4.2 Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems. Use number sentences involving multiplication, division and unknowns to represent and solve real-world problems; create real-world situations corresponding to number sentences.
Vocabulary
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Standard Benchmarks
Benchmark: 4.2.1.1 Input-Output Rules
Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. For example: If the rule is "multiply by 3 and add 4," record the outputs for given inputs in a table. Identify a pattern that is consistent with these figures, create an input-output rule that describes the pattern, and use the rule to find the number of dots in the 10th figure. Benchmark: 4.2.2.1 Real-World to Number Sentence Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. For example: The number sentence a × b = 60 can be represented by the situation in which chairs are being arranged in equal rows and the total number of chairs is 60. Benchmark: 4.2.2.2 Number Sentence to Real World Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. For example: If $84 is to be shared equally among a group of children, the amount of money each child receives can be determined using the number sentence 84 ÷ n = d. Another example: Find values of the unknowns that make each number sentence true: 12 × m = 36 s = 256 ÷ t. Big Ideas and Essential Understandings
Fourth graders further develop their understanding of a function as they work with input-output rules involving more than one operation. They create, complete and extend input-output tables. Fourth graders describe patterns in given input-output situations/tables and find a rule. Given a rule, fourth graders are able to find the output for a corresponding input and find an input for a corresponding output. They realize the value of the output varies depending on the value of the input. Fourth graders use input-output rules involving addition, subtraction and multiplication to solve problems in various contexts.
Fourth graders use number sentences to represent real world situations involving multiplication, division and unknowns. They create a situation that can be represented by a given number sentence involving multiplication, division and unknowns. For instance, arranging 24 children into different sized groupings can be represented in the following number sentences, 24 ÷ A = B or 24 = A x B. They find values for unknowns that make number sentences true using the properties of multiplication and the relationship between multiplication and division Input-Output Rules: What students should know and be able to do [at a mastery level] related to these benchmarks:
Number Sentences: What students should know and be able to do [at a mastery level] related to these benchmarks:
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From a small seed a mighty trunk may grow.
-Aeschylus
-Aeschylus