Singapore Math Training August 24, 2010
Today’s Training • Opening Prayer • Singapore Math Background • Become acquainted with the Key Pillars of Singapore Math through… • Grade 1 Lesson Demo (Lisa Jacobson) • Grades K-2 Math Strategies ( Laurie Ruwe) • Grades 4 – 5 Lesson Demo (Carol Lowry) • Singapore Model Drawing Demonstration (Laurie Ruwe and Carol Lowry) • Closing Comments
What is Singapore Math? • Background • Singapore Math refers to the mathematics curriculum in the country of Singapore • Its greatest natural resource, according to the Ministry of Education, is its people • Singapore Math description
Why Singapore Math at Spirit? Why are Singapore Math strategies being used by so many American teachers and schools? Singapore is an international leader in math. What is the TIMSS Report? -Trends in International Mathematics and Science Study Singapore's 4th & 8th grade students have scored first for Mathematics in 1995, 1999, and 2003. The latest TIMSS report (2007) shows Singapore in second place, topped by Hong Kong. (American students fall in the middle, out of 46 countries.)
Why Singapore Math at Spirit? • Typical math instruction is heavily weighted by procedures (algorithms) – we teach HOW to solve particular problems but fail to address the foundational knowledge that makes solving those problems meaningful, relevant, and reasonable.
Why Singapore Math at Spirit? • The goal of Singapore Math is conceptualization and mastery for all learners.
Key Pillars of Singapore Math • Mental Math of mastered concepts • Introduction of Concepts through Concrete, Pictorial, Abstract (CPA) Approach • Problem Solving with Model Drawing • Meaningful activities • Independent Practice until mastery
Grade 1 Lesson Number Bonds
“Facts on the Brain” • Groups – Three students • Materials – Playing or number cards • Directions: The object of this game is to practice finding sums and missing addends. One player will be the sum finder, while the other two will be the addends. • 1. The sum finder gives eachaddend a pile of cards that are face down. • 2. The sum finder counts aloud, “1..,2…,3!” • 3. On “3”, each addend lifts a card from his or her pile and places it on the heads. • 4. The sum finder announces the sum of the two numbers. • 5. Knowing the sum, each addend looks at their partner’s number to determine their missing addend. • 6. The first student to announce the correct missing addend wins that round and gets both cards. • 7. The student repeats steps 2 through 6 and continue until their card decks are used. • 8. When finished with the decks, students rotate roles and begin practicing again.
K-2 Grade Strategies • Number Bonds
K-2 Strategies (Continued) • Branching
½ of ¾ ¾ of ½
Grade 5 (Level 4A with extension to 5A)Product of Fractions • ½ of ¾ • Johnny had 16 cookies. He gave 3/4 of his cookies to his sister, Susie. She ate 1/2 of her cookies, and saved the rest for her dad. What fraction of all the cookies did Susie eat? How many cookies did she save for her dad?
Lesson 4.1a A Fraction of a Fraction (Taken from Primary Mathematics Standards Edition student Textbook 5A) Teacher Directed
Teacher Directed Instruction continues from the concrete to pictorial with students drawing the models in their math journals or dry erase boards. (Students create their own pictures) Notice that the colored boxes are not for writing, but discussion opportunities. (Students should not write in their textbooks.)
Lesson continues until purple pencil indicating workbook exercise to be completed as independent practice.
Notice the picture to the left. Students should determine from the picture what the correct fraction is. Then, verify their conclusion by the equation to the right. Students should be able to explain what is happening in the picture. Perhaps, even tell a story to match the picture…
Notice the space allowed on this practice page. The expectation is for the student to draw a picture, not just to simply multiply numerators and denominators.
Singapore Model Drawing Method Alice earned money from tips from her waitress job. She put ¼ of the money in her savings account. She gave ¾ of the remaining money to the local food bank. She had $12 left for herself. How much money did Alice earn in tips?
Let’s Get Started! • Share how you solve the problem. • "Get out your work paper." Not your scratch paper. • Use page protector sheet over text page. Use dry erase marker.
Step 1:Read the entire problem and underline the question. Alice earned money from tips from her waitress job. She put ¼ of the money in her savings account. She gave ¾ of the remaining money to the local food bank. She had $12 left for herself. How much money did Alice earn in tips?
Step 2: Rewrite question as an answer statement. How much money did Alice earn in tips? becomes… Alice earned _________ in tips.
Step 3: Determine who and/or what is involved in the problem. Alice earned money from tips from her waitress job. She put ¼ of the money in her savings account. She gave ¾ of the remaining money to the local food bank. She had $12 left for herself. How much money did Alice earn in tips?
Step 4: Draw a Unit Bar(s) Alice’s Tips
Step 5: “Chunk” the Problem Draw in information that you know 1/4 Alice’s Tips savings
Step 5: “Chunking”… Continue to fill in information that you know… 1/4 Alice’s Tips savings Remainder Can you see what each fourth is equal to in the bottom bar? Food bank contribution $12 3/4
Step 6: Perform Calculations 1/4 Alice’s Tips savings Remainder Each fourth is equal to $12, We use the calculation $12 x 4 = $48 So, we know the remainder was $48. Food bank contribution $12 $12 $12 $12 3/4
Step 6: Perform Calculations Remainder($48) 1/4 Alice’s Tips savings $16 $16 $16 On the top bar, the Remainder is divided into thirds. $48 / 3 = $16 Food bank contribution $12 3/4
Step 7: Conclusion Remainder ($48) 1/4 Alice’s Tips savings $16 $16 $16 $16 We see that each fourth on the top bar is equal to $16. So, the total tips that Alice earned were $16 x 4 = $64 Food bank contribution $12 3/4
Step 7: Conclusion Alice earned $64 in tips. 1/4 Alice’s Tips savings $16 $16 $16 $16 Food bank contribution $12 3/4
Singapore Model Drawing • You Try!
Manipulatives! • What do I need for my student? • What will they use in class? • What should I use at home? • Parent/student Make and Take. • Anyone have access to a laminator?
Sept. 8 Singapore Training • How do I use my curriculum? • What will my student be learning this year? • What does a typical week look like? • What can I do during the day or week if I need help? • Extra practice or Intensive Practice? • Future training workshops