Grade 3 Math Unit Planning 2016 to 2017
PS 105
Unit # / Book(s) / Topic / Unit 2 / Book 1 / Multiplication and Division 1 / Approximate Days or Dates / 24 daysStage 1 - Identify Desired Results
Learning Outcomes
What relevant goals will this unit address?
(must come from curriculum; include specific Common Core standards)
Represent and solve problems involving multiplication and division.
3.OA.1: Interpret 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.
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 unknown number to represent the problem.
3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5: Apply properties of operations as strategies to multiply and divide.2Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
3.OA.6: Understand division as an unknown-factor problem.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Enduring Understandings
What understandings about the big ideas are desired? (what you want students to understand & be able to use several years from now)
What misunderstandings are predictable? / Essential Questions
Are there any potential cross-curricular connections during this chapter?
Students will understand that...
● Relationships can be described and generalizations made for mathematical situations that have numbers that repeat in predictable ways (for example, there are patterns in the products for multiplication facts with factors of 0, 1, 2, 5, and 9). Another example: since 40 is equal to 4 tens, 6 x 40 equals 6 groups of 4 tens, which equals 24 tens, which equals 240.
● Multiplication and division are inverse operations.
● Some real world problems involving joining equal groups or separating equal groups can be solved using multiplication or division.
● There are a variety of ways to model multiplication and division.
Related misconceptions…
● Students may fail to interpret objects as a group.(Ex. shelves ,teams, people etc.)
● Students sometimes only conceive of division as equal sharing.
● Students sometimes struggle to properly identify the total when given a word problem. / Essential Question:
What kind of real world problems can we solve with multiplication and division?
What kind of models can we use to represent multiplication and division situations?
Cross-curricular connections…
Knowledge:
What knowledge will student acquire as a result of this unit? This content knowledge may come from the chapter’s goals, or might also address pre-requisite knowledge that students will need for this unit. / Skills:
What skills will students acquire as a result of this unit? List the skills and/or behaviors that students will be able to exhibit as a result of their work in this unit.
Students will know...
● In Equal Group problems, one factor indicates the number of objects per group and the other factor indicates the number of groups. In the United States it is customary for the first number to indicate the number of groups, e.g., 3 x 4 is used to mean 3 groups of 4.
● In Array situations, the roles of the two factors do not differ. One factor indicates the rows and the other the columns. But if the array is rotated 90 degrees, the rows and columns are reversed.
● Multiplication is commutative.
● Multiplication is associative.
● The identity property of multiplication.
● Zero property of multiplication.
● Division is represented by problem contexts in which the total is known and either the number of groups or the number of objects in each group is unknown.
● That division facts can be found by thinking about multiplication (i.e., fact families).
● When 0 is divided by any non-zero number, the quotient is zero, and 0 cannot be a divisor. / Students will be able to…
● Interpret multiplication situations of equal groups and arrays (multiplicative comparison situations are introduced in grade four).
● Use a variety of strategies to multiply basic facts (single digit by single digit), beginning with skip counting, moving to more complex methods, and culminating by the end of third grade with memorization.
● Recognize both types of division situations in story problems (partitive and measurement).
● Use a variety of strategies to solve basic division facts.
Stage 2 – Assessment Evidence
Evidence
Through what evidence (work samples, observations, quizzes, tests, journals or other means) will students demonstrate achievement of the desired results? Formative and summative assessments used throughout the unit to arrive at the outcomes. / Student Self-Assessment
How will students reflect upon or self-assess their learning?
Pre-Assessment: Measuring Up
Benchmark 1: Demonstrate an understanding of multiplication and division as involving equal groups. Quiz 3
Benchmark 2: Solve multiplication and related division problems by using skip counting or known multiplication facts. Quizzes 1, 2 & 3
Benchmark 3: Interpret and use multiplication and division notation. Quizzes 1, 2 & 3
Benchmark 4: Demonstrate fluency with multiplication facts x1, x2, x5, and x10. Multiplication Facts Resource Masters, A9 in Session 4.4
Post-Assessment: Pearson Realize Unit Test Questions 1-3, 5-12, 14-16 / Students will be given documents to keep track of their own progress on learning their addition, subtraction, multiplication, and division.
Stage 3 – Learning Plan
# / Content Goal / Lesson Notes/Planned Differentiation / Additional Resources or Math Centers
This year the multiplication and division unit will be split up. This first unit develops the concepts and begins fluency work with a focus on the easier tables (1, 2, 5, and 10). Even though we are not starting with addition and subtraction this year, you could decide to add an addition/subtraction fact practice center to reengage students and assess which students may still not be fluent.
4 sessions / Investigation 1:
Things That Come in Groups
1.1 / Many Things Come in Groups / This is a nice introduction to multiplication. Be sure to assign SAB p. 2 for homework so that students can look for more things that come in groups at home. Be sure to do the “Stickers and Cubes” activity as that will become your first ten-minute math activity beginning tomorrow. / TMM: 1.2.5
No centers today.
1.2 / How Many in Several Groups / Do this lesson as written, but see the differentiation advice on TG p. 34. Also, be sure to read the Math Note in the margin on TG p. 35. / TMM: 1.2.6
No centers today.
1.3 / Solving Multiplication Problems / Do this lesson as written, noting the differentiation advice on TG p. 43. / TMM: 1.3.1
No centers today.
1.4 / Solving Problems About Our Pictures / Supplement this lesson with the appropriate choice of activities from TG pp. 50 to 52. / TMM: 1.3.2
No centers today.
6 sessions / Investigations 2:
Skip Counting and 100 Charts / Remember to follow the book’s advice on Ten-Minute Math, so switch to Counting Around the Class for this investigation. Consider adding an addition and subtraction fact center during this investigation.
2.1 / Highlighting Multiples on 100 Charts / Do this lesson as written, noting the ELL sentence stems suggested on TG p. 61. / TMM: 1.3.3
Optional Addition/Subtraction Facts center.
2.2 / More Multiples / Do this lesson as written, noting the differentiation advice and the very important Math Notes in the margins. / TMM: 1.3.4
Optional Addition/Subtraction Facts center.
2.3 / Solving Related Story Problems / Do this lesson as written, noting the very important Math Practice Note on TG p. 71. / TMM: 1.3.5
Optional Addition/Subtraction Facts center.
2.4 / Patterns and Relationships / Do this lesson as written, noting the very important Math Practice Note on TG p. 78. / TMM: 1.3.6
Optional Addition/Subtraction Facts center.
2.5 / Finding Products of Related Problems / Do this lesson as written. Today is the first day with three math centers so be sure to take some time to discuss your routines for centers. “How Many Legs?” may be quick and easy for some students, so be sure to have an enrichment activity available. / TMM: 1.3.7
● Highlighting 100 Charts (remaining numbers)
● How Many Legs?
● Addition/Subtraction Facts
2.6 / Using Multiplication / Do this lesson as written (continuing centers) and supplement as needed with the appropriate choice of activities from TG pp. 93 to 95. If students finish their highlighting charts, they can use the charts to work on multiplication fact fluency. / TMM: 1.4.1
● Highlighting 100 Charts
(remaining numbers)
● How Many Legs?
● Addition/Subtraction Facts
7 sessions / Investigation 3:
Arrays / Most teachers find that having students make their own set of paper array cards is too cumbersome, so this is optional (unless laminated array cards are not available in your classroom). However, students should each create a set of paper multiplication cards.
3.1 / Arranging Chairs / Do this lesson for everyone in the class as it introduces an important activity that will become a center throughout this investigation. Be sure to have students work in pairs on a single recording sheet. Encourage them to work TOGETHER on one number at a time. Differentiate by the size of the numbers you give to students. The higher the numbers, and the more factors a number has, the harder it is to do correctly. / TMM: 1.4.2
3.2 / Investigating Arrays / Skip the part of this lesson where students create their own array cards. Instead have struggling students do the Intervention activity on TG p. 148 and ready students do the Extension activity on TG p. 150. Don’t forget to end the lesson with the “How Many Squares?” discussion on TG pp. 113 to 115. / TMM: 1.4.3
3.3 / What’s the Area? / Unless you are having students create their own array cards (not recommended), substitute EngageNY Mod 1 Lesson 7 as one of the two activities for today. Note that students will have time to complete the centers work tomorrow. / TMM: 1.4.4
● Finding the Area
● EngageNY Mod 1 Lesson 7
● Addition/Subtraction Facts
3.4 / Array Games—Part 1 / Do this lesson as written, adding in an addition/subtraction fact center if you wish. / TMM: 1.4.5
● Factor Pairs
● Finding the Area
● Addition/Subtraction Facts
3.5 / Using What You Know / Today’s lesson (and 3.6) are fine as written unless students already know all of their multiplication facts through 10 x 10. Those students should be given different work. Here are some possibilities: problem solving tasks from the Inside Mathematics or Math Pickle sites, the Product Game (computer version—google it), additional work with arranging chairs with a challenging set of numbers to find the factors of. / TMM: 1.4.6
Optional centers today.
3.6 / Learning Multiplication Facts / See 3.5 notes. / TMM: 2.1.1
Optional centers today.
3.7 / Array Games—Part 2 / Do this lesson as written, but include some of the alternative tasks (see 3.5 notes) for students who know their multiplication tables already. If making Multiplication Cards is too cumbersome, be sure to model a variety of strategies in a teacher-led center. / TMM: 2.1.2
● Count and Compare
● Making Multiplication Cards
● Factor Pairs Game
● Optional challenge centers
6
sessions / Investigation 4:
Division / Be sure to read Teacher Note 9 (TG pp. 208-209) before teaching this unit.
4.1 / Solving Division Problems / Do this lesson as written, noting the differentiation advice and Math Notes (TG p. 158). / TMM: 2.1.3
No centers today.
4.2 / Multiply or Divide? / Do this lesson as written. / TMM: 2.1.4
No centers today.
4.3 / Writing Story Problems / Do this lesson as written. / TMM: 2.1.5
No centers today.
4.4 / Missing Factors / Do this lesson as written. (However, if you don’t have enough Array Cards, do it along with a center activity of your choosing.) / TMM: 2.1.6