Singapore Math Strategies: Advanced Model Drawing for Grades 6-9

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

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

Do "before-and-after" word problems leave you with a room full of blank stares? Well, don't worry, because modeling quickly cuts these problems down to size. In this lesson, you'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 discover why it often makes sense to start at the end of your problem—not the beginning.

In this lesson, you'll add to your toolbox of skills 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, the lesson will talk about the importance of teaching perseverance as your students work on increasingly challenging problems.

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.

In this lesson, you'll focus your 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 then discover some secrets for making sure your learners have a strong math vocabulary.

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!

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!

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 this lesson, 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. You'll work your way from easy to complex problems and get some tips for helping kids grasp the concepts of speed, rate, time, and distance.

You'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, you'll finish the lesson with a twist in your third practice session: You'll create your own word problems based on the models you receive. It's a great way to boost your modeling creativity!

This is the final lesson, but it's just the beginning of your modeling adventure! In the lesson, 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 that you'll shine in the classroom. Finally, you'll look at how you can turn parents (even the skeptical ones) into allies by teaching them the basics of modeling.