The First 14 days of a Multigrade Math Class Overview

Using Debbie Diller's Book, "Math Stations" and Everyday Math, I came up with this plan of how to present math for the first 14 days. During this time, you will train your students how to work independently so you can teach math through guided math groups.

 

You will notice that I did not stop teaching math and just train students. By teaching similar lessons to both grade levels, you will also find the time to train your students.

 

 

 

The First 14 Days of Math Stations

 for A Multi-grade  1/2 Class

 Using Everyday Math and Math Stations

Schedule:

Mini-lesson 25 - 30 minutes

Whole Group EM Lesson: 30 - 40 minutes

This schedule is ONLY for the first 14 days of instruction.

Day	Mini-lesson	Learning Outcome	Resources	Whole Group Everyday Math Lesson
1	Take one photo of each child for Management Board. (or use the geography of the room to rotate your students systematically so they always know what area of the room to go to next without the work of a management board)		Complete the set-up of the Management Board for Day 2	Number Lines 1st/1.1  2nd/ 1.1
2	Introduce: Management Board . Model: How to obtain materials and where math stations are located. Model: Cleaning up a station	Sttroducig up a stationh stations are locatedor Day 2udents explore and learn how to obtain their instructional materials and where to go to work with their partners. Students will know what is expected as they clean up their stations.	Management Board Missing Pieces Box Numbered clear plastic tubs	Everyday Math Games: Monster Squeeze Number-Line Squeeze
3	Teacher and students model and practice: “Turn and Talk”. Model: The difference between hearing and listening to your partner.	Students will learn that as mathematicians we are capable of thinking in many different ways and sharing their thinking with others.	Chart: Thinking and Talking with a Partner Partners use 6 inch voices. Partners take turns talking. Partners listen to one another. Partners respect each others’ thinking	Introduce the Slate Routine Explain the Number Grid and it’s patterns 1st/1.2    2nd/ 1.4
4	Math Station Tub Teacher discusses how students have choices within one tub. Teacher shows how materials are labeled to differentiate levels. Model: Signals used to indicate it is time to stop and clean up, and signal to indicate to move to next station or to the small group teaching station.	Students realize that there are multiple activities to do with one math tub and those activities can be repeated. Students will move to different activities quickly and quietly.	Completed math tub Chart: How do we put materials away in our Math Tubs? Auditory signal	Introduce the Pattern-Block Template 1st/1.2   2nd/1.4
5	How to Obtain Help Model: “I Can” Chart “Instead” box for the Computer station	Teacher and students will create the first “I Can” chart together. Students will practice being adaptable and flexible.	“I Can” chart	Formative Assessment for 1st Graders: Use math master pg 304 to see what numbers they can all ready write. Challenge them to write their numbers to 20. Introduce the Class Scroll to the 2nd Graders.
6	Model and Practice: How to Use a Math Talk card to express their mathematical ideas.	Students will express their thinking using a math talk card as a support.	2 different “Math Talk Cards” for each group of 2 students	How to Use a Calculator 1st/  2.4          2nd/1.9
7	Represent your thinking through drawing, writing, Flip videos, and dramatizing. Where to put completed work.	Students learn to record their thoughts in short video clips. Students learn ways to represent their thinking, and where to put that completed document.	Flip Video Camera Examples of students drawings, and writings.	Whole Group: Odd and even Tally marks
8	How to handle problems:    Ask 3 and then ask me.   Disagreements What will happen when students don’t follow the procedures.	Students follow specific guidelines to solve problems.	Chart: How We Can Solve Problems Ourselves	EM Games: Penny-Dice Game Top-It Addition Top-It Rolling for 50 Rolling for 500 using a 400-500 number grid.
9	Introduce “Our Math Thinking “ Books	Students learn they are accountable for doing their best work at stations.	Book: “Our Math Thinking”	EM Games: Play your choice of game
10	Introduce First Station: Review and model use of management board, obtaining materials, correct voice level. Choose one student to be your partner, and go through the entire procedure while “thinking  aloud about what you are doing and thinking”	Students will revisit how to maintain organized classroom math stations	Chart:  Looks like, Sounds Like, Feels like One math tub of your choice	Whole Group: Modeling how the teacher will be teaching the small group guided math groups. All about Math Boxes using a teacher created math box page all about tally marks.
11	Continue to introduce another station. Establish student accountability by modeling and posting an example of a completed student work product.	Students will learn mathematical ideas through independent learning.	Example of student work	How to play: EM Facts Workshop Game that provides online practice of basic facts and computation.
12	Model:  How we share our experiences with our class members.	Students will engage in discussions and that they are accountable for their independent learning.		Reading books that relate to math such as counting books. How to create your own math related book.
13	Model: Computer Station “Instead Box”	Students will learn a routine to cooperatively use the classroom computer.	Chart: Step by step directions to use the computer Chart: Who is on the Computer Today?	How to read a number line on a thermometer
14	(After conducting an actual “Math Station”) Getting back together as a whole group to reflect on what went well.	Grand Opening Celebration: Beginning a station	Wrapped box that announces the beginning of math stations. Chart:  What We Did Well	Administer the Beginning of the Year Test to both grade levels. Recruit a volunteer to read the test aloud to one grade level while you read the other grade level test. See if the volunteer will also help score the test.

To Infinity and Beyond

My husband received a hand written card from our granddaughter that said:

I love you to infinity and beyond,
and that will never change.


Mathematically, can it get any better?

Deborah

Understanding the Common Core Fraction Progression for Grades 3, 4, and 5

Where do I start to understand the concepts students must internalize about fractions in the Common Core State Standards?

My suggestion is to go to the Illustrative Mathematics website and watch all 7 of the unit modules below.  They are easy to understand, and really get you thinking about how you should present these concepts to your students.
 
Ask yourself:
      What have I done in the past that will help students understand these ideas?
       What manipulatives will help my students understand these ideas?. Or what representational drawings, area models, or number lines will help them make sense of these ideas?
       What vocabulary words or "bridging lessons"  should I present to help my struggling students or English Language Learners?
      If our class created an ongoing bulletin board titled, "The Big Ideas About Fractions," what synthesized ideas MUST be on that bulletin board?
      What evaluation tools will I use so I can see if each individual students understands these concepts?


http://www.illustrativemathematics.org/pages/fractions_progression

 

Illustrative Mathematics

Fractions Progression Module

 

Introduction

Unit 1 — Meaning of Unit Fractions

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Illustrations

• 3.NF Find 1
• 4.NF Comparing Sums of Unit Fractions
• 2.G Representing Half of a Rectangle

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Unit 2 — Equivalent Fractions

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Illustrations

• 4.NF Fraction Equivalence
• 4.NF Explaining Fraction Equivalence with Pictures

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Unit 3 — Comparing Fractions

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Illustrations

• 3.NF Ordering Fractions
• 4.NF Using Benchmarks to Compare Fractions

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Unit 4 — Addition of Fractions

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Illustrations

• 5.NF Finding Common Denominators to Subtract
• 4.NF Making 22 Seventeenths in Different Ways
• 4.NF Writing a Mixed Number as an Equivalent Fraction
• 5.NF Do These Add Up?

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Unit 5 — Multiplication of Fractions, Part 1

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Illustrations

• 5.NF Running a Mile
• 5.NF Fundraising

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Unit 6 — Multiplying Fractions, Part 2

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Illustrations

• 5.NF Connor and Makayla Discuss Multiplication
• 5.NF Folding Strips of Paper

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Unit 7 — Dividing Fractions

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Illustrations

• 5.NF Dividing by One-Half
• 5.NF How Much Pie?

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May Calendar Board

Is that daily calendar routine becoming "too routine"?  Here is an idea to use in May to practice creating addition and subtraction stories. 

This is the completed pattern that you will use for the month using the + and - symbols, which is an AABBBB pattern.

Here is the printable pattern pieces from my Google Drive file.

Each student needs a  Whole-Part-Part laminated diagram,  and a  dry erase marker.

Here is a copy of this diagram.

The teacher presents the numbers to use on the chart. For example, "Today I have 10 in all.  (Hold up a set of ten linking cubes.)  One part of my ten is  8 (There are 8 green connecting cubes). The other part of my ten is 2 (There are 2 yellow connecting cubes). As the information is given, the students are filling in  their diagram.

"Now, let's look at our calendar. Predict whether the math symbol for today will be a plus sign or a minus sign."
"Yes, today is a plus sign. So we will be creating an addition story using our numbers on our Whole, Part, Part diagram. I'm going to give you 2 quiet minutes to write your addition equation, and think about your addition story.  No talking as this is quiet thinking time."

"Now, let's TURN AND TALK to our partner and share the addition story that you have been thinking about. Later, I am going to ask 2 student to share their story with the whole group.  Please share your story now with your partner."

Student One: " There were 8 girls playing at my house. 2 boys came over to play too. Now  there are 10  kids playing at my  house."

Student Two:  "I  have 2 pieces of gum, and 8 chocolate kisses. I have 10 pieces of candy to eat."

The  teacher writes the equations on her diagram as the students are sharing their stories.

Deborah

8 Times Tables Pattern

When I look at the multiplication tables, I see patterns. Let's take a look at the  8 Times Tables.

.

8	x	1	=	8
8	x	2	=	16
8	x	3	=	24
8	x	4	=	32
8	x	5	=	40
8	x	6	=	48
8	x	7	=	56
8	x	8	=	64
8	x	9	=	72
8	x	10	=	80
8	x	11	=	88
8	x	12	=	96

First look at the first five facts. Do you see a pattern?

8	x	1	=	08
8	x	2	=	16
8	x	3	=	24
8	x	4	=	32
8	x	5	=	40

If I look at the ten's digit that number is one less than the number multiplied by eight.

• Eight times 1 starts with 0
• Eight times 2 starts with 1
• Eight times 3 starts with 2
• Eight times 4 starts with 3
• Eight times 5 starts with 4

Now look at the next 5 facts. Do you see a pattern?

8	x	6	=	48
8	x	7	=	56
8	x	8	=	64
8	x	9	=	72
8	x	10	=	80

Eight times the number starts with two less than the number

• Eight times 6 starts with 4
• Eight times 7 starts with 5
• Eight times 8 starts with 6
• Eight times 9 starts with 7
• Eight times 10 starts with 8

Now look at the next 5 facts. Do you see a pattern?

 

8 x 11 = 88

8 x 12 = 96

8 x 13 = 104

8 x 14 = 112

8 x 15 = 120

Eight times the number starts with three less than the number

• Eight times 11 starts with 8
• Eight times 12 starts with 9
• Eight times 13 starts with 10
• Eight times 14 starts with 11
• Eight times 15 starts with 12

That might help your students remember the tens digit, but what about the ones digit?
 

Note that within each set of five facts, the ones digit follows a pattern :

8, 6, 4, 2, 0

 

This brings us the question....Does it keep repeating?  I'll let you figure that out yourself. I wouldn't want to spoil the surprise.

 

Deborah

Measures of Center Applet for 6th Grade Classrooms

I discovered  a great resource that visually helps to understand the 6th Grade Common Core Standards that develops understanding of statistical variability. The resource is a JAVA application called "Measures of Center" from www.maine.edc.org.  The site looks like a sign-in site, but the applets/technology tool lists for student and classroom use are located at the bottom of the page and no login is required.

"Measures of Center" lets you explore mean, median, and mode through the use of an interactive line plot. Modify the line plot by dragging on Xs representing data. The measures of center are shown graphically and the values are computed dynamically as data is added to the graph. The maximum data can be adjusted to accommodate a wide array of values. One to ten data points can be displayed at a time.

I like that  you can add pieces of data to the line plot and SEE the results of that additional data reflected in the median, mode, and mean immediately.

 This applet will allow you and your students to see the results of how the measures change based on the data.  What would be the effect of an outlier data point? What can I expect to be the effect on the measures of center when the data has a small spread?  What can I expect when the data has a larger spread or range? 

I think students need exposure to these types of questions so they can develop a sense of what to expect.  How can they ask themselves if their answers make sense, if they can't predict an effect that is normal?

Explore these questions one day, and then the next day create a line plot and have student PREDICT what to expect if you add an outlier, have a small range of data points, have a large range of data points. Make them start to predict... and think about math not just calculate the mean, mode. or median.

I just bought  a Jenn-aire refrigerator that had to be ordered and I waited for a period of 51 days for that appliance.  I think Jenn-aire should look at the mean number of days that their customers wait for appliances that are ordered from their company.  Is the spread of "number of days" that their customers wait for their products large or small? Are there outliers, and are those outliers satisfied with their customer service or be repeat customers in the future?  Remember that mathematical questions are asked about everyday life situations because MATH MAKES SENSE OUT OF THE WORLD.

Deborah