Category: Algebraic Thinking

Grade: 3-8

You’re planting in the garden and uncover a vase buried in the soil. After cleaning the vase, you place it on your bedside table.

You notice something shiny in the vase before you go to sleep. You pull out a handful of pennies and count them up. There are 6 pennies in the vase.

When you check the vase at the end of the second day, you count 12 pennies.

At the end of Day 3, you count 18 pennies.

How many pennies will be in the vase after 10 days? 25 days? 100 days? Can you come up with a rule to find the number of pennies in the vase on any day?

Anticipatory Set

Lesson Plan

Black Line Master

Magic Box

Grade: 3-8

Your Grandma gives you a wooden box for your birthday. When you unwrapped the gift and opened the box, you were expecting some cash inside but found the box was empty.

You felt bad for not appreciating the box, and decided you could use it to store important things. Just before you go to bed, you open the box to put a photo inside, and see 2 pennies.

When you check the box at the end of the second day, you count 4 pennies.

At the end of Day 3, you count 8 pennies.

How many pennies will be in the box after 10 days? 15 days? 20 days? Can you come up with a rule to find the number of pennies in the box on any day?

Anticipatory Set

Lesson Plan

Black Line Master

You’re cleaning out your closet and find a velvet bag in the corner. When you pick up the bag it feels heavy, and you find 24 pennies inside it. Before you go to sleep, you pull out the pennies and count them up again.

Now there are 27 pennies in the bag! When you check the bag at the end of the second day, you count 30 pennies.

At the end of Day 3, you count 33 pennies.

How many pennies will be in the bag after 10 days? 25 days? 100 days? Can you come up with a rule to find the number of pennies in the bag on any day?

Anticipatory Set

Lesson Plan

Black Line Master

Ichiro Problem

Grade: 3-12

It has been one month since Ichiro’s mother has entered the hospital. Ichiro decided to pray with his younger brother at a local temple every morning so that she will get better soon. There are 18 ten-yen coins in Ichiro’s wallet and just 22 five-yen coins in the younger brother’s wallet. They decided to take one coin from each wallet every day, put them in the offertory box, and continue to pray until either wallet becomes empty. One day when they were done with their prayer, they looked into each other’s wallets. The amount of money in the younger brother’s wallet was greater than Ichiro’s amount of money. When this happened, how many days had it been since they started their prayers?

Anticipatory Set

Lesson Plan

Black Line Master

Carlos’ Cell Phone

Grade: 3-12

Carlos is thinking of changing cell phone plans so he is comparing several different plans.

Plan 1) Pay as you go plan $0.99
Plan 2) Per minute $30 monthly fee plus $0.45
Plan 3) Per minute $40 monthly fee plus $0.35
Plan 4) Per minute $60 monthly fee plus $0.20
Plan 5) Per minute $100 monthly fee for unlimited minutes

What will Carlos need to consider to make his decision? How can Carlos figure out which plan is best for him?

Anticipatory Set

Lesson Plan

Black Line Master

Buying MP3s

Grade: 3-12

You have decided to use your allowance to buy an mp3 purchase plan. Your friend Alex is a member of i sound and pays $1 for each download. Another one of your friends, Taylor, belongs to Rhaps and pays $13 a month for an unlimited number of downloads. A third friend, Chris, belongs to e-musical and pays a $4 monthly membership fee and $0.40 a month per download. Each friend is trying to convince you to join their membership plan. Under what circumstances would you choose each of these plans and why?

Anticipatory Set

Lesson Plan

Black Line Master

Touchdowns & Field Goals

Spiders And Ants

Magic Vase

Magic Box

Magic Bag

Ichiro Problem

Carlos’ Cell Phone

Buying MP3s

Bicycles and Tricycles