Mathematical Actions and Process: Reasoning
This part of the math question is the MOST avoided by students. Have you heard any of the following?
- I just know.
- I don't know how I did it.
- I did it in my head.
If your students are reluctant to explain their reasoning, start with a non-math prompt to get them started. One method that you may want to try is a strategy we explored during Coordinator Day: Would You Rather.
Would You Rather simply gives the students 2 options from which they choose one, but they have to justify their reasoning. Watch the video to learn about this easy strategy that you can implement to help your students with reasoning.
Eat This, Not That (Or Say This, Instead of That)
We've all seen those books, Eat This, Not That, but have you ever thought about how we can use our words differently to help with math understanding? Below are some small changes we can make to help our students with math vocabulary and with conceptual understanding.
Say This: In this class, we put the bigger number on top when we subtract.
Instead of That: The bigger number always goes on top.
Say This: In this class, are are going to subtract from the larger number.
Instead of That: You can't subtract a larger number from a smaller number.
Say This: The bottom number of a fraction represents how many pieces to make a whole.
Instead of That: In a fraction, the larger number always goes on bottom.
Say This: Stand on the perimeter.
Instead of That: Stand on the outside edge.
Say This: Counting by Multiples
Instead of That: Skip Counting
Christmas Tree Composing and Decomposing
Use Christmas trees to practice addition, composing, and decomposing numbers.
Christmas Tree Counting
Put sticker dots (ornaments) on the tree and have students match the dots to a number on a clothespin. (Check with your 4th grade teacher. They may have some clothespins they would be happy to part with!)
Candy Cane Pipe Cleaner
Use a pipe cleaner and some beads to represent an addition problem or represent a number.
Candy Cane Colors
You need a printable candy cane and some crayons for this activity. Have the student roll the die and color in that many sections of the candy cane in one color. Repeat with a different color until the candy cane is colored completely.
Candy Cane Patterns
You need a printable candy cane and some crayons for this activity. Identify a pattern your would like to students to replicate.
Random Popsicle Math
You can use popsicle sticks in lots of different ways in math and in all grade levels. (4th grade science may have some sticks they are ready to part with now!) These are some ideas that you can do whole class or edit to make it a station.
Materials:
- Popsicle sticks
- Markers
Prep:
- Write numbers on popsicle sticks that are representative for your grade level.
- Put sticks in a cup.
Ideas:
- Count on from that number to 100 by ones.
- Count backward from that number to 0.
- Count my multiples from that number. (You will have to choose the multiple AFTER drawing the stick)
- Start at 0 and count to that number and hop with each number. (Great to get out extra energy!)
- Count down from that number for students to line up.
- One more, one less
- Ten more, ten less
- Identify factors
- Make an "I have, who has?" game.
- Make some sticks with math problems and some with solutions. Students draw one and find their partner.
Have any other great ideas for random number drawing?
Fraction Action
Materials:
- Game Board
- Pencil
- Paperclip
- Die
Procedure:
Using the pencil and the paperclip, spin (at the top left) to select a fraction. Roll a die and move to select the other.
Compare fractions. If the spinning fraction is larger, the player must move back to her pervious spot. If the board fraction is larger, the player will stay on that spot.
Alternative:
Instead of comparing fractions, you can do the following:
- Make models
- Add
- Subtract
- Multiply
- Divide
Christmas Tree Multiplication
Materials:
- Two Dice
- Sheet of paper
- Counters (to cover numbers)
Procedure:
- Make Christmas tree from squares, with four on the bottom up to one at the top. (Post-it notes or index cards cut in half work great for this.)
- Each player chooses 10 number from the products table (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36). This is simply all of the possible options you can get when multiplying the numbers between 1 and 6 together. If you want to make a point about prime numbers, you can just give the option of choosing numbers from 1-36.
- Write one number in each of the ten squares from the product table results above.
- The first player then rolls 2 dice and multiplies the two numbers together. If they have the product of the two numbers written on their tower, they can then cover it with a counter.
- The winner is the first player to cover all their numbers in the tower.
Alternative:
Use 0-10 or 0 -12 dice to use larger products.
Perfect Square
In Perfect Square by Michael Hall, an ordinary square of construction paper is transformed into beautiful objects such as a fountain, mountains, and a river. The square is changed by tearing, folding, cutting, and rearranging shapes and pieces in a variety of ways, and at the end transforms into a window that overlooks all of the creations.
This book is an instant spark for divergent thinking as students apply extraordinary possibilities to ordinary shapes and objects. It is also a great way to discuss composing and rearranging 2D and 3D shapes and patterns in many different ways. After reading and discussing this book, I like to give out sets of tangram blocks to my students to see how
many designs they can come up with.
The Perfect Follow-up STEM Challenge:
Have students create an original “Square Sculpture” out of one square of construction paper. Teach them a variety of paper sculpture techniques such as slots/tabs, 3D shapes, symmetry, and prop-ups to apply to their designs.
I Wanna New Room (2nd - 4th)
In this adorable sequel to I Wanna Iguana by Karen Kaufman Orloff, I Wanna New Room features a boy who desperately wants to be separated from his little brother and have a room of his own. His wild and crazy proposals to his parents about why he deserves his own space, paired with the outlandish features of the room of his dreams, instantly makes my students start imagining their own “dream rooms.” The story ends with the endearing construction of a tree house by the boy and his father….the perfect compromise to give him a space of his own.
The “Imagine” or planning phase of the engineering design process is clearly featured in this book as the boy draws elaborate blueprints of his dream room. This leads perfectly into discussions about perimeter, area, cost of materials, and realistic design plans.
The Perfect Follow-up STEM Challenge:
Have students create blueprints of their very own “Dream Rooms,” complete with every feature they can dream up. Have them calculate the areas and perimeters of the different features of their rooms. The STEM challenge below is included in our May Storybook STEM.
If I Built a House (4th - 6th)
In this book, a boy named Jack designs the house of his dreams, complete with a racetrack, flying room, and gigantic slide. His creativity and infectious enthusiasm immediately inspire young inventors to imagine their own fantastical designs.
Kids are immediately captivated by the possibilities of a “Dream House,” and it easily leads into a discussion about smart homes of the future that use cleaner forms energy, withstand natural disasters, and offer exciting entertainment features.
The Perfect Follow-up STEM Challenge:
Have students design and create models of a “Smart Home” with features of the future and rooms of their dreams. Have them research alternative energy sources, strong construction materials, and methods of insulation.
Math Is Figure-Out-Able
This podcast is one that found while I was stuck in the car on a long trip. The particular episode is 128: Do, Say, Represent. This one focuses on how to help students explain their reasoning. It is hard to write out our thinking. We have to teach students how to share their thinking. This episode focuses on that difficult concept.
However, all of these episodes are some great ideas! They have a new episodes every Tuesday and #mathstratchat on Wednesday that focuses on one particular problem and different strategies you can use to solve it.
Power of a Great Math Task
December 13th 4:00 - 5:00
Research tells us that students need to engage in open-ended math tasks that include mathematical discourse so they can develop reasoning and sense-making skills. Quality math tasks allow students to construct their own learning through a guided-inquiry approach. In this edWebinar, we will discuss the indicators of a quality math task and explore practical strategies to promote math talk in our classrooms. Join us, share your ideas, and walk away with several practical instructional strategies to use in your classroom! Attendees will:
- Learn about the research, barriers, and strategies around quality math tasks
- Understand learning environments that encourage math talk
- Experience a math task from both a teacher and student perspective
- Learn and practice language routines that will make your classroom math discussions more effective and intentional
Outdoor STEM Learning with Young Children
Dec. 15th 1:00 - 2:00 (If you register, you will be sent a recording.)
Dig in and discover how to implement playful outdoor STEM learning with young children. In this edWebinar, Lea Ann Christenson, Ph.D. and Jenny James, MA will offer ideas and approaches for child-led, nature-based STEM explorations to build understanding of the natural world and offer opportunities for literacy and language development. Find out how to use the learning life cycle to identify the seeds of experiences that lead to wonder. A discussion on starting your own outdoor classroom for STEM exploration will round out the presentation.
This edWebinar will be of interest to PreK-3 teachers and school and district leaders.
Fostering Equitable Interactions and Belonging in Mathematics with the 5 Practices
In this edWebinar, Sean Nank and Kathleen Sheehy explore how math educators using the 5 Practices can make this school year resonate for students in positive ways for years to come through positive interactions between students, teachers, and math.
