Where do equations come from, where do they go and how do they get there? The lesson goal and objectives: Given a word problem and manipulatives, students will be able to write and solve a two-step equation. By doing this we hope they will also gain a better understanding of where equations come from and why we use them.
Multiplication and Division Lesson 4. Solving and Explaining 2-Step Word Problems In this lesson, we discussed how to solve 2-step word problems, and represent the problem solving steps with bar diagrams.
The purpose of the bar diagrams is to provide a visual bridge between the in-words description in the word problem, and the number sentence computation that gives the answer. In a two-step word problem, the process involves deciding what should be computed first, and what second, and then determining and computing both steps.
Most of the examples in this lesson are taken from the textbook Primary Mathematics 3A. I'll include the page numbers and a few screen captures so you can look at the carefully polished examples included in the book.
Addition and subtraction First a reminder: When showing a difference, you need bars that represent the compared amounts, and a grouping symbol to show the difference. In this case one of the bars is labelled with a "?
It's important to know that both of these diagrams indicate a subtraction situation. Mary made paper flowers. She sold some of them. If were left over, how many flowers did she sell? John read 32 pages in the morning. He read 14 fewer pages in the afternoon.
Here, part a prompts for the first step you would need to compute, and part b uses the result from a to get a solution. Usually, you need two separate diagrams to show the two solution steps.
Sometimes, however, they can be combined. Here's how the authors of Primary Mathematics 3A combined the steps in this problem into one diagram: In a full 2-step word problem, the student must figure out the steps.
So to solve the problem: How many more boys than girls were there? In the previous sectionyou'll find examples of bar diagrams for 1-step word problems. There are additional good examples of multiplication and division bar diagrams on pages 78 and 79 of Primary Mathematics 3A.
Most 2-step word problems that involve multiplication and division have a multiplication or division step and an addition or subtraction step. In this example, the multiplication step comes first, and the subtraction step comes second--first you have to find the number of chickens, and then you can find how many more chickens than ducks: A farmer has 7 ducks.
He has 5 times as many chickens as ducks. How many more chickens than ducks does he have? You can represent this using two separate diagrams--one for each step: It's OK to write 7 into each part, as in the diagram on the left, and it's OK to write it just once so long as the bars look approximately equal.
It's OK to write the numbers in the bar, and it's OK to write the numbers above the bar. It's OK to use a bar to show the difference, and it's OK to leave that space blank that's what I'm trying to show by the dotted lines on the bar in the diagram on the right.
This problem is also one where you could get away with having only one diagram, if you put it together very cleverly: You can also find this example on page 79 in Primary Mathematics 3A. In that example, they only show a bar diagram for the first part.
I want you to know how to make bar diagrams to help you explain both parts, but as a teacher, you'll be deciding how much support your students need for understanding each part so with some problems or some classes you may choose to use a diagram for each part of a word problem, and with other problems or classes, you may choose to use diagrams with only one parts, or you may decide that the students are ready to make the transition from the in-words description to the number sentence without the aid of a diagram.
An example with multiplication and addition:In the previous lesson we learned how to write variable and numerical expressions involving addition and subtraction.
In this lesson we learn how to use multiplication and division to write expressions. A number right next to a variable is assumed to represent multiplication. Example 2.
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If a student can read a problem, write and solve an equation, they have an essential understanding of the mathematics. Middle school students do not need manipulatives.
Vertical Connections. The student will be able to: a. investigate and describe the concept of variable. b. write an open sentence to represent a given. Stay up to date with all of our great fitting styles and new season arrivals.
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