just in time math grade 3
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Just In Time Math Grade 3. Second Quarter Mathematical Thinking. Flow of Thinking (Number of days is only approximate—use your discretion for what your class needs.) . Establishing Meaning. Multiplication Things That Come In Groups. Things That Come in Groups. - PowerPoint PPT PresentationTRANSCRIPT
Just In Time MathGrade 3
Second Quarter Mathematical Thinking
Flow of Thinking (Number of days is only approximate—use your
discretion for what your class needs.)
• Establishing Meaning• Conceptual Understanding• Continue through problem solving
Idea of Multiplication5 days
• Prepare• 4 Stages
Use Tens5 days
• Prepare• 4 Stages
Doubling2s—5 days4s—5 days
• Lessons 2, 5, 6, 7, 8, and 9Patterns and Algebraic
Reasoning15 days
Establishing Meaning
Building a Rich Conceptual Understanding of Multiplication
Things That Come In Groups
Amanda Bean
Two Types of Multiplication
ProblemsFrom Navigating
Through Number and Operations
Multiplication Things That Come In Groups
Engage: Read poems about pairs (next slide). Make a list of things that come in
pairs like eyes, ears, etc.
Explore 2: Pose a problem with an example from the twos: If I had six children, how many eyes
would there be? Let the students model this with blocks. Make sure they know what the blocks
represent . Then the students create problems to solve that include using the items from the class
book for grouping problems. Explain 2: Share out their created problems with the group and have the group solve them. ELPS: 1F Use the phrase equivalent sets of objects
are joined to learn the meaning of multiplication.
Explore 1: Assign partners or triads to make a list of things that come in groups of 3, 4, 5, 6, 7, 8, 9, 10, 12 to
make a class book with.Explain 1: Share out what they
discovered.
Elaborate: Mrs. Jones third-grade class has four pairs of students who are going to the
science fair. She wants to honor all the partners with ribbons. Mrs. Jones was
responsible for making the ribbons. How many does she need to make? What
multiplication sentence could you write for this problem? What does each number in the
sentence represent (label). Have students make up another story that would fit this
same multiplication sentence.
Evaluate: What does multiplication mean?Pick one of the word problems you created and
explain how it relates to multiplication.
Things That Come in Groups
Things that come in Pairs
Salt and PepperPeanut butter and Jelly
Popcorn and Movies
Pictures and SoundMusic and Lyrics
Books and Heroes
Knights and SwordsWounds and Pain
Sickness and Cures
Chocolate and HeartacheYou and Her
Me and Myself
• Poem about Pairs Link
Amanda Bean’s Amazing Dream(See Navigation Lesson)
• Link to ARRC Lesson
• Which has more wheels—5 tricycles or 7 bicycles?
• Which has more cookies—3 rows with 8 cookies in each row or 4 rows with 6 cookies in each row?
• Which has more panes—a window with 5 rows and 4 panes in each row or a window with 3 rows and 6 panes in each row?
Two Types of Multiplication Problems with Amanda BeanNavigating Through Number and Operations NCTM Grades 3-5
Engage: If we have 6 cans with 3 tennis balls in each can, how many
tennis balls do we have in all?
Explore/Explain 2: In pairs, give students Blackline Masters
“Multiplication Work Mat” and Multiplication Recording Sheet and 70 small counters. See p. 53. Amanda Beans problem 1 with the illustration
that shows 8 sheep riding on bicycles. How many wheels is that? Follow directions p. 53 last paragraph.
Explain 2:
Explore 1: Have students model the problem by placing 3 balls into 6
groups (use manipulatives to represent the balls and the cans—could use
blocks and construction paper place mats.
Explain 1: Use the words “how many groups” and “how many in a group” to
discuss the problem. Explore 2: Continued Use the recording sheet each time to transfer
the data from the work mat. See figure 2.1 p. 54 to show labeling of
representations. Keep using this same recording page to finish pages 54-56.
Part 1 of lesson
Two Types of Multiplication Problems with Amanda Bean Navigating Through Number and Operations NCTM Grades 3-5
Explore 3: p. 56-58Suppose that Amanda Bean made 3
caramel apples yesterday for a party. Then today she and her mom made 5 times as many. How many caramel apples did they make today? Use a
new recoding sheet for these activities.
Reflect (Explain and Elaborate): p. 59
Students need a copy of Multiplication recording sheet and a copy of “Can
You Solve It with Multiplication?”. It is not important that students can
name the type of problem but that they can understand it as a
multiplication situation.
Skip the “Extend” part as it deals with division. We can use it later on when
we get to division. Evaluation: Give them a couple of multiplication problems to solve using a recording mat. Have them explain how the problem is a multiplication situation.
Part 2
Continued Problem Solving With Multiplication
• On a ppt entitled “Equal Groups Problem Solving Representations”, there are some problems that could be used to conceptually build the idea of representations for multiplication. You could continue to build on this concept during the fluency part of this timeline. The problems range from acting out the problems with real objects to making decisions on what manipulatives or pictorial representations to use to represent the problems.
Prerequisites to Multiplication Thinking Strategy of Use Ten
Addition Facts Including Doubles
Know the 10s facts
Familiar with Turnarounds
Two-digit Numeration
Read a standard clock to the nearest 5 minutes
Double Two digit numbers and
find half
Thinking Strategy: Use Tens“Since 5 is half of 10, the product of a 5s fact will be half of the product of a related 10s fact.
Use any of the “prepare” activities for students that you think do not understand the meaning of multiplication (p. 6-8).
Prepare: Last activity p. 8. Have the students count by tens as you place ten “tens” blocks, one at a time, using an overhead projector, document camera, or promethean models. Move one block to one side saying, “One ten is ten” repeat until “10 tens is 100”. Arrange the blocks into different arrays and ask students to describe what they see. “3 tens is 30”, “I see three rows (or columns) of 10 so 10, 20, 30.” You want to get them to be able to say 4 tens is 40 instead of counting.
Introduce Use Tens Thinking Strategy for Fives Facts p. 9 (Your choice)#2 Invite ten students to stand at
the front of class. The other students count by 10s as each student at the front raises both
hands. What number did we end at? Now the other students count
by 5s starting at 0 and the students at front raise only 1 hand. What do
you notice about the two totals? (Fifty is half of 100). Repeat with
other multiplies of ten. Do 40, 60, 80 first then harder ones to halve like 70. The fives total is always
half of the tens total.
#3 Clock face
#4 Use tens strategy cards (teacher set)
Reinforce Use Tens Strategy p. 10 # 2, 3, 4
• There are bags of 5 apples for sale. If you buy 3 bags, how many apples will you have?
• It takes 5 minutes to fill a wheelbarrow with soil. How long will it take to fill 6 wheelbarrows?
• There are 5 rows of 8 chairs. How many people can be seated?
• Nine cats each had 5 kittens. How many kittens are there in total?
• When Ben places 4 shoes from heel to toe in a line, They measure 1 meter. How many of these shoes will measure 5 meters?
• Jacob has to sow 7 rows of 5 seeds. How many seeds will he need?
• students lines up in 2 rows of 9. How many studentthere in total?
Reinforce Use Tens Strategy p. 10 #5
Practice Use Tens Strategy p. 11-12
• Game #2 p. 11. You need spinners BLM 7 numbered 1-9.
• Note: Using a blank transparent spinner over the copy of the spinner works very well. You can find them at Lakeshore but also online at http://www.educatorsoutlet.com/index.php?main_page=product_info&cPath=39_112&products_id=450
Extend Use Tens Strategy p. 12 #2
Extend Use Tens p. 13 #3
X 10 5
6
7
8
9
X 10 5
7
11
15
13
Prerequisites to Multiplication Thinking Strategy of Doubling (2s and 4s)
Addition Facts Including Doubles
Familiar with Turnarounds
Two-digit Numeration
Double Two digit numbers
Mentally add one and two-digit numbers
Thinking Strategy: Doubling
• See the other PowerPoint I am sending to you.
• This 9 weeks covers multiplying by two and four.
• Next 9 weeks has multiplying by eight.
If You Didn’t Know—Using known facts to figure out other facts
Lesson from Teaching Student Centered Mathematics John Van de Walle
• Building up or building down
Patterns and Algebraic Thinking
Lesson 2 Coins in your
Pocket 3 days
Thinking Algebraically Student Book p. 9-
14
ExemplarShould Jesse
Guess?
Growing PatternsMaking
Predictions
ExemplarsL is for Linda
Building Towers
Lesson 7 Animal Legs
2 days
Book; One is a snail, Ten is a Crab
Thinking Algebraically
p. 27-35
Lesson 8: Building Tables
2 days
Exemplars: Meg’s Muffin
MachinePopcorn
Measuring a Tulip
A Broken Gumball Machine
Algebra for All
p. 35, 37, 39, 41, 43, 63
Lesson 9: New Zoo
Sticker Book 2 days
Thinking Algebraically
Student p. 36-41
Thinking Algebraic
ally Teacher Edition p. 23-28
Lesson 5: What Comes Nex_? 2 daysName- Silent TeachAnimal ParadeCorrals
Lesson 2 Coins in Your Pocket
Engage: Review value of penny, nickel, dime and quarter. Tell students, “I have 2 coins in my pocket. What could they be? Suppose each of the coins is a nickel or dime, what are the possible combinations now? Record on chart. Thinking Algebraically p. 9 TE
Exploration: 1.Three Coins in your pocket pages 9-10 Thinking Algebraically Whole class #1, partners #2-4. 2. Thinking Algebraically p. 11 Discussion Questions 3. Thinking Algebraically p. 12-13 4. Thinking Algebraically p. 14.
Explain: Discussion questions for each section are listed under Explore in each section.
Elaborate: Exemplar: “Should Jesse Guess”
Informal: Are students able to organize data
systematically in a table? Are students able to
communicate choices and justify answers? Can
students describe patterns and make predictions based on patterns in the table? Do
students use a variety of strategies?
Formal: Page 16 of Thinking Algebraically Student Activity
Book, included in kit.
Lesson 2: Coins in Your Pocket Assessment
Should Jesse Guess?Seth has 21 cents in his pocket. Seth told Jesse
that he would give Jesse the 21 cents if hecould correctly guess what coins they were.
He would give Jesse 3 guesses. If Jesse did notguess correctly, Jesse would have to give Seth
21 cents. Should Jesse guess? Explain yourmath thinking.
Lesson 5 What Comes Nex_? Engage:
ANN is first in line
BRAD is second in line
CAROL is third in line
DARIUS is fourth in lineCan you tell me the name of the next person in line? (Silent Teach Activity)
•
Explore: Part 1: Animal Parade—students use a rule they make up to place animals in positionsPart 2: Corral—Sorting cards first by rule; then using horses with numbers to sort by a particular rule they choose.
Explanation: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations.
Elaboration: Students create list of numbers for someone else to sort.
Algebra for All p. 24-27 choose any of the activities.
Evaluation: Use the students' responses
on the Animal Parade activity sheet to
assess their understanding of
patterns.
Lesson 6 Building Patterns
Engagement: Students use transparent counters to build triangular numbers as on next slide.
Explore: Patterns to extend—see next slides. Students build patterns shown. Discuss numbering elements of pattern; Make prediction; write reason for prediction in writing; Extend the pattern checking prediction;
Explain: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations.
Elaborate: Exemplar “L is for Linda”Any of the activities on pages 28-31 from Algebra for All.
Evaluate: Provide Student Page
“Building Towers” for an assessment tool.
See the lesson “Building Towers” from Exemplars (provided with this lesson) for teacher directions.
Engagement: Lesson 2 Building Patterns
•What happens between the second and third triangle?•What patterns do you notice in the triangles?•How many counters would it take to make the sixth triangle? How do you know?•How can you record your information to find patterns or make predictions about how many counters it takes to make bigger triangles?
Exploration: Lesson 2 Building Patterns
Lesson 7 Animal Legs
Engage: Read Book: One is a Snail, Ten is a Crab by Sayre.Discuss some of the solutions suggested and invite students to offer alternative solutions.
Explore 1: Thinking Algebraically p. 27-29. Point out vertical and horizontal relationships if students don’t notice them. Discuss exercise 21 with a partner before writing response. Explore 2: Thinking Algebraically p. 30 Review how many legs 1 grasshopper
has, two grasshoppers;
do same with turkey.
Explore 3: Thinking Algebraically p. 31 Given number of legs, find number of animals. Suggest to make a table.Explore 4: Thinking Algebraically p. 33 Discussion as students find answers differently. Explore 5: Thinking Algebraically p. 34Open ended—more than one solution
Explanation: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. See Thinking Algebraically Teachers Guide pages 17-20, included in kit, for more information.
Evaluate: Look for Organized tables and
lists, understandings of relationship between
multiplication and division, concept of
equivalence. Thinking Algebraically p. 32 for
formal evaluation.
Lesson 8 Building Tables
Engage: Recipe on next slide; Students develop a chart showing relationship between the number of batches of cookies and the number of eggs needed.
Explore: See next couple of slides. Do the bike situation together then read the movie ticket situation to the students and see if they can build a table, extend it, and write a description for finding how much it would cost for 40 people.
Explain: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations.
Elaborate: Exemplar Meg’s Muffin and Exemplar Popcorn. Use any of the activities on pages 34-43 or 62-63 from Algebra for All.
Evaluation: Provide Exemplar “Measuring a Tulip and/or “Broken
Gumball Machine.
Lesson 8 Building Tables Engage
• Grandma’s Cookies3 eggs1 tsp vanilla3 c flour2 c sugar½ c butter½ bag chocolate chips
How many eggs would you need for 0, 1, 2, and 3 batches of cookies?
Batches of
Cookies
Number of Eggs
Needed
Can you make a table that will help figure out how many eggs you need?
Batches of Cookies
Number of Eggs Needed
Lesson 8: Building Tables Explore
• Imagine building a bicycle. How many tires do you need for 1 bike?
• How many tires for 2 bikes?• Write the number of bikes in a row: 1, 2, 3, 4, 5…• Write the number of tires in a row: 2, 4, 6, 8, 10…• We can organize our list in a table to show the related pairs
of numbers.Number of bikes
Number of tires
•If you wanted to build 6 bikes, how can we use the table to figure out how many tires we need to buy? •Can we use the table to find out how many tires for 20 bikes?•Can we find out without filling the table up to 20?•How can we write a description for finding the number of tires for any size bike?
Lesson 9 New Zoo Sticker Book Engage: Ask students what they know about zoos. This zoo has sticker books for sale in its gift shop. See next slide for sample page and questions about one particular sticker book.
Explore 1: Thinking Algebraically p. 36 in student book. Help students write an equation for #1 and 2. Explore 2: Thinking Mathematically p. 37-39 Multiple equations are possible for #2 p. 38.•
Explore 3: Thinking
Algebraically p. 40
Explain: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. See Thinking Algebraically Teachers Guide pages 23-26, included in kit, for more information.
Elaborate: Use the sticker page pictures (Thinking Algebraically Student Activity Book pages 36-41, included in kit) to create different equations in which the “result” (product or sum) comes first or in which factors (addends) are missing.
Evaluation: Is there more than one way to write equation for this
problem? Thinking Algebraically
student p. 41
Lesson 9: Zoo Stickers Engage
•If we put stickers like these on 2 more pages, what is the total number of stickers for all 3 pages? Is there another way to find the total?•How many giraffe stickers would there be on all 3 pages? Explain.