Certificate in Singapore Certificate in Math Strategies: Advanced Model Drawing for Grades 6-9 Online Course

What Is Model Drawing?

Jason groans when you say it’s time for math, Leona can’t get the hang of equations, and Sunny struggles to make sense of word problems. What’s the solution for all of them? Model drawing! In this lesson, you’ll discover the basics of model drawing and find out why this technique is a core part of Singapore Math—an approach that turns middle-school math-haters into eager, proactive problem solvers.

Part-Whole Word Problems

Today, we’re going to dive into modeling by exploring one the easiest types of word problems: a part-whole word problem. We’ll begin with simple problems and work our way up to trickier ones, ending up by modeling partitive and quotitive word problems. As we go along, you’ll get plenty of practice building your own models and using them to find solutions. In addition, I’ll offer helpful tips for getting all of your students involved in your model-drawing sessions.

Word Problems Involving Comparisons

Tom has three times as many apples as Nguyen. Nguyen has six more apples than Beth. How can we figure out how many apples they each have? With modeling, of course! Today, we’ll explorecomparison problems involving addition, multiplication, or both. By the time we’re done, you’ll be solving the trickiest problems with ease—and you’ll also have a good grasp on how to combine functions in a single model.

Before-and-After Word Problems

Do “before-and-after” word problems make your students go all wobbly in the knees? Well, don’t worry, because modeling quickly cuts these problems down to size. In this lesson, we’ll tackle three types of before-and-after questions: fraction, ratio, and age questions. You’ll learn how to draw two models (a before model and an after model) for each problem, and you’ll discover why it often makes sense to start at the end of your problem—not the beginning.

Shifting and Subdividing Units

We’re going to add to your toolbox of skills today by exploring two new model-drawing techniques: unit-shifting and subdividing. These skills are invaluable when you’re modeling complex problems, and you’ll find out how to use them separately and in combination. In addition, we’ll talk about the importance of teaching perseverance as your students work on increasingly challenging problems.

Comparison Problems Using Fractions, Decimals, and Ratios

You modeled comparison problems earlier, but now it’s time to kick it up a notch! In this lesson, you’ll solve comparison problems involving fractions, decimals, and ratios. You’ll also get ideas for fun classroom activities that will help your kids understand math concepts.

Problems Involving Consecutive Integers

Today, we’ll focus our sights on problems involving consecutive integers—that is, numbers that follow each other in sequence. In addition, you’ll learn how to model problems involving consecutive odd or even integers—and you’ll discover some secrets for making sure your learners have a strong math vocabulary.

Remainder Word Problems

Kids (and even teachers) often have trouble with remainder problems, but questions like these are a cinch when you put the power of modeling to work for you. In this lesson, you'll learn how to use remainder bars in your models and how to handle remainder problems involving fractions, decimals, and percents. You'll also discover how to differentiate your modeling lessons by creating "living models." It's a powerful learning technique—and it's fun!

Percents

Middle-school students need to be able to work easily with percents, and here’s your chance to help them ace this skill. In this lesson, you’ll move from simple percent problems to complex ones that also involve before-and-after concepts. By the time you’re done, 100% of your kids will have a new tool for conquering percent problems!

Rate-and-Distance Problems

Does your class groan when they see a problem that starts out, "A train leaves the station at 9 a.m. going 50 miles an hour . . . "? Well, after today, they'll actually look forward to brain teasers like this. (Really!) That's because with modeling, your students can ace even the toughest rate-and-distance problems in just a few minutes. We'll work our way from easy to complex problems, and along the way you'll get tips for helping kids grasp the concepts of speed, rate, time, and distance.

Putting It All Together: Practicing Your New Skills

We've worked a wide range of problems in this course, and now it's time to put it all together. In this lesson, you'll find two practice sessions that will help you hone your modeling skills. Then we'll end off with a twist in your third practice session: You'll create your own word problems based on the models I give you. It's a great way to boost your modeling creativity!

Getting off to a Successful Start

This is our final lesson, but it’s just the beginning of your modeling adventure! Today, you’ll get tips for starting that adventure off on the right foot as you introduce modeling to your students for the first time. In addition, you’ll find out how to hone your own modeling skills so you’ll shine in the classroom. And finally, we’ll look at how you can turn parents (even the skeptical ones) into allies by teaching them the basics of modeling.