In this Grade 4 lesson from Saxon Math Intermediate 4, students practice identifying and extracting the information needed to solve problems, including recognizing when extra information is present. Using real-world scenarios, students apply the tree diagram strategy to find all possible combinations, such as outfit pairings and key chain arrangements. The lesson builds critical problem-solving skills by teaching students to distinguish between necessary and unnecessary data before performing calculations.
Section 1
📘 Finding Information to Solve Problems
Part of the problem-solving process is finding the information needed to solve a problem.
Next, you will practice extracting the necessary information from paragraphs, tables, and diagrams to solve various word problems.
Section 2
Reading Math
Sometimes problems contain too much information. We need to look for the information that is necessary to solve a problem.
Example 1: Terell worked 3 hours in the morning and 4 in the afternoon for 6 dollars an hour. To find his total pay, you only need total hours () and the rate. The morning/afternoon detail is extra.
Example 2: A gift of 160 dollars is divided among 8 children on May 5th. To find each child’s share, you only need the total amount and the number of children: dollars. The date is not needed.
Think of yourself as a word problem detective! Your mission is to solve the case, but the story is often filled with extra details to throw you off track. You must carefully read the question to understand what you are being asked, then scan the information to pull out only the numbers and facts you absolutely need.
Section 3
Make a Diagram
A tree diagram helps visualize and list all possible combinations. For each choice at one stage, draw 'branches' to every possible choice at the next stage. This systematically organizes all outcomes so none are missed.
Example 1: A cafe has 2 breads (white, wheat) and 3 cheeses (cheddar, swiss, provolone). A tree diagram clearly shows the 6 possible sandwich combinations.
Example 2: For a coin toss (Heads, Tails) and a spinner with 3 colors (Red, Blue, Green), a diagram shows all 6 outcomes: H-R, H-B, H-G, T-R, T-B, T-G.
When a problem asks for all possible combinations, like different outfits or meal choices, listing them can get messy. A tree diagram is a fantastic visual tool to keep everything organized. By starting with one set of choices and branching out to the next, you create a clear map that shows every single possible outcome without missing any.
Section 4
Listing all arrangements
When asked to find the number of different ways to arrange items, create a systematic list. Start by fixing the position of one item and listing all arrangements for the remaining items, then repeat for each starting item.
Example 1: To arrange the letters A, B, C, first fix A: A-B-C, A-C-B. Next, fix B: B-A-C, B-C-A. Finally, fix C: C-A-B, C-B-A. This gives 6 total arrangements.
Example 2: Three friends, Tom, Sam, and Liz, are in a line. The possible orders are: Tom-Sam-Liz, Tom-Liz-Sam, Sam-Tom-Liz, Sam-Liz-Tom, Liz-Tom-Sam, Liz-Sam-Tom. There are 6 ways.
To find every possible way to arrange a group of items in a line, you need a system so you do not get lost or repeat yourself. The trick is to be methodical: place one item in the first spot and list all the ways the others can be arranged. Then, pick a new item for the first spot and do it again.
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Section 1
📘 Finding Information to Solve Problems
Part of the problem-solving process is finding the information needed to solve a problem.
Next, you will practice extracting the necessary information from paragraphs, tables, and diagrams to solve various word problems.
Section 2
Reading Math
Sometimes problems contain too much information. We need to look for the information that is necessary to solve a problem.
Example 1: Terell worked 3 hours in the morning and 4 in the afternoon for 6 dollars an hour. To find his total pay, you only need total hours () and the rate. The morning/afternoon detail is extra.
Example 2: A gift of 160 dollars is divided among 8 children on May 5th. To find each child’s share, you only need the total amount and the number of children: dollars. The date is not needed.
Think of yourself as a word problem detective! Your mission is to solve the case, but the story is often filled with extra details to throw you off track. You must carefully read the question to understand what you are being asked, then scan the information to pull out only the numbers and facts you absolutely need.
Section 3
Make a Diagram
A tree diagram helps visualize and list all possible combinations. For each choice at one stage, draw 'branches' to every possible choice at the next stage. This systematically organizes all outcomes so none are missed.
Example 1: A cafe has 2 breads (white, wheat) and 3 cheeses (cheddar, swiss, provolone). A tree diagram clearly shows the 6 possible sandwich combinations.
Example 2: For a coin toss (Heads, Tails) and a spinner with 3 colors (Red, Blue, Green), a diagram shows all 6 outcomes: H-R, H-B, H-G, T-R, T-B, T-G.
When a problem asks for all possible combinations, like different outfits or meal choices, listing them can get messy. A tree diagram is a fantastic visual tool to keep everything organized. By starting with one set of choices and branching out to the next, you create a clear map that shows every single possible outcome without missing any.
Section 4
Listing all arrangements
When asked to find the number of different ways to arrange items, create a systematic list. Start by fixing the position of one item and listing all arrangements for the remaining items, then repeat for each starting item.
Example 1: To arrange the letters A, B, C, first fix A: A-B-C, A-C-B. Next, fix B: B-A-C, B-C-A. Finally, fix C: C-A-B, C-B-A. This gives 6 total arrangements.
Example 2: Three friends, Tom, Sam, and Liz, are in a line. The possible orders are: Tom-Sam-Liz, Tom-Liz-Sam, Sam-Tom-Liz, Sam-Liz-Tom, Liz-Tom-Sam, Liz-Sam-Tom. There are 6 ways.
To find every possible way to arrange a group of items in a line, you need a system so you do not get lost or repeat yourself. The trick is to be methodical: place one item in the first spot and list all the ways the others can be arranged. Then, pick a new item for the first spot and do it again.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter