MATH STRATEGIES FOR GRADES 3-5 IDEAS 2015 June 3, 2015 By Dr. Jenny Williams and Dr. Nora Swenson
INTRODUCTIONS Dr. Jenny Williams, Ed. D. SLP Jenny Williams Educational Consulting Adjunct Professor - Coastal College of Georgia Dr. Nora Swenson, Ed. D., CCC-SLP Swenson Educational Consulting
MC SC BC Wt = 15 lbs MC Wt = 8 lbs SC SC MC BC Wt = 11 lbs BC Wt =?
Visual Strategies Multiple representations for Concepts Mental math Building mathematical language Early emphasis on building students understanding of ten Number bonds, ten frames, place value charts Concrete to Pictorial to Abstract (CPA) Model Drawing
Where are strategies used? In Co-taught classes Specialized Instruction used to focus and teach concepts to students who are lacking skills (IEPed and students who missed concept) Format- Station, parallel or alternative groups Accommodations or Universal Design for Learning - for all members in class Give multiple representations for concept to enhance learning for all Format-Whole group, station or alternative
Number Sense and Place Value Development Develop Cardinality (The final number stated while counting a group is the total number of the set.) Conservation of number (One-to-One Correspondence) Subitization (Instantly recognizing units of a number usually 1-6) Exemplars
Why Use Manipulatives? Makes abstract ideas concrete Gives students a way to get their hands on ideas Builds mathematical confidence Useful tools for problem -solving Makes learning math interesting and more enjoyable
Turn to your partner: Identify three spacial words Briefly describe the previous mat using those spacial words Identify three numeral words and have the other partner describe the mat with those words
Use Literature for Context Read a story with numerical concepts Use blocks to count Divide blocks into tens towers with students counting up to 10 to help break into towers Students count 10s towers Count extra by 1 s Use literature as context for presenting object Match blocks to numbers presented Put blocks into long string Break string into 10s towers Count by 10s and extras by 1s
Review Articles As a group we will define: Number Sense Subitizing
Sense of Number (Exemplars) Basic Counting Understanding Size Number Relationships Patterns Operations Place Value
Subitizing See article on Subitizing Read and discuss with your table. What are some new ideas you gained from this article?
Subitizing Math Dictionary Subitizing is instantly recognizing a number when group is presented a
SUBITIZING This exercise lets you know if the student has a concept of numbers and what they represent. If they have to peek to see how many fingers they are holding up, they don t understand numeracy. What strategies can you use to help them grasp this concept?
Hands for Counting-- If ten frames are difficult- relate back to Hands for counting
Ten Frames Establish recognition of numbers of objects Counting, grouping objects and leading to identifying groups without counting Focus on multiples of 10 Leads to number bonds or groups of numbers that equal 10- and Do your students have these? Where do you need to start?
Ten Frames - Game Do your students need practice at this level? Do they all have this concept or do you need to go back to the Ten Frames originated with Hands
Number Bracelets is another subitizing format This is another way to orient students to grouping numbers with rekenrek or arithmetic rack Number lines made of beads are color coded to help students group numbers and increase mental math skills
Number Bracelets with Rekenrek Pattern
NUMBER BRACELETS You will need the following: 10 chenille stems (pipe cleaners), all one color 55 beads, 40 red and 15 white Choose one color of pipe cleaner and add red beads for first 5 beads on each bracelet Numbers 6-10 will be white Make a number bracelet for each number 1-10
Number Bracelets Add beads to pipe cleaners, in increasing numbers. Beads 1-5 will all be red. Bracelets 6-10 will have the first five beads red and the remainder are white. After adding beads, bend pipe cleaners into circles and twist ends together to make circle large enough to go over your hand for a bracelet.
Number Bracelets Activity Each student will have 10 bracelets, one for each number to use like an abacus counting frame. Sequence bracelets on arm from smallest number to greatest numbers of beads. Have one students draw bracelets from a bag to see who can call out the correct number of beads first. http://www.thinkingmathematically.com
Rekenrek Rods Another way to stress Focus on Base 10 An Arithmetic Rack
To make a Rekenrek Rod One tongue blade 6 inch elastic string 5 red beads (right)-5 white beads (left) Put string through hole at one end of tongue blade Add beads and add other end of string through hole at opposite end of tongue blade
Learning to Think Mathematically With the Rekenrek A Resource for Teachers A Tool for Young Children Jeff Frykholm From Website:
Let s try another subitizing tool Make and Take: Make DOT CARDS You need: 5 x 7 cards Dot Markers Dot patterns
Domino Patterns to 6
Subitizing with dots Most adults see a dice and never count they know the number by the pattern Dot patterns help students identify the number Common dot patterns are used with number cubes like domino or dice patterns Use these patterns to make sets of cards
Dot Pattern Activity Use cards you made as flashcards Have group identify numbers when patterns are flashed
PROBLEM SOLVING WITH MODEL DRAWING The model drawing approach takes students from the concrete to the pictorial to the abstract stage. Students create bars and break them down into units. The units create a bridge to the concept of an "unknown quantity that must be found. Students can learn to use this strategy in the primary grades and continue with it through the middle grades. There are two types of model drawings: discrete and continuous
Discrete Model crete like concrete blocks Used with smaller numbers One-to-one correspondence Use with fraction problems Use with percentage problems
Concrete: Unifix cubes Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? Jan s cubes Bill s cubes 4 5 }9
Concrete to pictorial Jan has 5 dogs. Bill has 4 dogs. How many dogs altogether? Jan s dogs Bill s dogs 4 5 }9
Pictures to Dots Jan has 5 dogs. Bill has 4 dogs. How many dogs altogether? Jan s dogs Bill s dogs } 5 4 9
Numbers on the inside Jan has 5 dogs. Bill has 4 dogs. How many dogs altogether? You may want to use large grid paper at first Jan s dogs Bill s dogs 1 1 1 1 1 1 1 1 1 4 5 9
Numbers on the outside Jan has 5 dogs. Bill has 4 dogs. How many dogs altogether? First Grade Jan s dogs Bill s dogs 4 } 5 9
8 Steps of Model Drawing 1. Read the entire problem. Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? 2. Decide who is involved in the problem. Jan Bill
Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? 3. Decide what is involved in the problem. Jan s cubes Bill s cubes
Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? 4. Draw units of equal length. Jan s cubes Bill s cubes
Jan has 5 yellow cubes. Bill has STOP 4 STOP red cubes. How many cubes altogether? 5. Reread the problem, one sentence at a time, saying the word stop at each comma or period and draw the information on the unit bars. Jan s cubes 5 Bill s cubes 4
Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? 6. Determine the question and place the question mark in the appropriate place in the drawing. Jan s cubes 5? 4 Bill s cubes
Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? 7. Work all the computation to the side or underneath the drawing. Jan s cubes Bill s cubes 4 5?9 5 + 4 = 9
Jan has 5 yellow cubes. Bill has 4 red cubes. How many cubes altogether? 8. Answer the question in a complete sentence. Jan s cubes 1 1 1 1 1 5 9 Bill s cubes 1 1 1 1 4 Jan and Bill have 9 cubes altogether.
Model Drawing Problems Jan has 2 more kittens than Sally. Sally has 6 kittens. How many kittens are there in all?
Continuous Model Use with larger numbers Talk about what part-part-whole means Talk about what whole part-part means
Adam has 65 matchbox cars. He has 13 more than Peter. How many cars does Peter have? How many cars are there in all?
A necklace costs $15. Meg had $3 left after buying the necklace. How much money did Meg have at first?
Together Kim and Chris have 35 cards. Kim has 5 more cards than Chris. How many cards did Kim have?
One basket holds 10 apples. How many apples will 6 baskets hold?
Grandma baked 25 cookies. There were 6 children. She gave each child 4 cookies. How many cookies were left?
BRANCHING Mental math activity Number bonds come before branching Frames of ten come before branching Helps with understanding the abstract of addition and subtraction.
Branching with single-digit addition: Watch me What goes with 7 to make 10? 7 + 9 3 6 What goes with 3 to make 9? 10 + 6 = 16
Look at handout and change numbers to 5 +8 5 + 8 5 3 Always keep the tens on the outside! 10 +3 = 13
14 + 5 10 + 4 5 10 + 9 = 19
21 + 18 20 1 Always think of making the number 10. 8 10 Always keep the tens on the outside. 20 + 10 + 9 = 39
Mental Math Mental math starts with number bonds in kindergarten Number bonds are a precursor to mental math Number bonds are used after students have numeral recognition Number bonds are used after the concrete stage
ESSENTIAL QUESTION FOR THIS WORKSHOP What math strategies can be used to differentiate math lessons and improve math performance?
Websites http://pages.cms.k12.nc.us/michaelwhite/ http://www.nzmaths.co.nz/ http://www.bbc.co.uk/education/mathsfile/ind ex.shtml http://www.quickmath.com/ http://mathforum.org/dr.math/ Mathwire (mathwire.com) J. Meacham (jmeacham.com) http://www.thinkingmathematically.com Materials: www. Crystalspringsbooks.com
Key Concepts for K-2 Provided multiple ways to develop Number Sense and Subitizing with your students