June 7, 2016 - Cassy Turner (Beth)
[email protected]
[email protected]
bit.ly/SingaporeMathlinks
Competence and Confidence - we want our kids feeling this way about MATH
Strong math curricula share three characteristics:
1. Coherence 2. Focus 3. Rigor
1. Coherence: The program is a​ligned vertically​: it doesn’t repeat (foundation is
important - it doesn’t get re-taught again)
2. Focus: Teaching students to “think” about their learning
3. Rigor: Teaching to depth so you can transfer your knowledge to a new situation
(Personally I prefer the word vigor...from the growth mindset folks)
Jackie’s suggestion: Take the assessments yourself, because there are items in the
assessment that students have never seen before . . . and the idea is that if they’ve learned the
skills, they should be able to transfer the knowledge they have to a new situation. 65% scores
are ‘acceptable’ in the curriculum.
Key Ideas Behind the Curriculum
● Concrete​ - kids need to get their hands on math tools (manipulatives have to be out
and accessible all of the time, so students see them as a regular “tool” for learning)
● Pictorial​ - number bond visual representation (younger students) and bar modeling
method (older students)
● Abstract ​- the goal . . . understanding and applying algorithms
Young children need to see multiple representations (i.e. - triangles in variations, fractions)
Singapore teaching model:
We want students to be flexible thinkers with numbers.
We want children, at a young age, making story problems (important to scaffold what a story
looks like).
Number bonds replace fact families. Use for add/subt. Whole stands alone. Can use plastic
plates with 3 compartments or zoo plates.
Resources/Games:
www.sde.com/mathtalk.pdf​ - good for K-2 teachers (pictures to make up story problems)
Use ISPY books​ to make up story problems for kids (​ISPY Numbers)
Games: Sourcebook page 116
Rock, Paper, Scissors, Math
(we want our kindergarteners fluent making combinations to 10)
Salute! ​(Mental math strategy)
https://www.sumdog.com/​ (free)
http://www.mathplayground.com/index.html​ (browser version of Thinking Blocks)
Grade 1:
Make “Ten Strategy” - from numbers to 20 (Making 10 is a transfer strategy)
Important to use the tens frame for lessons
“Today is a clever day - we’re doing it two ways”
“Today is a genius day - we’re doing it three ways”
Keep showing and practicing . . . they’ll pick up an efficient strategy!
*​ Bar Model is a GREAT TOOL for gifted students​ - for explaining their thinking aloud
(metacognition)!
4000 - 278
I didn’t change my number (regrouping) - I just re-named it!
Question asked about iXL: another option is R
​ eflex math (game-based) - practice for math facts
“Differentiated Math Sprints” in grade levels (to replace Math Timings in grades 3-4) emphasizes personal improvements - part of Singapore program in grades 1-4) - naturally
differentiates for students.
Cassy Turner: ​[email protected]​ ​ 970-691-3180
bit.ly/SingaporeMathlinks
Important Communication to Parents
Quantity and Quality of homework:
Directly correlated to the day’s lesson
Should be easy to do independently
Let parents know that their anxiety about homework and temptation to help students takes away
the practice opportunity for students, sends a message that they aren’t capable of doing the
task, and creates anxiety (20 minute frustration time - then parents send an email to teacher)
For students who already have mastered the skill, give them a challenge (be sure they know it’s
a challenge . . may be a struggle for the brain)
Arrange parent night for sometime in October...importance of bar modeling, importance of math
facts vs. “helping” with home enjoyment.
Note: Metacognition is hard for parents to understand. It is hardest for gifted kids, but bar model
is a great tool for them.
Encourage parents to help with math by giving kids real life experiences such as cooking or
constructing, or by playing games such as cribbage, Set, Blink, Rush Hour, dice games, etc.
*** To learn more about bar modeling - - - Internet: Thinking Blocks - gr. 2 + / Thinking Blocks
Jr. app (Math Playground)
Materials
Teacher book:​ A-B
Workbook A-B:​ used often for ‘guided practice’ - consumable
Extra Practice:​ “on grade level worksheets” - can be used for homework
Reteach:​ remediation (available on Think Central) - might send with a student for an extended
vacation because there are notes that accompany the worksheets. If a student still needs more
work on a concept it is better to just get them working with manipulatives more.
Enrichment:​ for differentiation i​ n classroom ​(this book has non-standard type problems)
Assessments:​ Pretest checks if kids are ​ready​ for the chapter (it doesn’t test them out of the
chapter). TestPrep is good to use for the final assessment. Note that a score of 65% on test is
considered fine, because the test includes questions testing for transfer of knowledge and has
non-standard type questions. You don’t teach to the test. I suggest developing scoring rubrics
that distinguish between the different types of questions (basic knowledge, application, and
transfer). Developing a system for giving partial credit will also be important. (Will Cassy talk
about that in August?)
*** other good resource: Marcy Cook materials
Teacher’s Guide
*use post-it notes to keep track of what worked / didn’t work this year
*gauge the pacing of lessons to your class
*Jackie suggested using the “Test Prep” assessment for chapter test
*In the TEACH section, when it says “LEARN”, the student book should be CLOSED - your
anchor task should come from this section - this is the “hands-on activity”
*Not everything is great in the text . . . make decisions about what works!
*GUIDED LEARNING - students open their textbooks
Kindergarten and 1st grade - the A book will go quickly - slow down with the B book (skip
“doubles” lessons and “doubles plus one”
*Kindergarten - look at the student workbook BEFORE presenting the lesson
2nd and 3rd grade - the A book will take more time than the B book
4th grade - LOTS of content in A and B
Suggestions
*​Math Word Wall (esp. In K-2) ​- should be math vocabulary in the classroom
*Math JOURNALS - (start in 3rd grade)​ create sections: vocabulary, examples, something to
work on (like KenKens) if they complete work early, notes I want to remember to help me
*Don’t always have kids read if they finish early, have them do math (see journals above)
*​Create charts​ with strategies that students can use as a resource (i.e. - Writing)
*Individual whiteboards
*Heavy duty page protectors where can slip in a ten frame or other printout
*Display math work + math projects around the school and classroom
*HOW do we structure the LS day to allow 60-75 minutes of math everyday? What can we let
go (especially during the next couple years) while we get familiar with Math in Focus)?
*Manipulatives​ should be out ALL the time, don’t make kids have to get up and get them during
the middle of their practice. Manipulative kits are with Kris, hand out in August
Minimum (non-negotiable) grade expectations: for the following year:
● Give end of year assessment for the previous grade as “diagnostic” to see what students
know and where you need to start (DO NOT show to students or parents) - use ONLY
for instructional planning to look at gaps, starting with looking at “whole” class for trends,
then individual needs
Kindergarten: Recognizing numbers
Number order
Subitizing #’s on a tens frame
# combinations to 10
one:one correspondence
Number bonds
First grade:
1A
●
●
●
# combinations to 20
Learn “Make 10 strategy”
Only use “count on strategy” for 1, 2, 3 (and then 10, 20, 30 or 100, 200,
300 later)
Use “10 frames” properly (lines of 5) + manipulatives
1B
# to 40 and # to 100
● Counting
● One more/less - Before/After
● Addition/Subtraction with strategies
Skip vertical addition algorithm, get fluid in horizontal strategies)
Skip “doubles” and “doubles plus one”
Second grade: 2A: Addition/Subtraction algorithm
Multiplication/Division Facts 2, 5
Length with standard measurement
Bar Model drawing
2B: Multiplication/Division Facts 3, 4, 10
Fractions
Third grade:
3A:
Multiplication/Division Facts 6-9
Multiplication algorithm (35 x 4)
Division algorithm 4 into 35
3B:
Elapsed time
Fractions (equivalent)
Area
Over the summer:
● Look at the first two chapters closely
● Solve the problems in the student workbook with the TE closed - important to create own
solution guide
● Become familiar with ‘bar modeling” (use ThinkingBlocks)
During August workshop days:
● Include tutors in the Cassy’s training
● Arrange to videotape Cassy’s session, especially any lessons on bar models so teachers
can have a reference tool
● Each team should have some face time with Kris in order to prepare for the first couple
weeks, and to communicate what will work best for that particular team in terms of
utilizing Kris as a resource.
Singapore Math Training - August 23-24, 2016
***Order - Math Express: Speed Math Strategies for grades 1-6 (order by grade level-3)
Mental math is important! 3x/week: Practice-practice=practice! (In the mental math chapter)
*** Procedural fluency: ​Flexibly - Accurately - Efficiently​ TRUE mastery)
Sprints: goal is to improve fluency - don’t take score, throw away immediately
Moving away from memory to deeper understanding - how math works!
Compensation: ​making both sides the same as in:
(use a number line to show visually)
1000 - 364 = ?
-1
-1
999 - 363 = 636
OR
65 - 8 = ?
+2 +2
1000 - 364 = ?
-1
999 - 364 = 635 + 1 = 636
*** SKIP: front end estimation
What is problem-solving? (taking what you’ve learned and applying it to a new situation)
(NOT all problems need a bar model)
Bar models: it’s about creating a visual model so kids can see the math
begins in 2nd grade
must teach with easy numbers first and insist kids learn bar modeling
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Always start with a bar
Ask: What does the bar represent?
Always begin with concrete and move to the abstract
Steps: See - Plan - Do - Look Back
(understand the problem, then make a plan to solve the problem, then ‘do’ the
plan, then check “look back” your work)
Talk aloud through the problem/solutions with students.
Ask students to show the equation they used to solve the bar model problem
Teach students to read the problem CAREFULLY.
Some problems have more than one step - divide workspace into multiple steps
3rd/4th grades: make connection to pre-algebra with bar modeling
Ask students to ‘write about’ their solutions and illustrate their bar model
On thinkingblocks.com - bar modeling for instruction on SMARTBoard
(see websites on page 115 of Sourcebook)
More than​ or ​less than​ or ​times as many​ = ​COMPARISON bar
Use the digits 0-9 to make a correct multiplication sentence ______ ______
X
______
______ ______
Assessments and Journals
Pretest or first lesson Quick Check: A
​ ssesses prior knowledge to see that students are
ready for the upcoming chapter: “Are the students ready for the material in this chapter?”
Test Prep (Post test): ​Use to determine if students need extension BEYOND the content of
the chapter.
Journals:
Use as a reference tool for learning
Create table of contents
Use for consolidation of concepts
Use as formative assessment
Explain with pictures, words
Use to record strategies, vocabulary
In addition to content, give prompts to write about feelings (affective)
Create sections for content
***Resources from Cassy:
Singaporemathsource.com/resources/favorite-printable-math-resources/
Mental Math Sprints (number strings) - in Sourcebook page 123
Evaluating word problems - in Sourcebook page 78 - “Using Rubrics”
Use virtual HMH site for Math in Focus for blackline masters for School to Home and Transitions
Comparing numbers: greater than, less than, equal
Which is greater? Which is less? “Use dots, connect the dots”
October 2016
2nd grade:
Don’t focus on “doubles” - reinforces memorization . . . . rather,​ focus on making ten strategy
Give harder numbers with bar models to enrich higher learners
Make a strategies chart to hang in room - ask students to use “2” strategies to solve problem
Make connection between number bond and bar model in problem-solving
**Order Intensive Practice books for differentiation
1st grade:
Should have numbers to 20 solid with automaticity
Numbers to 40 should be part of teaching to work in addition strategies
Do not see any vertical math in first grade - only horizontal
Using the hardcover book:
“LEARN” - book closed
“GUIDED LEARNING” - book open (can project page rather than have each student with
hardcover book)
Use pictures from books to help students generate story problems. IF using the book, say “The
book sees this picture . . . what do you see?”
Kindergarten:
Make a decision about how much time to spend on a particular concept - compact the
curriculum where appropriate. If they show/tell you they understand, move on.
Journal activities:
● Number bond template: Family members
● Number bond classroom book: story in pictures (and words)
● My world in numbers - kids give clues (i.e.- I have ___ pets in my house). Drawing and
writing about numbers.
Intensive Practice books (Singapore) and Marcy Cook materials are worth looking at
3rd grade:
Homework - send daily to correspond with lesson taught that day
Students demonstrate their learning at the end of each chapter using Seesaw
Math fact practice is necessary and should be an expectation every night!
1st: to 20 addition, subtract
2nd: to 20 addition,subtract and 2-5 multi/division
3rd: to 20 addition, subtract and 2-5 multi/division and 6-9 multi/division
4th: 1-10 multi, division
How should we assess mastery of math facts through the year?
● Use timed tests: “5 minute frenzy”
● Worksheet generators for horizontal math facts
● Younger children: begin with individual assessment, by end of year looking for
automaticity
Enrichment
Present similar concept with larger numbers
Enrichment materials from book - partner kids to work with this
Intensive Practice (Singapore materials) *we will order
*Word Problems - increase level of thinking complexity
*Logic Problems (Marcy Cook math)
Nrich​ ​(​nrich.maths.org​)
Math Kangaroo
Continental Math League (grades 2-4)
Think about the “Do Now” . . . for more able learners, such as puzzles (Ken-Kens, Sudoku), a
Problem-of-the Week posted for kids to think about
About homework:
● Writing about math in the classroom on teacher blog’s is critical for parents to
learn/support our new math program.
● Math homework should happen Mon-Thurs.
● Math fact practice should be part of student’s daily routine.
● “Similar” homework expectations are necessary across grade levels.
● May be helpful to “shift” our thinking from our “usual” homework to find a place for math