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Grade 4 Math Unit 2

Multiplication and Division

Students will grow in their abilities to multiply and divide by working with multi-digit numbers. Students will also work with multi-step story problems with all four operations.

Note: Lessons will vary in length, depending on the amount of time you have with students, the resources that you choose to accompany the unit, the level of rigor within each learning target, and any other factors that may contribute to the pacing of your learning progressions. It is recommended that you adjust the pace and length of each learning progression(s) accordingly in response to these factors.

These learning progressions were developed using Next Generation Learning Standards and were cross-walked with the Common Core Standards.

Download the complete Grade 4 Math Unit 2 framework to customize for your own planning.

Essential Outcomes

Operations and Algebraic Thinking

  • NY-4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem.
  • NY-4.OA.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
  • NY-4.OA.3a: Represent these problems using equations or expressions with a letter standing for the unknown quantity.
  • NY-4.OA.3b: Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
  • NY-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.

Number and Operations in Base Ten

  • NY-4.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.
  • NY-4.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.

Other Standards Addressed in this Unit

Operations and Algebraic Thinking

  • NY-4.OA.1: Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. e.g.,
    • Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 or 7 times as many as 5.
    • Represent “Four times as many as eight is thirty-two” as an equation, 4 x 8 = 32.
  • NY-4.OA.5: Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself. e.g., 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.

Measurement and Data

  • NY-4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. e.g., Find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Essential Questions and Big Ideas

  • What are factors and multiples? What are patterns?
    • Factors are numbers that can multiply to make another number.
    • Multiples are numbers that are made when skip counting by a number.
    • A whole number is a multiple of each of its factors.
    • Prime numbers only have two factors, 1 and itself.
    • Composite numbers have more than two factors.
    • Patterns show relationships between things. 
    • In a pattern each term changes in a constant way.
  • What are efficient strategies to multiply multi-digit numbers?
    • Partial products can be used to multiply multi-digit numbers.
    • The area model is a way to organize partial products to multiply multi-digit numbers.
    • The multiplication algorithm is an organized method of partial products.
    • Multiplication is completed by multiplying by each place value. 
  • What are efficient strategies to divide multi-digit numbers by single digit numbers?
    • Partial quotients can be used to divide multi-digit numbers.
    • The area model is a way to organize partial quotients.
    • The division algorithm is an organized method of partial quotients.
    • Division is completed by dividing up each place value and then dividing the remainder.
    • In division the dividend is broken into multiples of the divisor. 
  • What is multiplicative comparison?
    • Multiplicative comparison represents comparisons based on multiplication.
    • Multiplicative comparison is phrased as “times as many”.
    • To solve multiplicative comparison you may need to multiply or divide, depending on if you are solving for a larger or smaller amount. 
  • How do I solve multi-step word problems?
    • Multi-step word problems have more than one unknown.
    • Sometimes an unknown is reliant on another unknown.
    • Multi-step word problems have more than one action or relationship.

Download the complete Grade 4 Math Unit 2 framework to customize for your own planning.