**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

February 7, 2023

Today we got more comfortable with saying large numbers properly. I think being able to read, write, and say large numbers properly helps to understand and use those big numbers in work and life.

We also practiced kinds of mental math and allowed the students to find their own methods of figuring out estimates and exact amounts. See notes.

We had a nice discussion about how to spot and avoid being the victim of scams sent through email and text.

2/7/23

Everyday number sense, lesson 2

Goals:

Understand place value in a way that you can pull apart a # (532 is 500 + 30 + 2) and then put it back together again.

Learn how to say big numbers

Estimate how much a purchase will cost by rounding and then adjust to find the actual cost.

Materials needed:

Deck of cards, play money

Game

3-digit war: Flip over 3 cards and see who can make the larger 3-digit #. They win their opponent’s cards. (Remove 10s, face cards, aces, jokers).

Place Value: how to read really big numbers (good video explaining) https://www.youtube.com/watch?v=DZ7fxH0C54Y

Now try the game, but do 5 or 6 digit numbers and practice saying the number out loud.

Activity 1: Math in Line (p 22-23) Estimate how much your purchase will cost, then do mental math to adjust your estimate to the exact cost.

Work alone or in pairs.

Let them figure it out, then talk about the steps.

Round up or down?

By how much?

What’s your estimated total?

Is that higher or lower than the actual amount?

By how much?

Take estimated total and add or subtract by the amount you rounded.

Activity 2 (p 25) has them fill out a table to see how to round & adjust. Maybe we could come up with our own table together instead of using the book’s example?

How to detect a text/email scam

Why so many? Why not in paper mail as much? (cost)

What are the signs of a scam?

-Greatest desire/greatest fear

-Plays on relationships and money

-ACT NOW! Emergency!

-Click on a link. What is malware?

Good rules:

-Do I know the sender?

-Never click on a link, just go to the trusted website yourself.

-WAIT. It isn’t really an emergency.

-Never give your personal information.

January 31, 2023

Multiplying by 10 and 100 in an instant and knowing how to quickly find 2 numbers that add to 100 can help with all kinds of money, job, and life applications. These skills are important foundations of “math sense”.

1/31/2023

Everyday Number Sense, Lesson 2 (Mental Math in the checkout line)

Goals:

Identify 2 digit numbers that add up to 100 and find a pattern.

Find a rule for multiplying by 10, multiplying by 100

Materials:

Deck of cards, print multiplication grid, bring some rod/cube manipulatives, paper, pencils, calculators? Print p 22, 23

Game

(We’ll use this when we practice finding 2 digit numbers that add up to 100. One’s place should add to 10

Ten’s place should add to 9.

Number bonds to 10: Pair up with a partner. (Ace = 1, J=11, Q=12, K=13). Goal is to find 2 #s that add up to 10 or 20. Amy draw some number bond that =10, some that = 20. When I say GO, player #1 makes 3×3 array and player 2 starts finding pairs. Player 1 replenishes the array with new cards once matches are found and removed from the existing array. Player 1 and player 2 switch jobs. If you come to a point in the game where all 9 cards are laid out and there are no combinations that equal 10 or 20, then shift to where you can pick up more than 2 cards. Ex: King + 4 + 3

Number bonds to 9: same game, but only use Ace and 2-8.Do this? Or not.

Making rules, seeing patterns: How to quickly multiply by 10, by 100

Tools available: multiplication grid, manipulatives, calculators, paper

*Explain notation for multiplication: can use “x”, but can also use ( ). An “x” can be confused with a “+”, and we often use variables like x in algebra, so it’s good to be familiar with the parentheses.

What is 15 x 200 or 15(200) You may not be able to do that in your head yet, but you will soon!

Create a rule for multiplying by 10. Any number multiplied by 10 should follow this rule. Prove it. (With a table, with manipulatives, pictures). Let them get started themselves.

Create a rule for multiplying by 100. Any number multiplied by 100 should follow this rule. Prove it.

Does your pattern work for 15×10? How can we check your guess? How about 23×10?

Practice your rule on the following and then check your work:

12 x 100 10(45) 20 x 3 11 x 50

20(30) 20 x 23 10(45) 15(200)

Make a rule for how to find 2 numbers that add up to 100.

What helped you when finding a rule for how to multiply by 10?

Hear some rules, test them out, see what class thinks.

January 24, 2023

We had a great discussion about what mental math is for and practiced rounding to the nearest 10. We played an online game to practice this skill. https://www.mathnook.com/math2/math-lines-rounding.html

We practiced using rounding to figure out some real life word problems:

A friend and I go out for a night on the town. We see a movie and have dinner. The movie costs $9.50 per ticket. Dinner for the two of us is $43.50. About how much will our evening out cost each of us?

Sharonda is setting tables for a wedding. There are 19 round tables, each seating 8 people. She places 2 forks at each setting, so that’s about ___ forks in all. Estimate! Show how you arrived at your estimate. Can you tell if your estimate is bigger or smaller than the actual amount? Explain?

January 17, 2023

Everyday Number Sense, Lesson 1

Close Enough with Mental Math

Goal:

Use mental math strategies to estimate totals (rounding, making friendly numbers) #CCR

“friendly numbers” are easy to work with (5, 10, 15, 20, 25, 30, … 100)

Get there by rounding, get there by adding #combinations (4+6, 7+3)

Understand commutative property of addition

Materials:

Deck of cards for each pair, print p 12, 18 for each student,

Game (Rounding)

Online game: Math Lines Rounding: shooting ball with a number on it to another ball with a multiple of 10.

Teach rounding (show bike going up/down hill).

Round to the nearest WHAT? If 10, then think of multiples of 10 (10, 20, 30, 40…) That’s your beginning and end point. That’s the only part of your original # that matters. If you have 2,345 and have to round to the nearest 10, then only focus on the numbers in the 10s place and lower. In this case: 45. Beginning point =40, End point is 50. Is 45 on the up slope? Is it at the midpoint? Is it on the downslope? 45 is at the top of the hill (midpoint) so it gets to ride down the hill to 50.

Opening discussion (Teacher’s book, p 10)

A friend and I go out for a night on the town. We see a movie and have dinner. The movie costs $9.50 per ticket. Dinner for the two of us is $43.50. About how much will our evening out cost each of us?

Figure this out without pencil and paper. Make estimates in your heads and be ready to tell us how you figured it out. Instead of getting exact answers, today we will make estimates that are “close enough”.

-Students share methods.

-Point out rounding up or rounding down, explain if needed.

Activity #1 How much?

In notes, find blackline master 4 with problems. Student options are on p 6. Instead of A, B, or C have them raise a colored piece of paper. a=yellow, b=blue, c=pink. Observe who is getting the answer easily and who needs help. (use zoom chat for online group)

Practice: It’s About… (p 12)

Sharonda is setting tables for a wedding. There are 19 round tables, each seating 8 people. She places 2 forks at each setting, so that’s about ___ forks in all. Estimate! Show how you arrived at your estimate. Can you tell if your estimate is bigger or smaller than the actual amount? Explain?

Which students know how to quickly multiply 8×20?

Extra practice:

Could do p 18 (finding combinations of $ that equal 10 )

January 10, 2023

Today we focused on mental math: rounding and being able to add “friendly numbers” in our heads or with minimal paper & pencil work. We talked about how this can be useful on the job or in everyday life. Sometimes it’s nice to add something in your mind before calculating something exactly to know if your answer is “in the ballpark”. I’ve caught my own mistakes many times because I knew approximately what the answer should be. We played a card game that asked us to find pairs of cards that added up to 10 or 20 and had a great discussion about why our pairs worked out perfectly when our only cards were 1-9, but how it didn’t work out perfectly when we added in 10, 11, 12, and 13.

November 15, 2022

#math. 11/15/22

Keeping Things in Proportion

Lesson 8: Playing with the Numbers

Materials needed

Student books, calculators, cubes or other small manipulatives (will need these to show fact families and to cover bingo card), paper for bingo sheets, print p 106

Multiplication fact families

Division is just the inverse of multiplication. It undoes it. If multiplication is like tying a shoelace, then division is like untying the shoelace. Show this with cubes.

Roll a dice twice. (4 and 6) Find multiplication family. Ex: 4×6 = 24

Write down 4 mult/div facts about those 3 numbers.

Let’s get a total of 12 families on our board.

Now create a BINGO sheet (5×5 grid). Put one mult/div fact in each square.

I will call out a mult/div fact. If I call yours exactly, you can cover it, but you can also cover it if it’s in the same fact family. Ex: If I call out 24 divided by 6 = 4, then you can also cover 4×6=24

Ratios show a relationship

What are a few examples?

Get on computer to find more relationships with currency or changing from metric system to “imperial system”.

1 foot = 12 inches

5280 feet= 1 mile

4 Tablespoons = ¼ cup

$4 = 1 gallon

$1 = 0.97 Euro; $1= 0.85 Pound sterling

We can call these relationships “proportions”. We’ve talked about them in recipes, mixing OJ concentrate. (It’s ok to double the salt if you’re doubling everything else. If you only double the salt, but not everything else, then that relationship is off and it will not taste right).

How to tell if two ratios are equal

Activity #1 (p98) Cross product property. Multiply top # of the first by the bottom # of the second. Then multiply to bottom # of the first by the top # of the second. If the products are equal, then the ratios are equal. (see p 98)

Let’s try this out. (see p 98)

Finding missing # is a proportional relationship

Activity 2 (p 99):

What value for the missing # would make the proportion true? Practice using cross product property as well as multiplication fact families (inverse relationship of mult/division).

Practice p 103, 106 (word problems)

In person lab: We didn’t get to p 106 (word problems), but we did everything else. The multiplication/division fact families bingo game was great. The concept was right within reach for everyone, but not so easy that it was boring. Finding the missing number in a proportional relationship was a pretty difficult concept for most, so it was really nice to have 2 volunteers there to help students individually.

November 8, 2022

We reviewed the ideas of dimension, perimeter, and area. We practiced situations where a length or width is unknown, but we have perimeter and/or area and found ourselves dipping our toes into algebraic concepts. During the last 30 minutes, we split into groups with graph paper and measuring tapes to draw, measure, and calculate the area of different tiled sections in the Provo library. One group measured the bathroom/drinking fountain area just outside the PR office, and another group measured the tile on the stairs leading up to the ballroom. I thought it was a good, practical, problem solving activity and I think the students enjoyed it.

November 1, 2022

Dimensions, Perimeter, Area

Build & draw a 2D rectangle

Find dimensions, perimeter, area

Combine all shapes to make a new one. Analyze.

Test practice

Materials needed

Yellow cubes, graph paper, tape/magnets to post shapes, copies of p 60 test practice, tape for composite shape, scissors (1-2)

Dimensions, perimeter, area (Use Google Slides)

x

x

Get out cubes, have each person build a rectangle out of 24 cubes.

Dimension: a measurable extent of some kind (length, width, height). Discussion of 2D and 3D? What does that mean? (Example: 3D movie, 3D printer)

Perimeter: measure of the distance around the 2D shape. Examples of usage:

To discourage cats from entering your property, sprinkle some cayenne pepper, ground coffee beans, dried mustard seeds or dried rosemary at the perimeter of your yard.

Shop the perimeter of the store — that’s where most of the unprocessed foods are placed.

Black-clad guards roamed the internal perimeter while others manned the walls of the compound.

Area: measuring the space inside the 2D shape.

Show dimensions, perimeter, & area of the shape I created.

Now ask students to sketch the shape they made on graph paper and tell us the dimensions, perimeter, and area. (Zoom students may need to sketch their own graph paper).

Create a chart on board comparing dimensions, perimeter, and area of different shapes. (Areas will all be the same).

Test Practice, p 60

x

x

Work alone or with a partner.

Composite shapes

x

x

Talk about taking all the rectangles students created and making a new, big shape. Use cubes to build robot superheros and watch retro clip of 1980s Voltron cartoon. (Just for fun!) Is it easy to predict the area? Is it easy to predict the perimeter? What can we do to break this large, complicated shape into easier chunks?

Test practice, p 69

Especially #5, #6.

VIRTUAL MATH LAB

I used sentence.yourdictionary.com to find sentences where the words dimension and perimeter were used online. I thought it was a nice way to show how mathematical concepts are used in everyday language. We made rectangles out of cubes and talked about dimensions, perimeter, and area, and practiced calculating them. We noticed that rectangles with the same # of cubes sometimes had different perimeters, but always the same area. We explored why that might be. At the end, we talked about composite shapes (several shapes come together to make an unruly/difficult to measure shape) and how you might break it into its smaller shapes to calculate the area. In my in-person lab, we made robot creatures out of our cubes and then watched a retro trailer for the 1980s cartoon, Voltron, about many “shapes” coming together to make a larger creature.

We introduced some geometry today. The part where we identified shapes and named them was instructive, but maybe a bit tedious. It got more fun when we created designs using geometry tiles and then tried to give instructions to a partner on how to draw it (without looking). Here are the notes!

Over, Around & Within: Geometry groundwork: shape names, vocabulary for describing shapes and angles

Materials needed

Dice, ice breaker game, copy of “Smart” poem, fake money, paper/pencil, collection of objects to sketch, copies of “shape description chart”, geometry tiles

Game

x

D-Icebreakers D-ICE BREAKERS questions

Warm up

x

Poem: “Smart” by Shel Silverstein: Where the sidewalk ends (get out fake money for this), print poem for all and have them show the money as the poem goes.

Activity #1: Making a Mind Map p 2)

x

x

Make a mind map using words, numbers, pictures, or ideas that come to your mind when you think of “GEOMETRY” and “MEASUREMENT”. Write your own. Group discussion.

Goals: recognize and describe shapes, find perimeter of rectangles & volume of rectangular solids, make drawings to scale, use linear, square & cubic units, use spatial reasoning to solve problems, make generalizations about 2D and 3D shapes (p 8 student book)

-Start vocabulary list in your notebook (acute, obtuse, parallel, perpendicular, right angle, congruent,

Activity #4: Sketch and object and shapes within (p 3-4)

x

x

Amy will have a collection of objects for in-person lab. Virtual students will find something in their home to sketch. Amy do this first, to demonstrate, then students will do. 1. Sketch (simply) your object, 2. What shapes make up your object? What can you find? 3. Name or describe shapes. How many sides? Angles different/same? Parallel/perpendicular.

Shape description chart (p 11-12)

x

x

As you do activity #4, start to fill in “shape description chart”(see pdf in lesson plan supplements). Can I get this to my virtual students? Start to define angles (right, acute, obtuse), talk about equal side lengths, parallel, perpendicular. Sign for 90 degree angle, hash marks for equal sides on a shape or angle. “Congruent” means “equal” for sides or angles. Begin to mark up the shapes with with these descriptions. (Teacher’s book p 223 gives names of shapes. I needed help with the names of the different triangles!)

Activity 2 Sharing Secret Designs (p 13)

x

x

Lab: use geometry tiles and work with a partner.

Virtual: Amy will make a shape with geometry tiles, cover it, and then give descriptions and have students try to draw it. Now try with a partner. One person create a design with 3-6 shapes. Then they give short statements to get the other person to be able to draw their shape. Use geometry terms (shape names, parallel, perpendicular)

Test practice, p 18

x

x

Good for practice with vocabulary.

We didn’t complete the entire worksheet, but we were able to figure out what our budget to buy a car would be, and we calculated what the interest would be for car #1 after 4 years. The students naturally wanted to talk about needs vs wants and how to get by without having to take out loans.

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.

Application:

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.

Example problems:

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:

Materials needed

Deck of cards for everyone, Life cereal boxes.

Warm up/game

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.

Life Cereal:

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)

Doritos:

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?

Test practice

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)

Materials needed:

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

Warm up/game

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.

Comparing numbers

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.

Write vocab

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.

Activity 1

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.