West-Orange Cove ISD3rd Grade Mathematics – 3rd Six Weeks2012 - 2013
Week 1 - 3Nov 5 – 9
Nov 12 – 16
Nov 26 – 30 / Learning Standards
4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to
(A) learn and apply multiplication facts through 12 by 12 using [concrete] models [and objects];
(B) solve and record multiplication problems (up to two digits times one digit); and
(C) use models to solve division problems and use number sentences to record the solutions. / Major Concepts
Multiplication
Problem Solving / Processes:
- Problem Solving Model
- Thinking about learning and making connections
- Use accountable talk by using the language of mathematics
Instruction / Resources / Math Stations
Interventions/Extensions / Assessment
Key Vocabulary– multiplication, division, equal groups, array, product, factor, horizontal, vertical, multiply, divide, divided by, input, output, fact family
The third six weeksis focused on multiplication and division. The first three weeks will be learning multiplication and the last three weeks, division. Students are expected to recognize and solve problems in multiplication and division situations.
Math background for teachers:
- Multiplication may be thought of as repeated addition and involves joining equal groups.
- An array involves joining equal groups and is another way to think of multiplication.
- Two numbers can be multiplied in any order.
- Help students make connections to multiplication through skip counting using number lines and hundreds charts.
- The ability to break numbers apart in flexible ways is very important as they use invented strategies to solve multiplication.
- Teach the distributive property is an important concept. Teach students that they can solve 43 x 5 by breaking it into 40 x 5 + 3 x 5 then adding the results. Provide numerous opportunities for students to manipulate and apply strategies for solving.
- Use number lines to solve multiplication problems.
- Students will not learn multiplication facts through “drill and kill”
- Students must learn to select ways to think about multiplication that makes sense and are meaningful to them.
- Students tend to use three categories when solving multiplication: (Van de Walle)
- Complete-Number Strategies – These students are usually not comfortable breaking numbers into tens and ones. For example 58 x 5. Students will do repeated addition and add 58 five times. When they could have multiplied 50 x 5 and 8 x 5 then added them together.
- Partitioning Strategies – (several examples of partitioning)
- 27 x 4 - 4 x 20 =80 4x7 = 28
- 46 x 3 double 46 = 92 + 46 = 138
- 27 x 4 = 10 x 4, 10 x 4, 7 x 4 then add the totals of each to get 108
- 27 x 8 = 25 x 4, 25 x 8, 2 x 8 add the totals to get 216
- Compensation Strategies –numbers are manipulated in a manner the student is comfortable using. For example 27 x 4 may be seen as 27 + 3 = 30 x 4 = 120, 3 x 4 = 12, 120 – 12 = 108
- Multiples of 10 and 100 – follows the familiar pattern of base 10 students are familiar with. Students will use 4 x 12 = 48 to solve 400 x 12 = 4,800. Students should not be taught to add zeros without understanding the concept of multiplying by 10 or 100.
- Arrays are excellent models for concrete learning of multiplication. (This is a good time to connect arrays to finding area.)
- Equal groups: Whole unknown.
- Jacob has 4 bags of oranges. There are six oranges in each bag. How many oranges does Jacob have altogether? (Repeated addition.)
- If oranges cost .10 each, how much will he pay for 5 oranges? (rate)
- If He walked for 3 hours at 4 miles per hour, how far did he walk? (rate)
- Comparison Problems – Product unknown.
- Susan picked 6 apples. Maria picked 4 times as many apples as Susan. How many apples did Maria pick?
- Combinations Problems – Product Unknown.
- Juan bought 4 pairs of jeans and 3 shirts and they can all be worn together. How many different outfits consisting of a pair of pants and a jacket does Juan have?
- Area and other product-of-measures problems – the product is a different type of unit from the other two factors.
- For example, length x width = area (usually square units.) (adapted from Van De Walle)
enVision Math Tools
Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:
Foam Tiles
Counters
Dice
Playing Cards
Base 10 / enVision Math multiplication games
Multiplication games using dice or cards
Problem Solving – word problems involving mixed operations including multiplication.
Journal writing – explain how multiplication is related to addition
Number of the week
Measurement Station
Interventions/Extensions
Often students “shutdown” when they hear the term multiplication. To help overcome this use egg cartons and counters to make the connection of multiplication being repeated addition. Pose fact problems to students such as 3 x 5. Students will put five counters in each of 3 compartments in the egg carton. Repeat several times then let students challenge each other.
GT:Students that are more familiar with multiplication and or know their facts can play a multiplication game. Student rolls two dice to get their first factor and write it down. Next they roll one die and multiply the 2 digit factor by it. Repeat 10 times, each time keeping a running total. Students then trade papers and check each other’s work. The student with the greatest ending total wins. / enVision Math Assessments
Products/project
Students will use newspaper or construction paper to make arrays for a given product
Students will work in groups to create and present visual representations of the properties of multiplication
Identify Patterns in Multiplication Facts
- Use concrete objects, pictorial models, and technology to identify patterns in multiplication facts.
Ms. Martin placed 4 vases on her desk. If there were 2 flowers in each vase, how many flowers were there all together?
Possible Answer: There are four vases, and each vase has 2 flowers. The number of flowers can be determined by 2 + 2 + 2 + 2 = 8 or
2 4 = 8.
Example:
Tamara purchased sheets of stickers for her sticker collection. Each sheet had 7 stickers on it. What are the possible numbers that Tamara could have said if she counted the stickers in groups of 7?
Possible Answers: The answers are multiples of 7. Possible answers are 7, 14, 21, 28 or 21, 28, 35, 42.
Example:
Ask the students, “What number sentence best represents the arrangement of the objects?”
Answer: 4 7
Example:
Albert placed the pencils from his pencil box in the arrangement shown below. How could you describe Albert’s pencil arrangement?
Possible Answers:
2 groups of 5 pencils, 2 equal groups of pencils with 5 pencils in each group, 2 rows and 5 columns, or 25
Example:
The pattern below shows a portion of the arrangement of stars in the floor tiles in Sharice’s room. Describe the arrangement of stars on Sharice’s floor tiles.
Possible Answers:
7 rows with 6 stars on each row,
6 columns with 7 stars in each column, 76, or 7 groups of 6 stars.
Learn and Apply Multiplication Facts
- Use concrete models to learn and apply multiplication facts through 12 by 12.
Prompt the students to use concrete models such as color tiles to represent the array 3 5. Prompt the students to multiply the number of rows by the number of columns in order to determine the value of the array.
Answer:
- Describe a pictorial representation of a multiplication fact with a number sentence.
Ask the students, “How can this representation of a multiplication fact be described with a number sentence?”
Answer: There are 3 equal groups of 4 butterflies for a total of
12 butterflies. 3 4 = 12.
Example:
While walking in the park, Jeremy saw 12 ladybugs. If each ladybug has 6 legs, how many ladybug legs did Jeremy see?
Prompt the students to use concrete models such as counters to solve the problem.
Answer: The product is 72.
6 12 = 72.
Multiplication
- Solve and record multiplication problems.
There are 8 spiders in a jar. If each spider has 8 legs, how many spider legs are there all together?
Possible Solution Strategies:
Draw a picture, use concrete models, use repeated addition, or use multiplication.
Answer: The product is 64. 8+8+8+8+8+8+8+8=64 or 8 8 = 64.
Example:
James loads boxes on trucks for a shipping company. On Tuesday, James loaded 5 trucks with 52 boxes in each truck. How many boxes did James load on trucks on Tuesday?
Possible Solution Strategy:
Use base ten blocks in an area model.
Using partial products:
5 / 2
/ 5
1 / 0 / 52 = 10
+ / 25 / 0 / 550 = 250
26 / 0
Answer: The product is 260.
52 5 = 260.
- Solve multiplication problems.
Jacquelyn’s choir had 95 members. Each member sang 3 solos for individual competitions during last month’s regional performance. How many solos did Jacquelyn’s choir sing all together?
Understanding the Problem:
- Ask the students, “What are you trying to find out?”
- Ask the students to restate the problem.
Making a Plan:
- Ask the students, “Are you joining equal sets or separating sets of objects into equal groups?”
- Ask the students, “What is the important information in the problem?”
Carrying out the Plan:
- Ask the students, “How did you solve the problem?”
95 by 3.”
Evaluating for Reasonableness:
- Ask the students, “How do you know your answer is reasonable?”
100 3 = 300 and 300 is close to 285. We multiplied 95 by 3 to get our answer.”
Answer: 285 solos
Week 4 - 6
Dec 3 – 7
Dec 10 – 14
Dec 17 - 21 / Learning Standards
4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to
(A) learn and apply multiplication facts through 12 by 12 using [concrete] models [and objects];
(B) solve and record multiplication problems (up to two digits times one digit); and
(C) use models to solve division problems and use number sentences to record the solutions. / Major Concepts
Division
Problem Solving / Processes:
- Problem Solving Model
- Thinking about learning and making connections
- Use accountable talk by using the language of mathematics
Instruction / Resources / Math Stations
Interventions/Extensions / Assessment
Key Vocabulary – division, dividend, division, quotient, array, difference, fact family, factor, product
Math background for the teacher:
- Multiplication and division have an inverse relationship.
- Every division fact has a related multiplication fact.
- Students can use near facts to solve problems.
- There are two concepts of divisire two concepts of divison:
to solve problems.
act.
p.
mly,ics 7 - 9.topic 6 - Multliplication 7 + 3 = 30 x 4 = 120, 3 x 4 = on: - The partition or fair sharing – Tom has 360 Pokeman cards and he wants to share them equally with three friends. How many cards will Tom and each of his three friends have?
- The measurement or repeated subtraction – Spot’s master has a bag of 125 dog treats. Spot loves his dog treats and will do tricks to earn them. If spot’s master gives him 5 treats a day, how long will the bag of treats last?
- Students must learn to solve both types of problems but you should start with the fair sharing because it is an easier concept for students to grasp and have success.
- Fact families can be used to make connections to multiplication and division.
enVision Math Tools
Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:
/ enVision Math multiplication and division games
Multiplication games using dice or cards
Problem Solving – word problems involving mixed operations including multiplication and division.
Journal writing – explain how division is related to multiplication
Number of the week
Measurement Station
Interventions/Extensions
Students will use manipulatives to demonstrate fair sharing and repeated subtraction to solve problems.
GT:Students will write a letter to their grandmother explaining how to multiply and divide using their favorite strategy. / enVision Math Assessments
Products/project
Students will work in groups to create and present visual representations of division problems
Division with Models
- Use models to solve division problems and use number sentences to record the solutions.
Example:
Andrea has a teddy bear collection with 15 teddy bears. She wants to put her teddy bears in 3 baskets. If each basket has the same number of teddy bears, how many will be in each basket?
Possible Solution:
Answer: 15 3 = 5
- Match a pictorial representation of a division situation with a number sentence.
Example:
Possible Answer:
There are 25 stars in all. The 25 stars are divided into 5 equal groups.
Answer: 25 5 = 5
- Identify how repeated subtraction can be used to solve division problems.
Example:
Riley placed a plate of 12 cookies on his kitchen counter for his family to share. Each family member took 4 cookies from the plate. There were no cookies left over. How many family members took cookies from the plate?
Person 1 / / / / / 12-4=8
Person 2 / / / / / 8-4=4
Person 3 / / / / / 4-4=0
1 / 2
- / 4 / Person 1
8
- / 4 / Person 2
4
- / 4 / Person 3
0
4 was subtracted from 12 three times.
Answer: 12 4 = 3
Identify Patterns in Multiplication and Division Fact Families
- Identify patterns in related multiplication and division number sentences.
Possible Answers:
- 3 rows of 4 (3 x 4)
- 4 columns of 3 (4 x 3)
- 12 divided into 3 rows ()
- 12 divided into 4 columns ()
Answer:
Prompt the students to identify the number sentences that create a multiplication and division fact family.
Example:
Which set of number sentences identifies a multiplication and division fact family?
Set A Set B Set C
Answer: Set A
- Make generalizations from sets of examples and nonexamples of related multiplication and division sentences.
What number sentence does NOT belong in the fact family?
Answer: 9 5 = 45
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day Page 1