Model Drawing to solve SAT mathematics problem from www.singaporemathsource.com

Solving SAT problems using the model method

From national Singapore Math trainer, Cassy Turner at http://www.singaporemaths.com/:

David Marin over at MathNotations has been periodically tweeting an SAT problem of the day via @dmarain. A recent series of tweets asked:

A 42 oz mix of nuts is 6 parts peanuts to 1 part cashews. How many ounces of cashews must be added to make a make the mixture 2 parts cashews to 1 part peanuts? Does Singapore (bar) model method work here?

Sure it can! Here’s one solution.
First model the beginning mixture at 6:1.

Next, we can figure out how many units need to be added to the cashews to make the cashews to peanuts ratio 2:1.

Since there are 11 additional units and the value of each unit is 6 oz, we can find the value of the added cashews.

66 ounces of cashews must be added to the peanuts to make the mixture 2:1.
"Content from http://SingaporeMathSource.com (c) Cassandra Turner reproduced courtesy of the Author."

Model Drawing

 Two great sites for help and practice are
http://www.thinkingblocks.com/  and  www.thesingaporemaths.com/index.html.
Both have guided overviews and offer ways to improve solving math
situations using the Model Drawing strategy. Try them out and share your
experience and your questions.

Math in Focus Resources

http://www.hmhelearning.com/Math/Math_in_Focus/index.html

Study on the Effect of Singapore Mathematics on Student Proficiency in a Massachusetts School District

This information is published in many places, but the information below comes from a blog entitled,
"Parents for a Quality Math Education" (PQME).
"In October 2009 Gabriella and Paul Rosenbaum Foundation released a report entitled The Effect of Singapore Mathematics on Student Proficiency in a Massachusetts School District:  a Longitudinal Statistical Examination. It shows that the longer students had Singapore Mathematics as their curriculum the better they performed on Massachusetts’s tests."

The Pentagon Framework for Singapore Mathematics

Trends in International Mathematics and Science Study 2003

Why Singapore ?

In 2003, some 46 countries participated in TIMSS, at either the fourth- or eighth-grade level, or both.
Table 1. Average mathematics scale scores of fourth-grade students, by country: 2003

 

What is Singapore Math? by Anni Stipek, Singapore Math trainer

 You may be wondering what Singapore Math is all about, and with good reason. 

What you may not know is that  Singapore has led the world in math mastery for 

over a decade; its students become competent and proficient mathematicians at very 

early ages. Even better, they grow to be capable problem solvers who think mathematically 

with ease. Wouldn’t it be nice if your child could enjoy the same success with math?  

 First, you need to know that Singapore Math takes a slightly different mathematical  

approach than what you may be used to. It revolves around several key number‐ 

sense strategies: (1) building number sense through part‐whole thinking, (2)  

understanding place value, and (3) breaking numbers into decomposed parts or  

friendlier numbers, ones that are easier to work with in the four operations  

(addition, subtraction, multiplication and division).   

 Second, Singapore Math does something dramatically different when it comes to  

word problems. It relies on model drawing, which uses units to visually represent a  

word problem.  Students learn to visualize what a word problem is saying so they  

can understand the meaning and thus how to solve the problem.  

 Third, we have mental math, which teaches students to calculate in their heads  

without using paper and pencil. Sure, your child will still need to commit  facts  

to memory, but mental math will teach him or her to do calculations using proven  

strategies that don’t require pencil and paper.   

 Fourth, the strategies taught in Singapore are layered upon one another. One  

strategy is the foundation for another one.  For example, students need prior

 knowledge of bonding in order to be successful at strategies they will learn later on 

(like vertical addition). 

Last, Singapore Math teaches students to understand math in stages, 

beginning with concrete (using manipulatives such as counters, number disks, dice, and 

so on), then moving to pictorial (solving problems where pictures are involved), and finally  

working in the abstract (where numbers represent symbolic values). Through the  

process, students learn numerous strategies to work with numbers and build  

conceptual understanding. 

Welcome!

Dear parents and community members,

This is the newest development in an ongoing effort to improve communication
and collaboration in our pursuit of excellence for the students of Warsaw Community Schools.
As the K-12 mathematics coach for the corporation, the primary focus of this blog will be growing
young mathematicians. Let's work together so that our children find the joy of solving puzzles, making
connections, and noticing patterns. Let's work together to enable our students to be fluent at skills and adept at solving problems. Thank you for investing your time to learn more about mathematics education.

Respectfully,

Lorinda Kline