This practical lab is designed to show students how they are already using math in their everyday lives and then help them improve those skills to make better decisions, improve problem-solving skills, and promote confidence. This lab is a learning community where participants share strategies, justify their reasoning, and interact with each other’s ideas.
MATH LAB NOTES
Place value, converting percentages/decimals/fractions, finding discounts & applying tax
Materials needed: Dice, calculators
Game: Place Value
In this game, you roll 2 dice and create numbers that need to find a place on an ascending number path. The video explains it well. 13 squares. Lowest possible is 11, and highest is 66 for our six-sided dice. You could have individuals work alone, or have 2 people work together, taking turns rolling the dice and deciding where to place the number. https://www.youtube.com/watch?v=Bd6uTclUHr8
Variation: Roll 3 dice, make 3 digit numbers. Decimals allowed. 35.2, 15.3. Which is easier and why?
Make a table with 3 columns: Percentage, decimal, and fraction. Give one number and practicing changing from one form to another. Students will need to get comfortable using a calculator to change a fraction to a decimal.
Calculate how much you’d save , then subtotal, then add 7% tax, then grand total. Teach students how to find percentages with a calculator (560 x .35).
$560 with a 35% discount
$900 with a 12% discount
$680 with a 17% discount
Delmy and I had a wonderful one on one tutoring session with lots of practice for adding fractions with unlike denominators.
With all adding and subtracting of fractions, the goal is to get each fraction to have a common denominator. Sometimes you only have to change one of the terms. Other times you have to change both of the terms.
Examples of changing one of the terms:
1/5 + 2/15 (can change 1/5 to 3/15)
7/8 + 1/2 (can change 1/2 to 4/8)
Examples where you have to change both terms:
5/8 + 7/6
You could make the denominator 48 (8×6), but I think it’s a good practice for students to make a list of multiples and find the “least common multiple” to use as the denominator. Multiples of 8 are 8, 16, 24, 32, etc. Multiples of 6 are 6, 12, 18, 24, 30. You can choose 24 as the denominator (since they are multiples of both 6 and 8) and then it also makes it easy to see what you need to multiply 8 by to get 24 (it’s the 3rd one on your multiple list, so you multiply by 3).
Then, you can work on simplifying your answer! That requires a student to find the “greatest common factors” and to divide numerator and denominator until it can’t be further simplified.
There are so many steps with this kind of problem. It can be a tricky process for students and it’s great to see them stick with it!
½=2/4= 3/6= 4/8=5/10=6/12=0.50
¼ = 2/8=3/12=4/16=5/20=0.25
⅓ = 2/6 = 3/9=4/12=5/15=.033
1=2/2=3/3=4/4=8/8=10/10Make playing cards out of each fraction the students found. (Should be 5-6 of each fraction group.
Play “spoons”. 4 cards to each player. The goal is to hold only cards that are equivalent fractions and to grab a spoon at the end of round. The dealer takes a card off of the draw pile and, since they must only have 4 cards at a time, decides which card to “discard”/pass to the next player. The next player takes that card, decides which card to discard/pass on, etc. Instead of passing cards to the original dealer, the card goes in a “discard pile” at the end. Players can draw and pass cards as quickly as they want, so cards may build up between players. That’s ok, but players can only look at one card at a time from their building pile. The first person to have all 4 cards be equivalent fractions gets to grab one of the spoons on the table. As soon as one person grabs a spoon, then the rest of the players must grab a spoon as quickly as possible. There will be one less spoon than the number of players, so someone will always be left without a spoon. You can either have that person be “out” or can give them a certain amount of times to be left “spoonless” before getting out. Once everyone has grabbed spoons, you must check that the first person to grab a spoon actually did have 4 equivalent fractions. If they didn’t, then that person loses.
Keep the equivalent fractions posted on the whiteboard so students can refer to it when deciding whether to keep or discard a card during play. (We decided to color-code these equivalent fractions on the 3×5 cards to make it a bit easier as we played the game).Make chex mix for students.
“Chex mix tripled” lesson supplement (like student book, p 41). We gave the recipe to the students and asked them to triple it.
August 23, 2022
We used cubes, rods, and 100 squares (manipulatives found in the PR office) to solidify place value concepts and to prove if two equations are equal (see examples below)
Starting from a certain number, give step by step directions like “add 10, subtract 11, add 55. See if we come up with the same answer at the end. Use manipulatives to add and subtract. Practice having to “cash in” a 100 square for 10 rods, etc.
Equal or Not Equal
Give everyone at least 2 3×5 cards. They need to write one equation that is equal and one that is not equal. For example: 52+23=100-25 (true) and 21-12=3+11. (not true) We will shuffle up the cards and ask people to prove with manipulatives.
-When you have an equality laid out on the table, ask questions like, what happens when I add 5 to both sides? Is it still equal?
Imagine you are volunteering at a community event and you’ve been asked to stuff 1000 envelopes and peel 50 pounds of potatoes. How will we figure out before hand how long this will probably take? Let students reason it out & hopefully decide to time someone doing a smaller amount and then use that rate/ratio to predict the larger amount. (Student Book pp 25-27). Bring paper, envelopes, potatoes, and a peeler.
Application: Wasting water (Student book: Keeping things in Proportion, p 30).
Go to restrooms by PR office and take samples of dripping faucets. Let students decide how to set this up. How many gallons of water might we waste in an hour? A day? A 30 day month? A year?
Set up a conversion chart:
3 teaspoons = 1 Tablespoon 60 seconds = 1 minute
4 Tablespoons = ¼ cup 60 minutes = 1 hour
4 c water = 1 quart
4 quarts = 1 gallon
August 16, 2022
We reviewed place value and especially focused on the numbers to the right of the decimal point. We practiced interpreting 1/10, 1/100, and 1/1000 and learned how to put decimals into words. For example: 543.278 is five hundred forty three and two hundred seventy eight thousandths. We also practiced expanding out decimals into their components. For example: 543.278 = 500 + 40 + 3 + 2/10 + 7/100 + 8/1000. After this, we went through some test practice questions on p 85 of Using Benchmarks: Fractions and Operations (student book). We filled the rest of the class time working through these and teaching mini lessons where more support was needed. I encourage you to always use fraction tiles first to understand the problem more deeply, and then we learned how to do the problem without fraction tiles.
August 9, 2022
We talked about number lines and measuring distances on the map. Worked on figuring out the distance between two number/locations based on where they are on the line/map route.
August 2, 2022
Keeping Things in Proportion:
Deck of cards for everyone, Life cereal boxes.
Pyramid: This link will explain it best. You form a pyramid with your cards and find pairs that add up to 10. There are specific rules involved that make it challenging and fun. Single player game, but you can compare scores and have a ranking on the whiteboard. One clarification: you can only use completely uncovered cards. One exception: if, by lifting one card, you can make a pair with the card in your hand and a card that is just now uncovered, then you can use that card that was partially covered before. (Remove J, Q, K, Jokers. Aces = 1)
Is buying in bulk a good deal?
Last week we imagined buying 2 pkgs of berries for $5 and then thought, what if I need 4 pkgs or 6 pkgs? The price for 2 pkgs never changed, but the amount that you decided to buy changed.
Now we are going to compare buying 2 pkgs of the same item, but at different prices. Sometimes you’ll see something labeled “family size” or “party size”, or will go to a bulk store like Costco or Sam’s club and see that you’re getting more, but you’re also paying more. How do you know if it’s a good deal?
Life cereal boxes. Find ratio ($/oz) for each box, then compare the fractions to see which is cheaper. Get fraction tiles to remind us that a larger denominator means a smaller fraction.
I have the Life cereal boxes for you here. Let’s go on Walmart.com to look up other prices.
Normal box: $4.59/18 oz
Costco box: $10.49/62 oz (take time to read the box to make sure they can find this info)
Normal bag: $3.48/9.25 oz
Party size: $4.98/14.5 oz
When is buying in bulk a good idea?
When is it NOT a good idea? (You need to know that you’ll like it and not waste it. Is it going to go bad if you don’t use it quickly enough and have to throw some away? Will buying more actually mean that you’ll just use more than you would have normally?
Student book p 33. Give students time to try some of these.
July 26, 2022
Randy has had his right arm in a sling for the last while and I asked him if he is right or left-handed. It turned out that he is left handed (or ambidextrous) and that out of 7 people in the class today, we had 3 lefties! We had to make a fraction out of this information (3/7) and then had to search the internet to find out that, on average, 1 out of 10 Americans are left handed. When comparing 1/10 and 3/7, we had a nice discussion about fractions and how a large denominator means that then value of the fraction is pretty small. It feels like this is a concept that every one of our students needs frequent help with. Drawing pictures and using fraction tiles can help! The rest of the time, we used the grocery store ads from last week to practice making fractions and then finding equivalent fractions. Ex: 2 pks of berries for $5. How much would 6 pks cost? If we multiply 2 x3, then we get 6 pks and $5×3 = 15. The student book gave us a good amount of practice with problems like this. Toward the end, the class figured out how find a person’s heart beats per minute using a stopwatch and taking a smaller sample (15 seconds) and then multiplying up. I was proud of Delmy for being brave enough to come to the board and show her reasoning. Alma, Randy, and Moroni all volunteered answers during class. Jade asked a really good question about dividing $3 by 2. We got out the “play money” and demonstrated splitting one of the dollars into 4 quarters before trying to divide the whole thing into 2 parts. I love it when our students feel comfortable asking their questions in the moment they have them. That means that they resolve it then and there and don’t have to feel lost for the rest of the problem.
July 19, 2022
Lesson 1: A close look at supermarket ads (Keeping Things in Proportion)
Grocery store ads with ratios, copies of entire lesson 1 student book for each student (pp 8-20), 2 dice with fractions on the sides for game, scissors, tape
Fraction tiles: “COVER”
Fraction tiles: “UNCOVER”
Need a dice/cube with sides: 1/12, 1/12, ⅛, ⅛, ¼, 1/2
This lesson/chapter is so good. I think I will copy off the entire student section for each student so they can do the exercises and keep them for reference.
Teacher’s book p 21
Examining the relationship between #s is an important math skill.
Give me some true statements about the following number pairs: (100, 25) (500, 50) (2, 6) (3, 9), (4, 12) You can use +/- statements, but also multiplication and division statements. (Remember our mult/division math fact families?) We’re going to talk about ratios today: a way of comparing numbers that relies on mult/division comparisons.
Definitions: ratio: a way to compare two numbers or quantities.
For every “a” of one thing, there are “b” of another thing.
Ex: “1 teacher for every 25 students”, 60 miles per hour, $4/lb, $5 a gallon.
Proportion: a statement that two ratios are equal. Ex ⅓ = 2/6
Per: “for each” or “for every”
A bit different than part/whole
A fraction can be used to show a part/whole relationship, but it can also be used to show a proportion. This is a different emphasis than in our previous discussion of fractions. (Teacher book p 13). A relationship is preserved, even though numbers may change.
Supermarket ads, create the ratio (round up to nearest whole #: $3.79 becomes $4), then create equal ratios and show picture of the ratio (see example in teacher’s book, p 14). What would be a better deal? What would be a worse deal?
We pulled out fraction tiles for the first time today. The “cover” game wasn’t as fun or useful as the “uncover” game. I like that it invites students to change one fraction in for another (change ¼ into 3/12). Just handling the tiles and becoming fluent with changing things back and forth is a great step toward literacy with fractions. Fraction tiles are available in the Project Read office for any tutoring pairs to check out and use.
July 12, 2022
Gathering and classifying data (Book: Many points make a point, lesson 2). We gathered data about our students’ favorite foods and had them analyze the data and group them into categories like raw/cooked, plant/animal based, etc. The groups made posters with their information and then calculate the fraction or percentage for each category. We talked about why it’s hard to make categories that work and how to make them better. (Each data item needs to clearly fit into one and only one category). We talked about different situations where data is gathered and which parties might care about the information (advertisers, health providers, insurance companies). We ended with a discussion about converting fractions to percentages and some want to work on that more next time.
July 5, 2022
We introduced the idea of data and graphs today. (Math book titled Many Points Make a Point: Data & Graphs). The teacher’s book suggested creating a “mind map” where you brainstorm everything the students already know or can observe about an assortment of graphs. I wasn’t sure how this part would work, but it was actually awesome. Some responses included: time (change over time), heartbeat, numbers, news, and even a “scope” (comparing the appearance of a pie chart to the scope on a rifle). Next, we started gathering our own data sets and analyzing our results. We laid out 20 items of clothing on the tables and gave each student 10 post it notes. They selected 10 items of clothing and wrote down the country of origin on a post it for each shirt. They organized the post-its and were able to see which countries appeared most often. We labeled each country on a map of the world, made more observations, and talked about why we care where clothes are manufactured, economic and political implications, and why clothes are more likely to be made in some countries. Perry has grown in confidence and often has really innovative and intuitive ways to solve problems. When looking at his data, he was able to say, “Asia manufactured 80% of the clothing compared to 20% in Central America”. I praised him and challenged the other students to make sentences with numbers that were true about their data sets. We talked about how having a larger data set can increase confidence in the reliability of the statements we make. Using 10 shirts vs 100 shirts might solidify the trends we saw. Great lab today! Our textbooks give such great, hands-on lesson plans.