with equations involving any of the four operations, where the unknown is the sum, difference, product, or quotient
- Step 2: Solve multi-step problems involving any of the four operations, where the unknown is in a variety of positions
GCG 2 – Learning Goal: As a mathematician, I can Extend or generate patterns for given one- or two-step rules
- Step 1: Extend a number or shape pattern that follows a given one-step rule
- Step 2: Generate and analyze number patterns of up to two-steps
- Step 3: Generate and analyze shape patterns of up to two-steps
GCG 3 – Learning Goal: As a mathematician, I can Use comparative relational thinking to determine the value of a variable
- Step 1: Determine whether an equation using addition and subtraction is true or false using comparative relational thinking
- Step 2: Determine whether an equation using multiplication and division is true or false using comparative relational thinking
- Step 3: Determine the unknown number in an addition and subtraction equation relating four whole numbers
- Step 4: Determine the unknown number in a multiplication and division equation relating four whole numbers