Fun with Coordinate Graphing

My notes from teaching a block with my older group on Linear Measurement in April to follow up on our Farming & Gardening block in February:

• Linear Measurement & Coordinate Graphing - Intro
• Linear Measurement Week Two
• Linear Measurement Week Three
• Linear Measurement Week Four

Cheese Puffs (age 9-10)

Day Fourteen

• do Area Exploration Inquiry Lesson: Parallelogram, Triangle, Circle; discuss the term "congruent"
• look at Area Model Multiplication: one digit by two digit problems; discuss the term "distributive property"
• preview tomorrow's test

Day Fifteen

• have students take Area & Perimeter Test in our Zoom session without help as a formal assessment

Day Sixteen

• discuss the Rene Descartes "Stay in Bed Scholar" story from the wonderful Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2 by Luetta and Wilbert Reimer

  

• do Coordinate Grid - Practice with Ordered Pairs
  (this is a nice introduction... shows an icon and asks "state the coordinates of"... leveled by difficulty... introduces four quadrants)
• reinforce the "always run before you jump"; solve mystery pictures from Graphing in Quadrant 1 of the Cartesian Coordinate Plane, with each child tackling a different picture:
  1) tree
  2) flowers
  3) lightning storm
  4) spider web
  5) optical illusion

It was a fun way to wrap up this busy & productive Math block!

Baby Wolves (age 7-8)

Today was the last day of the Math block in both classes. Knowing that, in the classroom, the younger group would have listened in on the above lesson and wanted to try it too, I went ahead and did the introduction and Coordinate Grid - Practice with Ordered Pairs (only first quadrant examples) with them as well. Coordinate graphing is just like Battleship, and it's fun! I'll give this group a bit of extra practice in their independent work packets next week as well, focusing on examples with alphanumeric grids. Much easier than the ordered pairs. You don't have to remember which number is which!

Resources for Mystery Pictures

I'll give every child in my classroom some of these follow-up activities next week in their independent work practice, but if you want more for May or for the summer, here are all of the "mystery picture" resources I have found on TpT that I like so far. They are all free, but you do need an account to download them. You can also ask me and I can get them using my account.

Alphanumeric Grid

Math Winter Activity Coordinate Grid - Penguin
she has this leveled by difficulty so there's a blank grid and there's also a grid with the coordinates for each box lightly written in it (A1, A2, A3, etc.)

Coordinate Graphing - Tangram Pieces
this is such a cool idea!
make the tangram pieces and then cut them out and solve tangram puzzles with them; available as alphanumeric grid or ordered pairs (first quadrant)

Ordered Pairs - First Quadrant

Graphing Mystery Picture - Alien

Coordinate Plane Graphing Picture - The Impossible Triangle

Coordinate Graphing Picture - United States
available as first quadrant or all four quadrants

Ordered Pairs - All Four Quadrants

Back to School Coordinate Plane Graphing Activity - Apple

Coordinate Grid Riddle - draw the solution to the riddle
"Why was it too hot in the stadium after the game?"

Graphing Mystery Picture - Bicycle

Other Coordinate Graphing Activities

First Quadrant

Coordinate Graphing Game for Holes by Louis Sachar game

Coordinate Grid Battleship game

Instructions: "Copy this gameboard, fold in half, and place in a file folder for an instant game of Coordinate Battleship. Students love to practice their coordinate graphing via this simple game. Students place their 5 ships (5,4,3,3,2) on their ocean grid. They alternating naming coordinate points and marking misses and hits on their target grid using two different colors. First one to sink 5 ships wins."

All Four Quadrants

Quadrant Match-Up! activity
(helpful teacher review notes at Four Quadrants)

Your Name in Coordinates activity

General

Five Cartesian Coordinate Plane Graph Paper templates
-1st Quadrant to 20
-1st Quadrant to 20 with Fractional Gridlines
-1st Quadrant to 20 No labels
-All 4 Quadrants to 20
-All 4 Quadrants to 20 No Labels

Counted Cross-Stitch

Counted cross-stitch, usually introduced in grade 4 in Waldorf schools to follow up on Fractions, is also the perfect follow up to coordinate graphing! Yes, you have tiny bits which create a whole, but you also have to be able to read the pattern to see where to put the next stitch on the grid. I highly recommend finding a kit or two for your child to do in May and over the summertime. If we were together in the classroom, I would have provided embroidery hoops and Aida cloth and floss and embroidery needles; luckily, this kind of thing is easy to find. You may even have some kits at home that you always meant to get to and never did... but make sure they are simple.

In grade 4 Norse Mythology (and the corresponding Form Drawing), we look at the beautiful art of Celtic knots. It would be lovely to find a counted cross-stitch kit with a Celtic knot motif. If you find (or create) one, let me know!!!

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Book Share Apr 29

Today, since it's the end of the month, we had a sharing of Passion Projects (these are simply any projects kids have assigned to themselves and worked on independently over the course of the month) at 1 pm and then we had our regular weekly Book Share at 2 pm as well.

I love seeing the Passion Projects! Kids talked about their homemade bubble stuff recipes, drawing and coloring intricate mandalas, knitting projects (including knitting with a circular needle for the first time), fairy houses, woodworking, sleeping in a tent for the first time, and figuring out what they need for self care. It was wonderful to see their enthusiasm and creativity!

Here are the books that students recommended and discussed this week in Book Share:

The Witches
by Roald Dahl

Pete the Cat and His Four Groovy Buttons (book #3)
by Eric Litwin

Legend of the Ghost Dog
by Elizabeth Cody Kimmel

Sammy the Seal
by Syd Hoff

Extreme Planet: Exploring the Most Extreme Stuff on Earth
by Bear Gryllis

Pink Snow and Other Weird Weather
by Jennifer Dussling

The Keepers: The Box and the Dragonfly (book #1)
by Ted Sanders

This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Is It a Math Problem?

Our block of Math Gnome Stories has been going very well. The link is to all of our lessons and activities. I have incorporated lots of activities to try to build Math Sense in my students. This is more important in the beginning, in my mind, than facility in computation... because without knowing what you're doing and why, computing can only take you so far. One of these we did for the first time today and it is a game called "Is It a Math Problem?"

In terms of difficulty, this game is more challenging than the Silks Game, which should be introduced first and is also explained below. As you can see, I start with the newer and harder work at the beginning of each session, and then we also go back and review concepts introduced earlier in the block.

Is It a Math Problem?
introduced on Day Fourteen

In "Is It a Math Problem?", I tell a short story which has numbers in it, and the students tell me whether or not they think it's a math problem.

The reason for taking the time to do this in first grade is that we don't want students to automatically think that anything with a number in it is a math problem, or even that every number in a story is important when it is a math problem. The only way to tell that it's a math problem is to have a sense of what the four operations are, which is why it is crucial that this game come at the end of the block.

Here is an example:

My Aunt Sally had four cats. Then she got three more cats. Then she invited me over for a cup of tea.

It's important that you ask them to explain their reasoning when they tell you if it is -- or if it isn't -- a math problem. Why or why not? In this case, it's NOT a math problem because it never asks us a question. We have some numbers but there's nothing that we need to do with them.

Here are some more:

Zac and Natalie made a pan of brownies to be shared fairly among the people in their family. There are three people in their family and 12 brownies. How many did each person get?

I went walking this morning. I picked 13 flowers. When I got home, I put them in a vase along with the 12 flowers I had picked yesterday. What color is my hat?

It can have a question in it but still NOT be a math problem! Always think about what the question is asking. Is it an operation? Which one?

Here are a few more:

When we went Christmas caroling we sang five songs at each house. We visited ten neighbors. How many songs did we sing in all?

My big dog weighs 55 pounds and my little dog weighs 16 pounds. They both have wet noses.

You can also ask your child to convert a story that isn't a math problem into one that is. What would it take to make it into a math problem? In the last example, you could add something like "How much heavier is the big dog?" or "How much do my two dogs weigh in all?" or "If my little red wagon can carry 65 pounds, can I use it to carry both dogs at the same time?"

These are super-fun to make up, and after enough examples you can ask your child to make some up too. Then you are the one who has to answer the question, "Is It a Math Problem?" Asking your child to create word problems which are examples of each operation is a great way to assess whether they understand the fundamental quality of that operation. (Often, children will happily create addition and subtraction problems but struggle to come up with an example of multiplication or division. Practice makes progress.) Asking them to create a story which has numbers in it and may or may not be a math problem that makes sense is good assessment too.

Silks Game
introduced on Day Twelve

The Silks Game is also a game of my own invention, and it is fun because it lets kids move around! In this game, you tell a math story problem aloud. Again, they don't have to solve it. Instead, they listen to hear what kind of problem it is, and then either put on a play silk that is that color (green - Plus, blue - Minus, yellow - Times, red - Divide) or hold up the correct math gnome or just hop up and act out the part of that character!

This is really nice assessment and it forces the child to think about what the problem is really asking, instead of getting bogged down in the numbers. Again, you can ask them why they think it's the math gnome they chose.

Here were today's problems for the Silks Game (adapted slightly from Understanding Math Story Problems 2, pages 24 and 21):

Joyce has a Valentine's Day party and a Christmas party. 63 people came to the Valentine's party, and 48 people came to the Christmas party. How many fewer people came to the Christmas party than the Valentine's Day party?

Sandy practices the piano 2 hours each day. What is the total number of hours she will practice in a week?

Ruth wants to buy a robe for a gift. The robe she wants to buy costs $32. She has $27. How much more money does Ruth need?

In June, Laura spent 11 hours sailing on Lost Pines Lake. In July she sailed for 14 hours, and she sailed for 18 hours in August. What is the sum of the hours Laura spent sailing?

Every day Mrs. Hering spends 3 hours reading to blind persons. In one week how many total hours will she spend reading to blind persons?

Mrs. Everett makes yummy chocolate cakes. To make a cake she needs 2 cups of sugar. If she has 6 cups of sugar, how many cakes can she make?

One Friday night 34 people stayed at the Sandy Beach Hotel. On Saturday night 57 people stayed there. How many people stayed at the hotel over the course of both nights?

Rita can play 67 songs on her guitar. Beverly can play 89 songs. What is the difference in the number of songs Beverly can play and the number Rita can play?

One of the simplest things about this activity is that you can use workbooks from other older children, if you have some handy, by just reading aloud the problem to to your younger child and not requiring that they solve it. Because it doesn't matter how big the numbers get! That way you don't have to constantly come up with word problems. My older students have enjoyed the Bedtime Math series, and that could be a source of word problems too.

Working with the Gems
introduced on Day Five

After we play the Silks Game for 8-10 problems, we go back and get out our wooden boards and gems and solve a few of the ones with littler numbers in them. Today we solved the one about Mrs. Hering reading to the blind, and the one about Laura sailing on the lake.

We are still learning all of our skip counting songs, so we ended by singing 6 and listening to the tune for 7.

by 2 to 24 -- London Bridge (start at 0:21)

by 3 to 36 -- Row, Row, Row Your Boat (start at 0:49)

by 4 to 48 -- Kookaburra (start at 1:23)

by 6 to 72 -- Happy Birthday (start at 2:04)

by 7 to 84 -- This Little Light of Mine (start at 2:43)

by 8 to 96 -- You Are My Sunshine (start at 3:34)

by 9 to 108 -- Baby Beluga (start at 4:25)

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The Kindness Curriculum Theme 5

I am so excited to be using the Kindness Curriculum from the Center for Healthy Minds. You can download this free mindfulness curriculum easily. Each week consists of three short lessons, about 20 minutes each.

Zac and I are doing this together as a family; we are on Week Five, which has "CALMING AND WORKING OUT PROBLEMS" as its theme.

Week One notes
MINDFUL BODIES AND PLANTING SEEDS OF KINDNESS

Week Two notes
I FEEL EMOTIONS ON THE INSIDE

Week Three notes
HOW I FEEL ON THE INSIDE SHOWS ON THE OUTSIDE

Week Four notes
TAKING CARE OF STRONG EMOTIONS ON THE INSIDE AND OUTSIDE

Lesson 13: Mindful movement

Invite bell, GFW, and Kindness Garden. Show a picture of an Armadillo. Luckily, Becca had a picture of one in her Creative Coloring Animals book.

Move like animals according to directions in lesson plan (Eagle, Cat, Cow, Snake, Snail, Armadillo, Frog, Monkey). Read From Head to Toe by Eric Carle and/or use cards to review movements. Rest with Belly Buddies. Invite bell.

Lesson 14: Forgiving myself

Today's lesson requires a book about forgiveness. I used the book they suggest, which is Down the Road by Alice Schertle, but you could substitute any picture book you have on hand where one character forgives another.

Great-big Bear hug. Little-tiny Ant hug. Curled-up Snail hug. Many-armed Octopus hug. Another kind of hug?

Nice follow ups for this include climbing trees together and, of course, making apple pie for breakfast! We made Apple Crisp.

Lesson 15: Forgiving others

Water our plants on the Nature table and in our vegetable garden. Play "Pass the egg" game with our basket of wet felted eggs. Review how to use the Peace Wands. Do "White Light" on page 61 of Bedtime Meditations for Kids.

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Fun with Play Dough

Zac and I have been making up all different kinds of play dough recipes lately. So I thought I'd take a minute to share our family favorites from all the recipes we have tried over the past sixteen years.

If you have a great recipe for homemade play dough, please share it!

The "Gingerbreadiest" Play Dough is one I use in the first grade Capital Letters block (K is for King, Q is for Queen, C is for Cinnamon, G is for Ginger). It is a wonderful sensory experience as well as a perfect tie-in to The Queen Who Couldn't Bake Gingerbread by Dorothy Van Woerkom.

However, this recipe dries out overnight, even when stored in an airtight container. So instead of trying to keep it for a long time, just take it outside for Forest Putty play... and we did that today. Thank you to the fine folks at Tinkergarten for coming up with this great outdoor creative play idea!

Now, on to the recipes!

Cooked Play Dough

Homemade Play Dough (PDF)
classic cooked play dough recipe
dyed with Kool-Aid powder (do not use grape; it makes black)
from Jazzy Jars: Glorious Gift Ideas by Marie Browning

Pumpkin Spice Play Dough
from Messes to Memories
perfect Autum scent! lasts a long time

Gluten Free Homemade Play Dough
from Wellness Mama
good recipe for a gluten-free family, or if there's no regular flour left in your grocery store right now so all you have is GF
this one is a little stiffer so it's nice for cutting with scissors

No-Cook Play Dough

"Gingerbreadiest" Play Dough (PDF)
a fun no-cook play dough recipe (but only lasts one day)
adapted from a recipe I found online to include more spices

Chocolate Play Dough (PDF)
our absolute favorite! lasts for months and smells terrific
an excellent no-cook play dough recipe which uses boiling water, so you still get that nice sensory experience of kneading warm dough; I found this recipe online at Fantastic Fun and Learning as part of a Reggio provocation

This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Fun with Word Bags

Word Bags are a fun way to do SWI with a class and easy to do at home with your child. Thank you to Rebecca Loveless for turning me on to this strategy, and for sharing some resources to do this online via Zoom!

~ ~ ~

For more on SWI, I strongly recommend reading the article
Understanding SWI: “Structured Word Inquiry” or “Scientific Word Investigation” by Pete Bowers, originator of the term.

He has explained the process and linked to lots of good examples of investigations, including videos of class discussion while analyzying a word.

~ ~ ~

In today's SWI class, we first looked at two words of student interest: peanut and hazelnut. We noted that these were both compound words made up of two bases (hold up two fists side by side), and we were amazed to see how ancient the word < hazel > is. It's nearly unchanged from Old English!

From there we used Rebecca's Keynote slides 5, 6, and 9 to look at the base < quest >, some word sums which can be make from it, and a matrix for it.

After reviewing these concepts, it was time for the Word Bag activity, slide 10. Today's word was < cycle >. When I asked "What does cycle mean?" (meaning is always the first step in SWI), he responded, "Water cycle." The young child will give an example intead of a definition. I expanded his idea, adding that the water cycle goes around and around (evaporation, rainfall, and evaporation again)... and he added, "Like with salmon also." Yes! A life cycle is another good example.

In Rebecca's slide, the Word Bag is set up so that you can move aside colored shapes to reveal each word below, then move the word into a large square if it is part of the family of < cycle >. If it was not part of the family (shares a meaning relationship and a structural relationship), we left it alone. You can easily do this with a pack of index cards and a square carpet or a tray, or stickie notes and a chalkboard, a whiteboard, or a fridge door.

The reason for the square is that it emulates visually the shape of the matrix. The words in the square are words that would be in the matrix!

"Does it belong in the family?" is the question you ask when looking at each word in the bag.

In the family morphologically means that it shares a base with < cycle > and they would go in a matrix together.

In the family etymologically means that it is a different kind of relationship; it shares a deep historical root with < cycle >, but doesn't share a modern-day spelling pattern.

Should you want to show both options, Pete Bowers talks about placing a square inside of a circle. The word can go in the square (shares a base), in the circle (shares a root but not a base), or outside of the circle completely (not related at all). A hula hoop or a piece of string works nicely for a circle. Maybe you are lucky enough to have a circular rug! In that case, you could lay down something rectangular or square on top of your circle or oval rug.

If you want to try this with your child at home, you can make the following cards and put them in a bag: cycle, cycles, recycle, recycling, recyclable, unicycle, bicycles, universe, circles

After sorting them, maybe you can find some more words to add to either the square or the circle.

We had a lively debate about < bicycle > and < unicycle >. My young student recognized the connection with the structure of < cycle > but was not sure these words shared a meaning relationship with < cycle >. He did realize that if one was in the family, the other would be automatically. When we looked them up on etymonline.com, it became clear that they did belong in the family. He rejected < universe > right away, laughing, but was less sure about < circles >. It shared a meaning relationship but not a structure relationship. When we looked up < circle > we found it came from Latin circulus; when we looked up < cycle > we found it came from Late Latin cyclus from Greek kyklos "circle, wheel, any circular body." Thus, cycle comes to us from the Greek word for "circle" but the word circle itself comes to us from Latin. They do not share a root, so they are not relatives at all. The meaning relationship isn't enough to make them in a family (otherwise, hot dog, ketchup, pickle relish, and chips would be related!).

We ended with slides 17 and 18, which show an example of the "in the circle / in the square" setup. < Eat > was the base in the matrix. < Ate > was outside of the square but in the circle. They both come from Old English etan. But you cannot put < ate > in a matrix with < eat >... quite simply, because they do not share a base!

Here's a beautiful visual example that I found online which illustrates this:

You can click on the image to enlarge it. Enjoy exploring this with your child!

Linear Measurement Week Four

Here's some background info on this Math main lesson block:

Linear Measurement & Coordinate Graphing - Intro

Linear Measurement Week Two

Linear Measurement Week Three

Here is what we did this week:

Day Ten

• what is another way that we could measure our gardens?
• explain the difference between perimeter and area as the difference between walking around the outside of a garden and going inside the fence, lying down on the ground, and doing snow angels everywhere
• do Area Differentiated Task Cards #1-24

  we pretended for the composite figures that one side of the garden was the Montagues and one side was the Capulets and they built a wall between them! we first calculated the area of each garden and then, when Romeo and Juliet fell in love and broke down the wall, we figured out the total area of the shape

  we also spent a lot of time on #23 since it has a missing quantity and cannot be solved as drawn (ultimately, we guessed a quantity and solved for the area using our guess, then looked in the answer key to see what she had, then went back and calculated what the missing quantity would need to be in order for her to arrive at her answer)

This week for extra practice at home, students worked on their Area and Perimeter Robot Craft. Each child was asked to do one robot using all perimeter OR all area, and one robot using both perimeter AND area.

Day Eleven

• have students calculate the area of their own gardens
• review the formula for the area of a rectangle and square; explain the formula for a right angle triangle (area is 1/2 of base ⋅ height) and how it is derived; explain the formula for the area of a circle (A=πr²)
  our gardens range from
  9.6 square inches
  12.57 square inches
  16 square feet
  194 square feet
  442 square feet
• ask students to consider the plants they want to plant and how much space each takes up
• research the area taken up by a plant by looking at how far they should be planted apart from one another using Cinder Block Gardens by Lynn Gillespie

  

• look at diagrams of how many plants can fit in a cinder block garden (having the garden bed be the same size in each diagram makes it really easy to compare the area each plant takes up) in chapter 13:
  carrots, p.150
  Swiss chard, p.156
  cucumber, p.160
  garlic, p.162
  kale, p.164
  lettuce, p.168
  melons, p.170
  onions, p.164
  potatoes, p.184
  pumpkin, p.186
  radish, p.188
  spinach, p.190
  summer squash, p.192
  tomatoes, p.198

• ask students to add their vegetables to their graph paper garden bed designs and color in the number of squares for the area taken up by each when full-grown; don't forget to color your path if you have one
• discuss other factors to take into account when planting such as soil requirements, light requirements, and companion plants
• watch How Trees Secretly Talk to Each Other ("The Wood Wide Web")

Day Twelve

• do Mrs. T's Raccoon Room (part 1)
• look at Geometric Cabinet Control Chart; identify the parallelogram

• discuss formula for the area of a parallelogram and how it originated; make a rectangle using the Geometric Stick Material and Working Board, then remove two nails, shift the angle, and replace the nails

• enjoy chanting "The Area Rhyme" to the tune of "Miss Mary Mack"
• share graph paper diagram of my 2020 vegetable garden and the companion plantings; use Louise Riotte's Roses Love Garlic and Carrots Love Tomatoes to look up the answers to student questions about companion plants for pumpkins, roses, and tomatoes

Day Thirteen

• have students share their scale garden drawings on graph paper and their Area & Perimeter Robots (these were a big hit!)
• do Volume and Perimeter Greeting Card Box Activity

  I modified the questions to only include three:
  What is the area of the top of the box?
  What is the volume of the box?
  Challenge Question: What is the surface area of the box?

This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!