Topic+One

= Topic One: Multiplication and Division: Meanings and Facts = Pacing (Duration of Unit): days 1. Makes sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. **Model with mathematics.** 5. **Use appropriate tools strategically.** 6. Attend to precision. 7. **Look for and make use of structure.** 8. Look for and express regularity in repeated reasoning. ||
 * ~ = Desired Results = ||
 * __**Transfer:**__
 * __**Established Goals:**__
 * 4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 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 multiplication comparison, e.g., by using drawings and equations with a symbol for the unknown number to represnt 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.


 * __Student "I Can" Statements__**
 * I can understand that multiplication fact problems can be seen as comparisons of groups (e.g., 24 = 4 x 6 can be thought of as 4 groups of 6 or 6 groups of 4).
 * I can multiply or divide to solve word problems by using drawings or writing equations and solving for a missing number.
 * I can use what I know about addition, subtraction, multiplication and division to solve multi-step word problems involving whole numbers.
 * I can represent word problems by using equations with a letter standing for the unknown number.
 * I can determine how reasonable my answers to word problems are by using estimation, mental math and rounding.
 * I can find all factor pairs for a number from 1 to 100.
 * I can determine whether a given whole number up to 100 is a prime or composite number.
 * I can create a number or shape pattern that follows a given rule.
 * I can notice different features of a pattern once it is created by a rule.


 * __Pre-Requisite Standards__**
 * 3.OA.1: Interpret products of whole numbers, e.g. interpret 5x7 as the total number of objects in 5 groups of 7 objects each.
 * 3.OA.2: Interpret whole number quotients of whole numbers, e.g., interpret 56/8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
 * 3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g. by using drawings and equations with a symbol for the unkown number to represent the problems.
 * 3.OA.5: Apply properties of operations as strategies to multiply and divide.
 * 3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of addition. ||
 * **__Big Ideas:__**
 * Operation Meanings and Relationships: There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.
 * Patterns, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.
 * Properties: For a given set of numbers there are relationships that are always true called properties, and these are the rules that govern arithmetic and algebra.
 * Basic Facts and Algorithms: Some strategies for basic facts use equivalence to transform calculations into simpler. ones.
 * Variable: Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.
 * Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems. || __**Essential Questions:**__
 * How can patterns and properties be used to find some multiplication facts?
 * How can unknown multiplication facts be found by breaking them apart into known facts?
 * How can unknown division facts be found by thinking about a related multiplication fact? ||
 * __**Students will know...**__
 * Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication. Repeated addition and arrays involve joining equal groups and are two ways to think about multiplication.
 * Some real-world problems involving joining or separating equal groups or comparison can be solved using division. Sharing and repeated subtraction involve separating equal groups and are two ways to think about division.
 * Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.
 * There are patterns in the products for multiplication facts with the factors if 2, 5, and 9.
 * Two numbers can be multiplied in any order. The product of any number and 0 is zero. The product of any number and 1 is that number.
 * Any number (except 0) divide by itself is equal to 1. Any number divided by 1 is that number. Zero divide by any number (except 0) is zero. Zero cannot be a divisor.
 * Basic multiplication facts with 3, 4, 6, 7, or 8 as a factor can be found by breaking apart the unknown fact into known facts.
 * Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation.
 * Some problems can be solved by identifying elements that repeat in a predictable way.

__**Vocabulary:**__ array, product, factor, multiple, Commutative Property of Multiplication, Zero Property of Multiplication, Identity Property of Multiplication, Distributive Property, inverse operations, fact family || __**Students will be skilled at...**__
 * Recognizing multiplication as repeated addition of equal groups used in arrays and comparison.
 * Using patterns to find products with factors of 2, 5, and 9.
 * Using multiplications properties to simplify computations.
 * Using the Distributive Property to find products of the factors of 3, 4, 6, 7, and 8 by breaking apart problems into simpler problems.
 * Recognizing patterns and being able to continue the pattern.
 * Using and drawing models to solve division problems.
 * Using arrays to write and complete multiplication and division fact families.
 * Using multiplication facts with 0 and 1 to learn about special division rules with 0 and 1.
 * Identifying multiplication facts related to division facts in order to solve division problems.
 * Drawing pictures to problem solve multiplication situations and use their pictures to write number sentences. ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment Tasks:**__
 * [|Performance Assessment Task-Bikes and Trikes-4.OA.2]
 * [|Performance Assessment Task-The Baker-4.OA.3]
 * [|Performance Assessment Task-Number Train-4.OA.4]
 * [|Performance Assessment Task-Buttons-4.OA.5] || __**Formative Assessments:**__


 * [[file:Formative Assessment-4.OA.1.docx]]
 * [[file:Formative Assessment-4.OA.2.docx]]
 * [[file:Formative Assessment-4.OA.3.docx]]
 * [[file:Formative Assessment-4.OA.4.docx]] ||
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__


 * 1-1:** Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication. Repeated addition and arrays involve joining equal groups and are two ways to think about multiplication.
 * 1-2:** There are patterns in the products for multiplication facts with the factors if 2, 5, and 9.
 * 1-3:** Two numbers can be multiplied in any order. The product of any number and 0 is zero. The product of any number and 1 is that number.
 * 1-4:** Basic multiplication facts with 3, 4, 6, 7, or 8 as a factor can be found by breaking apart the unknown fact into known facts.
 * 1-5:** Some problems can be solved by identifying elements that repeat in a predictable way.
 * 1-6:** Some real-world problems involving joining or separating equal groups or comparison can be solved using division. Sharing and repeated subtraction involve separating equal groups and are two ways to think about division.
 * 1-7:** Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.
 * 1-8:** Any number (except 0) divide by itself is equal to 1. Any number divided by 1 is that number. Zero divide by any number (except 0) is zero. Zero cannot be a divisor.
 * 1-9:** Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.
 * 1-10:** Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation. ||
 * __**Resources:**__


 * Problem of the Month: **
 * [|Measuring Mammals-4.OA.1]
 * [|Digging Dinosaurs-4.OA.3]
 * [|Friends You Can Count On-4.OA.3]
 * [|Squirreling It Away-4.OA.3, 4.OA.4]
 * [|The Wheel Shop-4.OA.3]
 * [|Courtney's Collection-4.OA.4]
 * [|Once Upon a Time-4.OA.4]
 * [|Between the Lines-4.OA.5]
 * [|Circular Reasoning-4.OA.5]


 * Centers:**
 * [|Representing Multiplicative Comparison Problems-4.OA.1]
 * [|Sample Multiplicative Comparison Problems-4.OA.2]
 * [|Multi-step Word Problems-4.OA.3]
 * [|Interpreting Remainders-4.OA.3]
 * [|Finding Multiples-4.OA.4]
 * [|Prime Number Hunt-4.OA.4]
 * [|Common Multiples-4.OA.4]
 * [|Least Common Multiples-4.OA.4]
 * [|Find the Factor-4.OA.4]
 * [|Square Numbers-4.OA.5]


 * SmartBoard Games:**
 * [|Multiplication-Speed Grid Challenge]
 * [|Multiplication-Sum Sense]
 * [|Multiplication-Ghost Blasters]
 * [|Division-Bingo]
 * [|Division-Sum Sense]
 * [|Division-Challenge] ||