In third grade, students were introduced to the concepts of multiplication and division. They created models to show the operations, explored their properties and worked to master the basic multiplication and division facts. In Unit 2, students will extend their understanding of multiplication and division by working with larger numbers.
The key ideas focused on for multiplication (Standards 4.OA.2 & 4.NBT.5) in this unit include:
- Expressing multiplicative comparison with equations
- Solving problems using multiplicative comparison
- Using models to understand the process of multi-digit multiplication
- Multiplying a whole number of up to four digits by a 1-digit whole number using strategies based on place value and properties
- Multiplying two 2-digit numbers using strategies based on place value and properties
By using concrete models to show the process of multiplication, students are able to visualize the process, seeing the connections to place value concepts and the distributive property. The goal of visual models is not for students to use them for years because there are more efficient ways to multiply multi-digit numbers. The goal is for students to develop a strong understanding of the process as they visualize it through these models and make connections to their understanding of place value and properties. Students will also estimate products prior to multiplying, which is a critical way for them to build their number sense and also check the reasonableness of their answers. Students will be introduced to the standard algorithm for multiplication in fifth grade.
The key ideas focused on for division (Standard 4.NBT.6) in this unit include:
- Using place value strategies to find whole number quotients with up to four-digit dividends and one-digit divisors
- Interpreting remainders to division word problems
The emphasis in fourth grade is on developing strategies that are based on an understanding of place value, properties, and the relationship between multiplication and division. These strategies provide the foundation for the standard algorithm for division, although the standard algorithm is not expected until sixth grade. The goal is for students to understand the division process through contexts and investigation. They will primarily do this through word problems which give a context for the division process. Rather than simply memorizing steps to a procedure, they build an understanding of when and why we divide.
Although multiplication and division of whole numbers is the primary focus of Unit 2, there are several other non-prioritized standards ( that will also be covered at the beginning of the unit.
The key ideas focused on for those standards will include:
- Building an understanding of multiples and factors
- Investigating the concepts of prime and composite numbers
- Exploring number and shape patterns to solve problems
Your child will be taking notes on the standards throughout the unit in their Math Journals. Please remember that these are wonderful study tools that we encourage the students take home (as long as they remember to bring them back!) We will be teaching the students how to take very neat, detailed notes that will make awesome study tools!
4.1 Standards for Unit 2:
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 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. 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.
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.
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.
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.
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.
4.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.
*4.MD.2 is a standard that will appear in every unit in 4th grade and will be covered more thoroughly in Unit 7