Unit 8: Problem Solving · Lesson 7
Problem Solving - Lesson 7
What this lesson is for
- Students will understand and practice Problem Solving - Lesson 7
- Students will solve problems related to this topic
Train up a child in the way he should go: and when he is old, he will not depart from it.
Proverbs 22:6
Make a Table
Making a table is a strategy that organizes information systematically into rows and columns to reveal patterns, track progress through a problem, and make complex situations easy to understand. Tables are especially powerful for problems with multiple cases, rates, or growing quantities.
When to use a table: problems with a pattern that grows over time, rate problems (cost per item, distance per hour), problems where you need to check multiple possible answers, and problems with two related quantities that change together.
How to make a useful table: (1) Label the columns clearly (what each column represents). (2) Fill in values you know from the problem. (3) Look for a pattern between rows. (4) Extend the table to reach the answer. Example: 'A library fines borrowers $0.25 per day for overdue books. After how many days will the fine exceed $2.00?' Table: Day 1 → $0.25; Day 2 → $0.50; Day 3 → $0.75; Day 4 → $1.00; Day 5 → $1.25; Day 6 → $1.50; Day 7 → $1.75; Day 8 → $2.00; Day 9 → $2.25 (first day over $2.00). Answer: 9 days. The table makes it obvious.
Tables also allow solving problems with multiple solutions at once. 'For what number of bags ($3 each) does the total cost exceed $20?' Table shows: 7 bags = $21. Answer: 7 bags. Tables serve as a visual 'simulation' of the problem's scenario.
A candle is 15 inches tall and burns 2 inches per hour. When will it be less than 5 inches tall? Make a table. (Hour 0=15; 1=13; 2=11; 3=9; 4=7; 5=5; 6=3 inches — less than 5 at hour 6.)
Bible Verse: "Write the vision, and make it plain upon tables, that he may run that readeth it." — Habakkuk 2:2. God commanded His prophet to make the vision plain in a table — organized clarity serves everyone who reads it.
Activity: Use a table to solve: 'A person saves $5 the first week, $10 the second week, $15 the third week, increasing by $5 per week. After how many weeks will total savings exceed $100?' Create the table with columns: Week | Saved That Week | Total Saved. Continue until the total exceeds $100.
Guided practice
Apples cost 50 cents each. Make a table showing cost for 1, 2, 3, 4, and 5 apples. How much do 8 apples cost?
Show the steps and the answer
Step 1: Create a table: 1 apple=$0.50, 2=$1.00, 3=$1.50, 4=$2.00, 5=$2.50. Step 2: See the pattern: cost = quantity × $0.50. Step 3: 8 × $0.50 = $4.00.
Answer: 4.00
A farmer earns $15 per hour. Make a table for 1, 2, 3, and 4 hours worked. How much does he earn in 6 hours?
Show the steps and the answer
Step 1: Table: 1 hr=$15, 2 hrs=$30, 3 hrs=$45, 4 hrs=$60. Step 2: Pattern is: earnings = hours × $15. Step 3: 6 × $15 = $90.
Answer: 90
A candle is 15 inches tall and burns 2 inches per hour. Make a table for hours 0, 1, 2, 3, 4. When is it less than 5 inches?
Show the steps and the answer
Step 1: Table shows: Hour 0=15 in, 1=13 in, 2=11 in, 3=9 in, 4=7 in, 5=5 in, 6=3 in. Step 2: After 6 hours it is 3 inches (less than 5).
Answer: 6
Homework
Complete the practice problems for Problem Solving - Lesson 7.
Note for the parent
Today's lesson covers Problem Solving - Lesson 7. Estimated time: 40 minutes. Encourage independent work but be available for questions.
The first three of this lesson's 10 questions
Making a table is most useful for problems that involve ___.
Show the answer
Answer: Multiple cases, rates, or growing quantities that can be organized in rows and columns
A table for 'cost of apples at $0.50 each': 1 apple=$0.50, 2=$1.00, 3=$1.50, 4=$2.00. Cost of 8 apples = ___.
Show the answer
Answer: $4.00 (8 × $0.50)
A table shows distance traveled at 60 miles per hour: 1 hr=60 miles, 2 hrs=120, 3 hrs=180. Distance after 5 hours = ___.
Show the answer
Answer: 300 miles (5 × 60)
Another 7 questions follow in the lesson itself, each one graded the moment it is answered.