5 Weeks
In this unit, students will:
●Review all standards based on student needs.
●Master standards:
○Add and subtract within 20 from memory
○Add and subtract within 100
●Extend standards to preview 3rdGrade:
○3.OA.1 Interpret multiplication with arrays
○3.OA.2 Interpret division with arrays
Unit Resources
Unit 7 Overview Video Parent Letter
Topic 1/2 Extend 3rdGrade:
Big Ideas/Enduring Understandings:
- Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups and arrays; multiplication is finding an unknown product, and division is finding an unknown factor in these situations.
- How are multiplication and division related?
Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.
Represent and solve problems involving multiplication and division.
MGSE3.OA.1Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
MGSE3.OA.2Interpret 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 (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groupscan you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Instructional Strategies
“Multiplication and division are commonly taught separately. However, it is very important to combine the two shortly after multiplication has been introduced. This will help the students to see the connection between the two.” (Van de Walle and Lovin, Teaching Student-Centered Mathematics
3-5, p. 60)
Sets of counters and tiles are great manipulatives to illustrate equal groups. This will aid students in solving both multiplication and division problems. They should represent the model first, then students should illustrate with drawings attaching the equations to all models.
This shows multiplication using grouping with 3 groups of 5 objects and can be written as 3 × 5.
Third graders begin division by sharing. Three students need to share 12 trapezoids equally.
Students find the total number of objects using rectangular arrays, such as a 5 x 5, and wrote equations to represent the sum. This is called unitizing, and it requires students to count groups, not just objects. They see the whole as a number of groups of a number of objects. This strategy is a foundation for multiplication in that students should make a connection between repeated addition and multiplication.
Common Misconceptions
Some common misconceptions that students may have are thinking a symbol (? or ) is always the place for the answer. This is especially true when the problem is written as 15 ÷ 3 =? or 15 = x 3. Students also think that 3 ÷ 15 = 5 and 15 ÷ 3 = 5 are the same equations. The use of models is essential in helping students eliminate this understanding.
Another key misconception is that the use of a symbol to represent a number once cannot be used to represent another number in a different problem/situation. Presenting students with multiple situations in which they select the symbol and explain what it represents will counter this misconception.
Evidence of Learning
By the conclusion of this unit, students should be able to demonstrate the following competencies:
- use arrays to interpret products of whole numbers
- use arrays to interpret whole number quotients of whole numbers
Adopted Resources
My Math:
Chapter 4: Understanding Multiplication
4.1 Hands on modeling
4.2 Repeated addition
4.3 Arrays
4.4 Arrays and multiplication
Chapter 5: Understanding Division
5.1 Hands on modeling
5.2 Equal shares
5.3 Relating to subtraction
5.4 Relating to multiplication
*These lessons are not to be completed consecutively as it is way too much material. They are designed to help support you as you teach your standards. / Adopted Online Resources
My Math
Teacher User ID: ccsde0(enumber)
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
Exemplars
User: Cobb Email
Password: First Name
Suggested Exemplar:
- Equal Snacks
Chapter 2: Multiplication
2.1 Rectangular Arrays
2.2 Arrays of Square Tiles
Additional Web Resources
Suggested Manipulatives
sets of counters
base ten blocks
multiplication table / Vocabulary
equation
expression
multiplication
factor
product
multiple
area
division
dividend
divisor
quotient / Suggested Literature
Each Orange Had Eight Slices
Two of Everything
State Task Descriptions
Scaffolding Task / Task that build up to the learning task.
Constructing Task / Task in which students are constructing understanding through deep/rich contextualized problem solving
Practice Task / Task that provide students opportunities to practice skills and concepts.
Culminating Task / Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.
Formative Assessment Lesson (FAL) / Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.
3-Act Task / Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.
Task Name / Task Type/
Grouping Strategy / Content
Standard / Content Addressed / Brief Description
One Hundred Hungry Ants! / Scaffolding Task
Individual/Partners / Multiplication and Arrays / MGSE3.OA.1 / In this task, students will determine the factors of a product by creating equal groups of counters/colored tiles.
What’s My Product? / Scaffolding Task
Individual/Partners / Multiplication / MGSE3.OA.1 / This task allows students to interpret products of whole numbers by creating equal groups with manipulatives.
The Doorbell Rang / Scaffolding Task
Individual/Partners / Division / MGSE3.OA.2 / In this task, students will be introduced to division.
Stuck on Division / Scaffolding Task
Individual/Partners / Division / MGSE3.OA2 / In this task, students will experiment with a set of 12 connecting cubes to determine the division patterns when the dividend is 12.
Base Ten Multiplication / Practice Task
Partners / Multiplication / MGSE3.OA.1 / In this task students determine the factors of 100 by creating addition and/or multiplication models by using Base Ten Blocks.
Egg Tower / 3-Act Task
Whole Group / Multiplication and Arrays / MGSE3.OA.1 / In this task, students will view a picture and tell what they noticed. Next, they will be asked to discuss what they wonder about or are curious about. Students will then use mathematics to answer their own questions.
Shake, Rattle, and Roll Revisited / Practice Task
Individual/Partners / Multiplication / MGSE3.OA.1
MGSE3.OA.2 / In this task, students will roll two cubes to get factors and use factors to find the product.
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2ndGrade Unit 72015-2016