1.cdn.edl.io Web viewSAP p. 44 has a good explanation of how they are used. ... See TE pp. 1EE-1II for an explanation of the plan to develop student fluency with basic multiplication

North Adams Public Schools Grade 3 Math Multiplication with 0-5, 9, and 10 Unit 1 (30 days)

In this unit, students learn a variety of ways to practice basic multiplication and division. They learn strategies, investigate the relationship between multiplication and division, and use math drawings and equations to represent and solve word problems. Students begin to develop fluency with multiplication and division facts through the use of strategies. The first two units in Math Expressions are devoted to this topic so that students can work throughout the year to become fluent with single digit multiplication and division facts.

Throughout the program, daily lessons include suggestions for differentiating instruction, ELL students, Math Talk, fluency activities, teaching notes, math background, center activities, and formative assessment ideas. Teacher Edition, TE p. 11 lists the materials and manipulatives used throughout grade 3. The Appendix of each Teacher Edition is another valuable resource, with reference tables, problem types, vocabulary activities, student glossary, teacher glossary, and more.

Math Vocabulary

array equal groups oddcolumns even productCommutative Property factor quotientdividend multiple rowsdivisor multiplication strategy

multiplier variable


Big Idea 1: Meanings of Multiplication and Division: 5s and 2s3.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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8.3.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.1

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 = ?.3.OA.5 Apply properties of operations as strategies to multiply and divide.2 Examples: 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. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.3.OA.8 Solve two-step word problems using the four operations. 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.3

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.

1 See Glossary, Table 2.2 Students need not use formal terms for these properties.3 This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).


Day Lesson Student Learning Objective(s) NotesMon.9/7/15

Unit 1 Lesson 1Multiply with 5MX pp. 1-10

Explore patterns counting by 5s Learn the Home-Practice routine

Formative Assessmentp. 8 Check for Understanding. How can multiplication be used to solve an addition problem like this one: 5 + 5 + 5 + 5 + 5 + 5 + 5 =

Throughout Math Expressions, the second factor represents group size, i.e. 5 x 7 can be read as five groups of seven. This language promotes understanding of the operation. Include practice representing expressions with counters over the course of the unit to help all students understand the concept.

Relate the MathBoard representation to a number line.

The Home-Practice routine is established early on. Enlist parent and parent helpers to practice multiplication facts with children.

Tue.9/8/15

Unit 1 Lesson 2Multiplication as Equal GroupsMX pp. 11-18

Write multiplication equations for equal group pictures

Make math drawings to help solve equal group problems

Make equal shares drawing to represent equal groups

Formative Assessmentp. 16. Check for Understanding. When is an Equal Shares drawing better than an Equal Groups drawing?

Quick Practice routines can be used to transition into math or may be used at other times of the day.

TE p. 14 Make a Math Drawing would be a great chart to create that students can reference to remember what each number in a multiplication problem means.

TE p. 18 Art Connection. This activity would make a good display of student work on multiplication, maybe adding more numbers to show the number or groups, the size of the groups, and an equation to show how many in all.


Wed. 9/9/15

Unit 1 Lesson 3Multiplication and ArraysMX pp. 19-32

Use the Signature and Study sheets with a partner

Write multiplication equations for arrays Apply the Commutative Property as a

strategy to multiply

Formative Assessmentp. 30 Check for Understanding. Explain why switching the order of the factors does not change the product. Use arrays to explain your answer.

Set up classroom routines for using the signature sheet to be sure students get additional practice with facts.

TE p. 24 This example of Less than/Greater than could be a small chart hung where all can see. Instead of the alligator, teach children that when reading the sign, they say “is less than” if the small end of the symbol comes first and they say “is greater than” when the larger end of the symbol comes first. The alligator story only helps students when they can see which is more or less right away. If the problem makes that difficult, they struggle to read the symbol properly.

Thu.9/10/15

Unit 1 Lesson 4The Meaning of DivisionMX pp. 33-44

Solve division word problems where the number of groups is unknown

Solve division word problems where the group size is unknown

Formative Assessmentp. 42 Check for Understanding. What multiplication with an unknown can you write to find the answer to 20 ÷ 5?

TE p. 34 Activity 2 Model with Mathematics. Put this representation of an equation with associated explanations on a chart or poster for student reference. TE p. 37 Differentiated Instruction note is another gem for a chart or poster.

Choose a few of the word problems for students to complete. They do not need to finish them all.

TE p. 44 would look great hanging on the wall. Ready-made hand cutouts could be used.


Fri.9/11/15

Unit 1 Lesson 5Multiply and Divide with 2MX pp. 45-54

Explore patterns in multiplication with 2 Practice multiplying with 2s and 5s

Formative Assessmentp. Check for Understanding.

Circling groups of two on the MathBoard helps students develop the concept of even number. They were introduced to this in second grade, but most will need additional practice.

Mon.9/14/15

Unit 1 Lesson 6Building Fluency with 2s and 5sMX pp. 55-62

Practice multiplication for fluency Use the multiplication chart to practice

multiplication and division Write equations to solve word problems

with multiplication or division

Tech G3-5: 1.16 Explain terms related to the use of networks.Tech G3-5: 1.14 Explain and use age-appropriate online tools and resources.Tech G3-5: 1.17 Identify and use terms related to the internet.

Quick Quiz 1 Objectives

1A: Solve basic multiplication and divisions with 2 and 5.

1B: Identify and use patterns, properties, rules, and area to multiply and divide.

1C: Write and solve a multiplication equation with an unknown to solve a division problem.

1D: Use multiplication and division to solve real-world word problems involving equl groups and arrays.

Use the results of this quiz to plan next learning steps for your students. Most student needs can be addressed during the thirty-minute RTI block, though if the majority of the class struggled with a concept, consider how to reteach it to the class so that student learning improves.

Show students how open a browser and navigate to www.mobymax.com. Show them how to enter their username, password, and school code to access their student account; show them how to identify the math icons and take the placement test.

http://www.mobymax.com/



Big Idea 2: Patterns and Strategies: 9s and 10s3.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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8.3.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.4

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 = ?.3.OA.6 Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.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.Day Lesson Student Learning Objective(s) NotesWed. 9/9/15


Explore multiplication and division patterns in 10s

Write equations with variables for word problems

Formative Assessmentp. 70 Check for Understanding. Explain how you know a number is a 10s count-by. Give an example.

Letter variables are new to grade 3. Throughout the year, as you are writing equations to solve problems, represent the unknown with a related lowercase letter, such as in the example below.

If I have 2 groups of 3 stickers, how many stickers do I have? 2 x 3 = s

4 See Glossary, Table 2.


Thu.9/10/15


Identify patterns in 9s multiplications and divisions

Learn a strategy for quickly multiplying and dividing with 9

Formative Assessmentp. 80 Check for Understanding. Explain how to find the product of 4 x 9 using a 10s multiplication and the Quick 9s method.

MathBoards help students see patterns that develop when counting groups of 9.

Activity 2 provides a good opportunity for students to explain their thinking. If a student gives a clear explanation, you may want to record it on chart paper as a reference.

Fri.9/11/15

Unit 1 Lesson 9Building Fluency with 2s, 5s, and 10sMX pp. 83-88

Explore patterns in 9s for multiplication and division

Quick Quiz 2 Objectives 1A: Solve basic multiplication and

divisions with 2, 5, and 10. 1B: Identify and use patterns, properties,

rules, and area to multiply and divide. 1C: Write and solve a multiplication

equation with an unknown to solve a division problem.

1D: Use multiplication and division to solve real-world word problems involving equal groups and arrays.

Choose several problems from SAB 43. There is no need to do every one.

Fast Array drawings are unique to Math Expressions. SAP p. 44 has a good explanation of how they are used.


Big Idea 3: Strategies for Factors and Products: 3s and 4s3.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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8.3.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.5

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 = ?.3.OA.5 Apply properties of operations as strategies to multiply and divide.6 Examples: 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. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.3.OA.8 Solve two-step word problems using the four operations. 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.7

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.3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to

5 See Glossary, Table 2.6 Students need not use formal terms for these properties.7 This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).


measure area.b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).3.MD.7 Relate area to the operations of multiplication and addition.

b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

Day Lesson Student Learning Objective(s) NotesMon. 9/14/15

Unit 1 Lesson 10Multiply with 3MX pp. 89-98

Look for patterns in 3s. Learn a new strategy for finding products for

multipliers greater than 5.

Formative Assessmentp. 96 Check for Understanding. Explain the different strategies you can use to find 9 x 3.

Spend some time every day on the vocabulary of multiplication and division. For many students, this will be the first time they are learning these terms.

Skip-counting practice helps students develop multiplication and division skills. Use skip-counting throughout the day to fill a few minutes, to line up, etc. Charts can be made with visual examples, i.e. skip count by 5s with hands, by 2s with shoes, etc.

Tue.9/15/15

Unit 1 Lesson 11Multiplication and AreaMX pp. 99-108

Use the area model for multiplication.

Formative Assessmentp. 106 Check for Understanding. Explain different ways to find the area of a rectangle that is 6 rows by 4 columns.

Spend time discussing the Strategy Cards in the SAB.

Tiles give students hands-on experience building rectangles to represent multiplication. Two colors should be used to illustrate how the Distributive Property works (see TE p. 106).


Wed.9/16/15


Look for patterns in 4s Learn a strategy for solving problems with 4s

Formative Assessmentp. 116 Check for Understanding. Explain how you can use the answer to 2 x 4 and 6 x 4 to find the answer to 8 x 4. Draw a picture to show the strategy.

TE p. 112 Teaching Note discusses the importance of developing flexible thinking as students work through the strategies for multiplication and division. Use Math Talk to help students learn from one another how these more complex strategies work.

Thu. 9/17/15

Unit 1 Lesson 13Use the Strategy CardsMX pp. 119-126

Develop multiplication and division strategies and use them to solve problems

Formative Assessmentp. 124 Check for Understanding. How can you use the relationship between multiplication and division to find the answer to a division problem using Fast Arrays?

The Fast Array introduces students to the format for long division. Reading problems in the long division format is usually a challenge for students. Visuals provide a good reference throughout the year.

Choose problems strategically on SAB pp. 69-60. There is no need to complete them all.


Fri.9/18/15

Unit 1 Lesson 14Building Fluency with 2s, 3s, 4s, 5s, 9s, and 10sMX pp. 127-132

Build multiplication and division fluency with 2s, 3s, 4s, 5, 9s, and 10s

Quick Quiz 3 Objectives: 1A: Solve basic multiplication and

divisions with 2, 3, 4, 5, 9, and 10. 1B: Identify and use patterns, properties,

rules, and area to multiply and divide. 1C: Write and solve a multiplication

equation with an unknown to solve a division problem.

1D: Use multiplication and division to solve real-world word problems involving equal groups and arrays.

Path to Fluency: Math Talk about fact strategies has to continue all year. Practice with games, activities, computer practice, partner practice, skip-counting, etc.

Use results of Quiz 3 to plan targeted learning activities for the 30-minute intervention period.


Big Idea 4: Multiply with 1 and 03.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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8.3.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.8

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 = ?.3.OA.6 Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.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.Day Lesson Student Learning Objective(s) NotesWed. 9/23/15

Unit 1 Lesson 15Multiply and Divide with 1 and 0MX pp. 133-144

Use multiplication properties and division rules as strategies to multiply and divide with 1 and 0.

Formative Assessmentp. 124 Check for Understanding.

See TE pp. 1EE-1II for an explanation of the plan to develop student fluency with basic multiplication and division facts.

8 See Glossary, Table 2.


Thu.9/24/15

Unit 1 Lesson 16Solve and Create Word ProblemsMX pp. 145-150

Identify, solve, and create multiplication and division word problems.


Each lesson has math practice standards embedded. www.debbiewaggoner.com math practice poster for students is at the end of this document.

Fri.9/25/15

Unit 1 Lesson 17Play Multiplication and Division GamesMX pp. 151-156

Practice with 2s, 3s, 4s, 5s, 9s, and 10s.


Path to Fluency TE p. 153 activity can be taught to the whole class then used in centers for several weeks or longer.

Mon.9/28/15

Unit 1 Lesson 18Building Fluency with 0s, 1s, 2s, 3s, 4s, 5s, and 10sMX pp. 157-162

Practice multiplication and division and solve word problems for 0s, 1s, 2s, 3s, 4s, 5s, 9s, and 10s.


Choose word problems strategically or assign groups to certain problems.

Tue.9/29/16

Unit 1 Lesson 19Focus on Mathematical PracticesMX pp. 163-168

Skip this lesson. Review based on formative assessment results and complete unfinished work.

Wed.9/30/15

Unit 1 Test 1 NAPS District Test

http://www.debbiewaggoner.com/


Assessment Examples: Do not use the examples below exactly as written as they may be used on District Tests. Change the situation and numbers to create a new example.

3.OA.1 2014 MCAS #14 B;

3.OA.1 PARCC EOY #2 A,D


3.OA.2 2014 MCAS #8 A;


3.OA.2 PARCC EOY #22 B,C,E

3.OA.3 2013 MCAS #9 C;


3.OA.3 PARCC EOY #25 36;



3.OA.3 PARCC PBA #1 C;


3.OA.3 PARCC PBA #10 6


3.OA.4 2014 MCAS #17 B;

3.OA.4 PARCC EOY #20 A


3.OA.5 2014 MCAS #6 D


3.OA.6 2013 MCAS #2 A;

3.OA.6 PARCC PBA #11 C


3.OA.7 2014 MCAS #1 C;

3.OA.7 PARCC EOY #10 D;


3.OA.7 PARCC EOY #16 A,B,E;

3.OA.7 PARCC EOY #31 B,D,E;


3.OA.7 PARCC EOY #39 A;

3.OA.7 PARCC PBA #2 B,D,E


3.OA.8 2013 MCAS #11 B;


3.OA.8 2014 MCAS #4 B;




3.OA.8 PARCC PBA #3 PT A: 880 PT B: 32;



3.OA.8 PARCC PBA #12 PT A: B PT B: C


3.OA.9 2013 MCAS #12 24;


3.OA.9 2013 MCAS #18 OR;


3.OA.9 2014 MCAS #13 A


Mathematical PracticesI can …

1.Make sense of problems and persevere in solving them

5. Use appropriate tools Strategically

2. Reason abstractly and quantitatively

a b c . . .1 2 3 . . .

6. Attend to precision


3. Construct viable arguments & critique the reasoning of others

7. Look for and make sense of Structure

4. Model with mathematics 8. Look for & express regularity in repeated reasoning

Source: www.debbiewaggoner.com

Documents

1.cdn.edl.io Web viewSAP p. 44 has a good explanation of how they are used. ... See TE pp. 1EE-1II for an explanation of the plan to develop student fluency with basic multiplication