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Katie Costello K-5 Intervention
[email protected] 973-476-8440
Kimberly Beane K-5 Supervisor of Math & Science [email protected] 973-769-2413
K-5 Math & Science New Teacher Institute Welcome!
We’re excited to do math & science with you!
Think of a number that
has meaning to you. Build it
with manipulatives.
Agenda & Goals
• Favorite Numbers and Describing Numbers
• Instruc9onal blocks and minutes
• Singapore Math & Math in Focus
• Lesson Structure • Curriculum Documents and Pacing
• Assessment and Progress Reports
• Mee9ng individual student needs
Use chips to show 7
Math Instruc,onal Blocks and Minutes
K-‐1
2-‐5
Pedagogy: C-‐P-‐A
• Concrete (manipula9ves) to • Pictorial (visual models or drawings) to • Abstract representa9ons (numbers, symbols)
Jerome Bruner’s research proved that instruc9onal strategies build understanding for students when they move from…
Pedagogy: Rela9onal Understanding
Richard Skemp’s research proved that for long term learning to occur rela,onal understanding is more successful than instrumental learning.
Rela,onal Understanding Instrumental Understanding
Conceptual WHY before HOW One to One Correspondence Quan99es and Values Anchoring to 10 or Tens PART-‐WHOLE models Reading with understanding
Procedural How Oral Coun9ng Wri9ng numbers, Spelling numbers Isolated steps or steps without meaning Phone9c or word calling
Pedagogy: Perceptual Variability
Zoltan Diene’s research proved that children gain the most conceptual understanding when they are exposed to a concept through a variety of materials or experiences.
Perceptual Variability
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Reflec9ng On Pedagogy
v Concrete-‐Pictorial-‐Abstract (Bruner)
v Rela9onal Understanding (Skemp)
v Mul9ple Representa9ons (Dienes)
Turn & Talk: Summarize each with a partner
Kindergarten
Anchor to 5. Bonds to 5.
K & 1st
Anchor to 10. Bonds to 10.
Visualiza,on: Anchor to 10
Anchoring to 10
Decomposing Numbers
Composing Numbers
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Visualiza,on: Parts and Whole
1st Grade Number Bonds
Number Bonds in Upper Grades
Visualiza,on: Parts and Whole
3rd Grade Number Bonds
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MS_Assess_1_Ch02_007-014.indd 11MS_Assess_1_Ch02_007-014.indd 11 1/13/09 11:46:45 AM1/13/09 11:46:45 AM
Grade 1 Singapore Math! Please solve.
Place Value Strips
1. Find a partner to compose one of these numbers: 61 42 23 35 14 56
2. With your partner say these about your number:
a. ____ tens and ____ ones make _____ b._____ + _____ = _______
Place Value Strips 3. Find another pair to add these numbers mentally:
61 + 35 = 42 + 23 = 56 + 14 =
4. Use the hundreds around the room (and a partner) to make these numbers…
142 361 523 435 614 256
Place Value Strips
5. Come to the front of the room and put the 3-‐digit numbers in order from least to greatest.
6. Find another pair to add these numbers mentally:
435 + 361 = 523 + 142 = 256 + 614 =
Place Value Strips
Build two 3-‐ digit numbers
Lesson Structure & the Teacher’s Guide
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• Teacher Modeling
• Guided Prac9ce
• Independent Prac9ce
Kindergarten
Inves9gate Discover (Teacher Model) Explore (Guided Prac9ce) Apply (Indep)
C-‐P-‐A & Tradi9onal Algorithms
Linking Cubes & Base Ten Blocks
Solve these problems using base ten blocks… 124
+315
579 -‐ 432
33 x 4
323 -‐ 265
267 +145
Place Value Discs Gr. 3-‐4
Solve these problems using base ten blocks… 124
+315
579 -‐ 432
33 x 4
323 -‐ 265
267 +145
Homework
K-‐1 • Number Sense Games or Hands-‐on Tasks • Fact Games • ST Math Gr. 2-‐5 • FACT PRACTICE Online Games and Tasks (LiveBinder, Math in Focus) • Extension word problems of what has been taught • ST Math
Bar Models Gr. 2-‐5 !"#$%&
Part-‐Whole
Part-‐Whole Bar Models
Introducing Bar Models
Addi9on Part-‐Whole Bar Model 1. Allison jogs 6,860 meters and Calvin jogs 5,470 meters. How far do they jog altogether?
2. Mr. Michaels has $1,685. Ms. Kajy has $2928 more than Mr. Michaels. How much money does Ms. Kajy have?
Subtrac9on Part-‐Whole Bar Model
1. Brad has 1,300 stamps. He has 938 Canadian stamps and the rest are Malaysian. How many Malaysian stamps does Brad have?
2. There are 3,160 books in a shop. 1,226 are in English. 817 books are in Spanish and the rest are in French. How many French books are there?
Mul9plica9on Part-‐Whole Bar Model
1. A refrigerator costs 5 9mes as much as a television. The televisions costs $429. How much do they cost all together?
2. Lilian sold 114 9ckets to the fair. Rohani sold 2 9mes as many 9ckets as Lilian. Daquan sold 3 9mes as many 9ckets as Lilian. How many 9ckets did they sell all together?
Division Part-‐Whole Bar Model
1. Desmond and Melissa collect cards. They have 92 cards in all. Melissa has three 9mes as many cards as Desmond. How many cards does Desmond have?
2. The florist buys 4 boxes of carna9ons. There are 21 carna9ons in each box. The florist puts the carna9ons into bouquets of 6 carna9ons each. How many bouquets of carna9on are there?
Frac9on Part-‐Whole Bar Model
1. Rachel bakes a pie for her friends. Priscilla eats 2/6 of the pie and gives the rest to Tom. How much pie did Tom get?
2. Three friends share a grapefruit. Elena at 1/3 of the grapefruit. Lee at 1/9 of the grapefruit. Sara at 4/9 of the grapefruit. What frac9on of the grapefruit did they eat altogether?
Scoring and Progress Reports
Differen,a,on vs. Individualiza,on 60 Minute Math Lesson
30 Minute Individualized Math Instruc9on
Follows curriculum
Covers all standards
New content
Similar, ,ered tasks
Same concept for all
Meets child where he/she is
Focuses on founda,onal skills
Familiar content
Individualized tasks
Concepts individualized
Kim’s Math PD Resources Find ALL of Kim’s PowerPoints by searching Kbeane on SlideShare.net. hjp://www.slideshare.net/KimberlyBeane/presenta9ons
Find ALL of Kim’s STEM LiveBinders by searching Kbeane on LiveBinders.com hjp://www.livebinders.com/shelf/search_display_author?terms=KBeane
Follow Kim’s educa9onal research, policy, and STEM tweets @KimberlyLBeane For STEM updates, PD discussions, and general collegiality friend Kimberly Beane on Facebook
