Math Resources – Page 26

Seeking Singapore Math Assessments?

October 29, 2010 by Cassy Turner 1 Comment

A recent visitor left this comment:

I am part of a team of first grade teachers at my school. We are piloting Singapore Math this year. We are creating assessments and were looking for ready-made assessments to genuinely fit the curriculum.

One of the challenges for a classroom teacher using the U.S Edition is that there aren’t any assessments ready-made. The Standards Edition of Primary Mathematics has assessments, however they won’t correspond directly to the U.S. Edition Materials.

Keep in mind that if you write the questions, you can tailor them to the objectives of your lessons. Are you assessing for basic competency? Are you assessing for deeper understanding? Additionally, for a teacher-created assessment, you need to create an answer key. I frequently hear from teachers who tell me, “Well, I gave this test, but all I have is the answer and I’m not sure how to work the problem.”

That being said, I know teachers’ time is valuable. Many teachers use questions from the Review sections of the textbook. Other basic questions from Intensive Practice books or practice problems from the Challenging Word Problems books could be used as well.

Be sure to save any well-written assessments for future use. After one year of working with the materials, you should have a good bank of assessments for future years.

One site that offers Singapore test paper problems for free (with registration) is Old School. At the first grade they have several mid-year and end-of-term papers available. Teachers can select the questions, either short answer or multiple choice, and create an assessment. Additionally, you can choose problems from a list of topics. Topics for first grade are:

Addition and Subtraction

Combination Questions (3%)

Comparing and Ordering numbers (13%)

Division (1%)

General (1%)

Graphs (5%)

Measurements (7%)

Multiplication (3%)

Notation and Place values (9%)

Shapes and Patterns (12%)

Would you be interested in a test bank of questions? How about a place for sharing some teacher-made tests?

Filed Under: Math Events, Math Resources Tagged With: materials, Singapore Math resources

Solving SAT problems using the model method

August 8, 2010 by Cassy Turner 1 Comment

David Marain 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.
Changing Ratios is taught in level 6A in the Primary Mathematics materials (U.S. Edition), typically used in 6th grade classrooms.

Filed Under: Math Resources, Singapore Math Problems Tagged With: Model Method, Word Problem

Singapore Math and Math Journal Writing

July 14, 2010 by Cassy Turner 4 Comments

Out in Left Field posts a Math Problem of the Week comparing different curricula that schools use. Last week’s Riddles in 2nd Grade Investigations vs. Singapore Math and the ensuing comments brought up discussion on the value of writing in the mathematics classroom. I picked up a book entitled: Journal Writing in the Mathematics Classroom (Primary) when I was in Singapore. It is written and published by professors at Singapore’s National Institute of Education.

Among the chapters listed:

Why use Journal Writing?

Journal writing reinforces the learning and provides pupils with opportunities to engage in reflection, question their own understanding, connect the abstract and the concrete, and apply the knowledge they have acquired to solve problems.

How to Carry Out Journal Writing?

This section starts with an this powerful statement about journal writing in the classroom:

Journal writing is a complex process that requires effort and patience.

The authors further suggest that these open-ended prompts encourage pupils to write about their opinions and feelings on mathematics. They have adapted and describe three types of general writing prompts:

1. Affective or Attitudinal (How do you feel?)

My best kept secret about math is …

If math could be a colour (shape, sound) it would be … because

2. Mathematical content (What is it about?)

How would you describe a …

What patterns do you notice in …

3. Process (Explain how!)

Find something that you learned today that is similar to something you already knew.

You know several ways to … Which method is you favourite? Why?

There is a list of 15 of each type of general writing prompt. The bulk of the book, however, focuses on specific writing prompts that are based on mathematical topics.

Possible Negative Aspects of Journal Writing

(Lessons learned the hard way when I was teaching!)

Scoring Rubrics and Student Examples

This section includes examples of two types of scoring rubrics: Analytic, which allows for separate evaluation of selected factors and Holistic, which can be used when teachers want to rate student responses more generally.

A Collection of Specific Writing Prompts

Finally, there are 55 specific writing prompts differentiated by grade level and topic. Topics include: Whole Numbers, Fractions, Decimals, Percentage, Ratio, Rate, Measurement, Geometry, Statistics and Algebra. Some examples:

Topic: Whole Numbers
Level: Primary 2 – 6

Write a word problem and make a picture that goes with 4 x 3.

Topic: Decimals
Level: Primary 4 – 6

Find two decimal numbers between 0.2 and 0.3. How many decimal numbers are there between 0.2 and 0.3? Explain.

Filed Under: Math Resources Tagged With: math journals, Singapore Math resources

Singapore Math Must-Know Word Problems

June 9, 2010 by Cassy Turner 3 Comments

From publisher Frank Schaffer and Singapore Asian Publications comes a series of books: Singapore Math: 70 Must-Know Word Problems. From the back cover:

This book is designed to help students master word problems, which are often tricky and challenging…This book is perfect for students familiar with Singapore Math and for those who just need extra practice with word problems.

The 70 Must-Know Word Problems books are marked by levels that are considered a grade above for the U.S. market. For example, the Level 6 book claims to be appropriate for students in grade 7 and the Level 4 book is listed as appropriate for students in grade 5. If your child has been learning with Primary Mathematics and you’d like to pick up one of these workbooks, you should probably pick up the level that correlates to their current grade. Meaning, if your child is currently working their way through the Level 4 Primary Mathematics textbook, then the level 4 70 Must-Know Word Problems book will work as a supplement. The problems in the books are extra practice type problems, designed to give students similar to the ones in the Primary Mathematics textbooks. If you student is look for something harder, you might want to consider the Challenging Word Problems for Primary Mathematics series.

The 70 Must-Know series does not follow the Primary Mathematics lesson progression, the questions jump between concepts. Questions #3 and #47 in the Level 6 book, for example, are both on Volume. Question #2 & 5 cover the four operations with money and Question #4 is on percentages, so you may need to verify that a topic has been covered in class if your planning on using the book at home. The books have little instruction, however they do include a four page Introduction to Singapore Math (be forewarned, it’s written in six-point font!). Each problem has its own full page for work and there are fully worked solutions included in the answer key.

Here’s Question #70 from the Level 4 book. It’s listed in the table of contents under “Addition, Subtraction, Multiplication and Division of Whole Numbers”.

At a movie, 1/4 of the people in the theater were men, 5/8 were women and the rest were children. If there were 100 more women than children, what was the total number of people in the theater?

And Question # 48 from Level 6:

A box contained some red, blue, and green markers. For every 5 red markers, there were 2 blue markers. For every 3 blue markers, there were 5 green markers.

(a) Find the ratio of red markers to blue markers to green markers.

(b) When 6 red markers were removed from the box, 3/7 of the remaining markers were red markers. How many markers were left in the box?

Singapore Math: 70 Must-Know Word Problems was $12.99 at my local Barnes and Noble and Borders stores. The easy accessibility of these books make them great for parents looking for additional problems for their students. Teachers looking to use these materials in class need to keep on mind that these books may already be in their students’ homes!

Filed Under: Math Resources, Singapore Math Problems Tagged With: Singapore Math resources, Singapore Math word problems

i-Excel: Heuristic and Model Approach

January 19, 2010 by Cassy Turner Leave a Comment

From a discussion on the Well-Trained Mind Forums is a question about some the supplemental material available for the Primary Mathematics curriculum:

On the (SingaporeMath.com) site there are some supplemental books I don’t recognize, but I can’t tell what they’re for–if they’re new-new or replacing-CWP-new

Math Works?
i-Excel?
Math Express?
Brain Maths?

I wrote here about the MathExpress: Speed Maths Strategies.

i-Excel Heuristic and Model Approach (Update 2/2013 – Series going out of print and will be replaced with: Process Skills in Problem Solving)
Author: Li Fanglan
Published by Fan-Learning
Levels 1-6 available in the U.S. from Singaporemath.com

The i-Excel: Heuristic and Model Approach is a completely different type of workbook than the MathExpress series. i-Excel books focus on problem solving. Can you deduce the meaning of “heuristics” based on the following description from the introduction?

At primary levels, Model Approach has been proven to be the most versatile and effective method to help pupils solve many difficult problems.Heuristic Approach, on the other hand, helps them handle the higher level problem solving by unconventional means.

Heuristic Approach

The first part of each book includes eight different Heuristic Approaches and then focuses on different Model Approaches based on topics taught at each level. Heuristic Approaches in Level 2 include the following:

Guess and Check

Act it Out

Draw a Diagram I

Make a List

Look for a Pattern I

Draw a Diagram II

Draw a Diagram III

Look for a Pattern II

Upper level Heuristic Approaches include: Simplify the Problem, Work Backwards, Make a Supposition, Solve Part of the Problem, Use Before-After Concept and Restate the Problem in Another Way. Each Heuristic Approach has a worked example, four or five practice problems and one more challenging problem to solve. (Some levels put these challenging problems into a separate unit.)
Here’s the challenge problem from Level 2 – Draw a Diagram II:

A pizza was cut into halves.
Jolene took one half and ate 2/3 of it.
a) What fraction of the pizza did she eat?
b) What fraction of the pizza was left?

Completed guided examples are included in the Answer Key at the end of this section. Make a note, however, not all questions have worked solutions.

Model Approach

The second portion of the books works with the Model Approach as it applies to mathematical topics.

Levels 1-3 focus on applying the Model Approach with the four operations. They also have yellow, pink and blue rectangular stickers in the back of the book for students to use with the model drawing problems. These are important for students who are learning or struggling with drawing proportional bar models.
Level 4 has two parts consisting of 28 units on the Model Approach: Whole Numbers and Fractions. There is also a Part IV: Non-Routine Problems – Challenge Yourself 4.
Level 5 has sections on Whole Numbers, Fractions, Ratio, Decimals, and Percentage. Part VII includes 3 assessments.
Level 6 parts include ratio and Proportion, Percentage and Speed. The final section is entitled “Examination Practice”. Some of these problems are double starred for extra challenge.

Here’s an example of a ** problem from that unit:

Grace had a total of 120 red and blue pens in the ratio of 3:5. After she gave away an equal number of each type of pens, the number of red and blue pens left was in the ratio 3:8. How many pens did she give away altogether?

Good news if you’re scratching your head right now. All problems in Level 6 have detailed solutions worked in the answer key.

In the classroom

Most who have used Primary Mathematics would agree; the focus is on the bar model as the main problem solving strategy. The i-Excel series brings explicit instruction in additional problem solving strategies into the classroom. This is one of my favorite supplemental books to use with students. The challenge and variation makes it a favorite of students as well. I have incorporated the heuristics into a self-directed activity and have used the challenge problems for a “Problem of the Week”.

The Level 3 book includes a unit entitled “Act it Out” that became a great independent activity/group center. The example given is to use 10 coins to form the figure below. Moving only one coin at a time, what is the least number of moves to turn the shape upside down?

After working this example as a whole group activity, I could now have chips (coins) and new problems available in the classroom: as part of centers, as a substitute lesson plan, or for students to use as a quiet desk activity.

Have you used the i-Excel or Brain Maths series? Share your experiences in the comments below. I’d love to know how the books have worked in a classroom or in your home.

Filed Under: Math Resources Tagged With: materials, Singapore Math resources