OVERVIEW
In this unit students will:
● solve multi-step problems using the four operations
● use estimation to solve multiplication and division problems
● find factors and multiples
● identify prime and composite numbers
● generate patterns
● There are two common situations where division may be used: fair sharing (given the total amount and the number of equal groups, determine how many/much in each group) and measurement (given the total amount and the amount in a group, determine how many groups of the same size can be created).
● Some division situations will produce a remainder, but the remainder will always be less than the divisor. If the remainder is greater than the divisor, that means at least one more can be given to each group (fair sharing) or at least one more group of the given size (the dividend) may be created.
● How the remainder is explained depends on the problem situation.
● The dividend, divisor, quotient, and remainder are related in the following manner: dividend = divisor x quotient + remainder.
● The quotient remains unchanged when both the dividend and the divisor are multiplied or divided by the same number.
● Estimation is a helpful tool when finding the products of a 2- digit number multiplied by a 2-digit number.
● Multiplication and division can be represented using a rectangular area model.
● Multiplication may be used in problem contexts involving equal groups, rectangular arrays/area models, or rate.
● Multiply up to a 4-digit number by 1-digit number using strategies.
● Divide whole-numbers quotients and remainders with up to four-digit dividends and remainders with up to four-digit dividends and one-digit divisors.
In this unit students will:
● solve multi-step problems using the four operations
● use estimation to solve multiplication and division problems
● find factors and multiples
● identify prime and composite numbers
● generate patterns
- The properties of multiplication and division help us solve computation problems easily and provide reasoning for choices we make in problem solving.
● There are two common situations where division may be used: fair sharing (given the total amount and the number of equal groups, determine how many/much in each group) and measurement (given the total amount and the amount in a group, determine how many groups of the same size can be created).
● Some division situations will produce a remainder, but the remainder will always be less than the divisor. If the remainder is greater than the divisor, that means at least one more can be given to each group (fair sharing) or at least one more group of the given size (the dividend) may be created.
● How the remainder is explained depends on the problem situation.
● The dividend, divisor, quotient, and remainder are related in the following manner: dividend = divisor x quotient + remainder.
● The quotient remains unchanged when both the dividend and the divisor are multiplied or divided by the same number.
● Estimation is a helpful tool when finding the products of a 2- digit number multiplied by a 2-digit number.
● Multiplication and division can be represented using a rectangular area model.
● Multiplication may be used in problem contexts involving equal groups, rectangular arrays/area models, or rate.
● Multiply up to a 4-digit number by 1-digit number using strategies.
● Divide whole-numbers quotients and remainders with up to four-digit dividends and remainders with up to four-digit dividends and one-digit divisors.
Standards
Use the four operations with whole numbers to solve problems.
MGSE4.OA.1 Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity. a. 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. b. Represent verbal statements of multiplicative comparisons as multiplication equations.
MGSE4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
MGSE4.OA.3 Solve multistep word problems 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 symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Gain familiarity with factors and multiples.
MGSE4.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. Generate and analyze patterns.
MGSE4.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. Explain informally why the pattern will continue to develop in this way. 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.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
MGSE4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
MGSE4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place 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.
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
MGSE4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and 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.
Geometric Measurement: Understand concepts of angle and measure angles.
MGSE4.MD.8Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.