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 / odd
columns / even / product
Commutative Property / factor / quotient
dividend / multiple / rows
divisor / multiplication / strategy
multiplier / variable
Big Idea 1: Meanings of Multiplication and Division: 5s and 2s
3.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.
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 568.
3.OA.3Use 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.4Determine 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.5Apply 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.6Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.
3.OA.7Fluently 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.8Solve 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.9Identify 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) / Notes
Mon.
9/7/15 / Unit 1 Lesson 1
Multiply with 5
MX pp. 1-10 /
- Explore patterns counting by 5s
- Learn the Home-Practice routine
p. 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 2
Multiplication as Equal Groups
MX 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
p. 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 3
Multiplication and Arrays
MX 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
p. 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 4
The Meaning of Division
MX pp. 33-44 /
- Solve division word problems where the number of groups is unknown
- Solve division word problems where the group size is unknown
p. 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 5
Multiply and Divide with 2
MX pp. 45-54 /
- Explore patterns in multiplication with 2
- Practice multiplying with 2s and 5s
p. 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 6
Building Fluency with 2s and 5s
MX 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: 1.14 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.
Show students how open a browser and navigate to 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.
Big Idea 2: Patterns and Strategies: 9s and 10s
3.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.
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 568.
3.OA.3Use 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.4Determine 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.6Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.
3.OA.7Fluently 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.9Identify 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) / Notes
Wed. 9/9/15 / Unit 1 Lesson 7
Multiply and Divide with 10
MX pp. 63-72 /
- Explore multiplication and division patterns in 10s
- Write equations with variables for word problems
p. 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
Thu.
9/10/15 / Unit 1 Lesson 8
Multiply and Divide with 9
MX pp. 73-82 /
- Identify patterns in 9s multiplications and divisions
- Learn a strategy for quickly multiplying and dividing with 9
p. 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 9
Building Fluency with 2s, 5s, and 10s
MX pp. 83-88 /
- Explore patterns in 9s for multiplication and division
- 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.
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 4s
3.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.
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 568.
3.OA.3Use 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.4Determine 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.5Apply 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.6Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.
3.OA.7Fluently 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.8Solve 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.9Identify 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 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.7Relate 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 andb+c is the sum of abandac. 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) / Notes
Mon. 9/14/15 / Unit 1 Lesson 10
Multiply with 3
MX pp. 89-98 /
- Look for patterns in 3s.
- Learn a new strategy for finding products for multipliers greater than 5.
p. 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 11
Multiplication and Area
MX pp. 99-108 /
- Use the area model for multiplication.
p. 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 / Unit 1 Lesson 12
Multiply and Divide with 4
MX pp. 109-118 /
- Look for patterns in 4s
- Learn a strategy for solving problems with 4s
p. 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 13
Use the Strategy Cards
MX pp. 119-126 /
- Develop multiplication and division strategies and use them to solve problems
p. 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 14
Building Fluency with 2s, 3s, 4s, 5s, 9s, and 10s
MX pp. 127-132 /
- Build multiplication and division fluency with 2s, 3s, 4s, 5, 9s, and 10s
- 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.
Use results of Quiz 3 to plan targeted learning activities for the 30-minute intervention period.
Big Idea 4: Multiply with 1 and 0
3.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.
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 568.
3.OA.3Use 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.4Determine 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.6Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.
3.OA.7Fluently 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.9Identify 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) / Notes
Wed. 9/23/15 / Unit 1 Lesson 15
Multiply and Divide with 1 and 0
MX pp. 133-144 /
- Use multiplication properties and division rules as strategies to multiply and divide with 1 and 0.
p. 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.
Thu.
9/24/15 / Unit 1 Lesson 16
Solve and Create Word Problems
MX pp. 145-150 /
- Identify, solve, and create multiplication and division word problems.
p. 124 Check for Understanding. / Each lesson has math practice standards embedded. math practice poster for students is at the end of this document.
Fri.
9/25/15 / Unit 1 Lesson 17
Play Multiplication and Division Games
MX pp. 151-156 /
- Practice with 2s, 3s, 4s, 5s, 9s, and 10s.
p. 124 Check for Understanding. / 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 18
Building Fluency with 0s, 1s, 2s, 3s, 4s, 5s, and 10s
MX pp. 157-162 /
- Practice multiplication and division and solve word problems for 0s, 1s, 2s, 3s, 4s, 5s, 9s, and 10s.
p. 124 Check for Understanding. / Choose word problems strategically or assign groups to certain problems.
Tue.
9/29/16 / Unit 1 Lesson 19
Focus on Mathematical Practices
MX 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
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.