Fly on the Math Teacher's Wall -- February Hop -- Fractions!!

Welcome to another wonderful math blog hop!  This blog hop is devoted to fractions and will not disappoint--so after reading this post, take a hop around to see what goodies you will find from some amazing math bloggers!

Each of our Fly on the Math Teacher's Wall hops are devoted to squashing teacher and/or student misconceptions.  I am not really discussing a misconception, but I would like to focus on some key ideas I feel most important in helping my students develop a solid foundation in fractions that will be built upon as they progress from year to year. If students understand these key ideas, hopefully some future misconceptions can be avoided.

The following is the second grade Common Core Standard for fractions:

CCSS.Math.Content.2.G.A.3
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

There are several key ideas for understanding:

• A whole represents all of something (1 whole).
• A fraction represents part of a whole (for introductory understanding, this is important--as we know, a fraction can represent any number of equal parts--as with improper fractions, but students also need to understand when working with improper fractions that an improper fraction is greater than one whole.  This understanding will be developed in later years for my students.)
• A fraction represents part of a whole that has been divided into EQUAL parts (for my students this understanding is developed with the use of circles and rectangles, not equal sized parts of a set)

How do I help my students develop a working understanding of each of the above ideas?

We begin our explorations by identifying objects that are in the form of a whole and those that are not.  We examine items around the classroom that are and are not whole (an unsharpened pencil vs. a sharpened pencil, a unopened Kleenex box vs. a box that is part full, etc), and I also bring in various items (cookies, bottles of soda, fruits, etc.) in whole and part form.  Items are sorted into two categories.  The group of items that are not whole are then labeled as fractions.

To help students understand that a fraction represents part of a whole that has been divided into equal parts, we explore wholes that have been divided into equal and unequal parts.  A lesson about equal sharing is done.  Students seem to understand the concept of equal parts when it is related to sharing the whole of something with a friend.  Posing various sharing scenarios with items divided into equal and unequal parts is helpful.  My kids love when I choose students to share my pizza and candy bar with. I divide both unequally, share with volunteers, and then ask my students if my sharing is fair.  This naturally leads to a discussion of how my sharing is not fair because the parts I shared were not equal.  I then ask students how the items CAN be shared equally.  They, of course, can always tell me.  We continue our explorations by cutting out circles and rectangles.  We fold the shapes to create equal parts, cut them out and create models.

Only after students have a solid understanding of these three ideas do we move on to the concepts outlined in the standard.  Guided math groups are easily formed based on what I have observed in our initial explorations.  In small groups I am able to further develop some students' understandings of the key concepts before moving on, work more with some students on partitioning wholes, and challenge those who already have understanding beyond the second grade standard.

UPDATE: Totally forgot to post these little gems that I use in guided math groups.  So simple to make and use. How could I have forgotten? Enjoy!

Fraction Mats

Providing multiple opportunities for independent practice is always important, so this is done in rotations while I am meeting with guided groups.  Options for practice are differentiated.  Please feel free to download a few of my activities for independent practice.

Pizza Parts: Fraction Models Task Cards

Pizza Parts: Comparing Fractions Task Cards

Four Leaf Fractions Board Game & Spinner

Flying High with Fractions Board Games & Spinners

I have also made up some fraction foods you might be interested in using.  Foods are labeled and unlabeled.  These can be used in guided groups and for independent practice. I especially like to use the parts that are labled--in this way students can see that 3/4 is equal to 3, 1/4 pieces.  If you download this freebie, please take some time to share how you plan to use them by leaving a comment. Would love to hear your ideas!

Hope you have found something you can use with your students!

Please take the time to hop around to all of the participating bloggers.  Your next stop is Brandi from The Research Based Classroom!

Happy hopping---

Number Talks Book Study -- Chapter 9

Today our book study of Number Talks by Sherry Parrish comes to a close with a brief discussion of chapter 9.

To read past book study posts, visit our Number Talks Book Study Archive! 

Chapter 9: What Does a Number Talk Look Like at My Grade Level?

Chapter 9 is a facilitators guided and provides a closer look at the schools/teachers highlighted in the DVD (grades K, 2, 3, and 5).

A math time structure is shared for each level and discussion questions for the videos are presented.

A school-wide perspective is also given so readers can understand the importance of consistency among number talk content from year to year even with the natural variation in personalities, classroom structures/environment, etc.

Parrish stresses the importance of/consistency in ...

• the teaching of the big ideas in mathematics
• instruction as asking not telling
• the development of safe learning communities
• an unwavering quest for making sense

Love, LOVE this closing quote from Parrish, "The mark of a master teacher is the ability to reflect on his practice."  SO TRUE! For this reason, a series of questions for personal reflection are given. 

If you have participated in this book study along with us, or have read Number Talks, you undoubtedly had many moments of personal reflection.  I have found affirmation for what I strongly believe to be true about teaching mathematics, have a new-found knowledge of the power of using the number talk structure presented in the text, and am inspired as I move forward with my students.

Even more important are the cheers I hear from my students when I say it's time for a number talk and the mathematical thinking and sharing that follows!  Thanks to Sherry Parrish for her phenomenal contribution to our profession!

Speaking of Sherry Parrish, we will announce the date of her Q & A as the day draws near, so look for a facebook shout out coming soon.

A thank you also goes out to Tara, the Elementary Math Maniac, for hosting the book study and all of our adventurers who have followed along.

Lastly--you will want to stop back this coming Sunday for another Fly on the Math Teacher's Wall Hop! The topic is fractions, so we'll see you then!

All the best--
Sarah

Makin' It Math Mid-Month Linky -- Money, Money, Money!

Glad you stopped by! Welcome to our Makin' It Math Mid-Month Linky--a linky dedicated solely to math made-its.  If you are interested in linking up your math made-its, check out the details by clicking the logo below.  We would love to have you join us! 

Our kids have been working a lot with money in the past few weeks, and are quickly becoming money masters!  We thought we would give you an inside look at our explorations and share some made-its.

Our money explorations began with a simple pretest.  Students were asked to name each coin, tell the value of each coin, and count a small selection of coins (if able).  Students were pulled to do the assessment individually with real coins while other students were engaged in math game play.  This quick assessment made it easy to group students based on need.  Four groups were formed and guided instruction of small groups began.

Small Guided Math Groups

The following have been key in our small guided groups:

• the use of coins that students can touch/feel and manipulate
• mastery of coin identification and values before moving on to counting (some groups moved on sooner than others and students who showed mastery quickly were worked into a different group)
• a gradual progression in coin counting (mastery of counting like coins and adding coins from least to greatest--pennies and nickels; pennies, nickels, and dimes; pennies, nickels, dimes, and quarters)
• multiple opportunities to count random groups of coins and write the total value using numbers and symbols (students would count a collection of coins for the group two times and the other students in the group would agree/disagree, recount to check accuracy, and discuss order in which coins were counted)
• acceptance and discussion of multiple ways of counting (including discussion of counting on coins to create landmark tens for ease of counting remainder of coins)
• self and peer-evaluation and justifying of thinking
• use of the open number line to illustrate how coins were counted
• lots and lots of practice 

Students carefully counted in their heads as their peer counted aloud.  Students then agreed or disagreed and gave proof.  Discussions of how coins were counted (order) happened here as well.

Students showed their thinking with an open number line.

Students evaluated their peers and provided justification for their thinking.  The students on the left drew faces to provide evaluation for their fellow classmates as they worked their way from desk to desk around the room.

 Students showed multiple ways to represent a dollar.

Independent Practice

The following are a few independent practice opportunities we  provided for students to work on while meeting with guided math groups (differentiated based on each group's needs and all designed for practice of money skills).  Please feel free to download any you can use.  Some were created this year and others we have used for several years.

Math Journals:

Coins in My Pocket Journal Prompts - These prompts can easily be differentiated.  My kids use half-sized notebook journals and simply cut and paste the prompts and solve.

"Show What You Know" independent tasks (premade/teacher created activity sheets, roam the room activities, Scoot activities, What's a Word Worth?, etc.) that can be used as assessment:

I don't find too many premade activity sheets that I like, but I inherited an OLD version of this workbook years ago. I think it's one of those for parents to use at home, not sure. It's great!  It follows a logical progression of practice from like coins to pennies and nickels, pennies/nickels/dimes, etc.  It also has some great problem solving sheets.  I pick and choose the sheets to use based on student need and place them in folders labeled A, B, and or C.  Cups of coins are always made available for use with these activity sheets.

What's a Word Worth? -- I'm sure you have seen or used something like this before.  Students can use any word list and the coin key to figure out what each word is worth.  I have three different sheets made and labeled A,B, and C so students practice with the coins they can count independently.  

Counting Coins Scoot:  Stop back to download soon!

Games:

Bank It! Board Game -  This game can be played after students have learned to count pennies, nickels, dimes, and quarters.  It requires addition and subtraction of coins. My kids love this! Games like these are easy to send home for at-home practice. 

You may also like my This Little Piggy! Money Fun games on TpT.


Workstations (task cards, money bag activities, etc.):

Money Bags!: Coin Tasks - This differentiated workstation is used with bags of coins (fill with coins appropriate to student need).

You may also like my Show Me the Money! task cards on TpT.

Assessment

Ongoing assessment is easily done in guided groups.  Much is assessed through observation.  Courtney and I also created a performance task that we use to assess students' levels of mastery.  Please feel free to download, Suzy's Piggy Bank.  If you use this task, we would love to hear your comments and thoughts about how it went.  Feel free to email us anytime!

Please share your thoughts and ideas in a comment OR link your blog post up with us!

All the best--

An InLinkz Link-up

Number Talks Book Study -- Chapters 7/8

Hello!  Welcome back to our Number Talks book study!  Today I discuss chapters 7 and 8--two chapters focused on multiplication and division for grades 3-5.

To read past book study posts, visit our Number Talks Book Study Archive!

Chapter 7: How Do I Develop Specific Multiplication and Division Strategies in the 3-5 Classroom? 

As in the beginning of chapter 5, Parrish presents the overreaching goals for number talks at this level: number sense, place value, fluency, properties, and connecting mathematical ideas.  For a discussion of the importance of each at the 3-5 level, visit my previous post of chapter 5. Accuracy, efficiency, and flexibility are always encouraged with number talks as well. 

Parrish goes on to stress the importance of using array models to anchor student strategies with multiplication and division.  She compares the importance of the array model with multiplication and division to the importance of the number line to addition and subtraction.  If you are not currently using arrays to help students understand the concepts/strategies associated with multiplication and division, it is important to make this shift.  With an array, students can apply their understanding of the factors/dimensions of an array to find the product/area. See array for 6 x 22 below.

From an array with boxes delineated within the area, students can move to the use of an open array.  Like an open number line, and open array can be customized to model thinking/strategies.  Below is an example of 6 x 22 and 132/6 using an open array.

Also, as presented in chapter 5 with addition and subtraction, it is important to use real-life contexts for multiplication and division, explore and discuss the efficiency of different strategies, and anticipate student thinking.

The remainder of chapter 7 illustrated five common strategies for multiplication and four common strategies for division.  I will give examples of many of these strategies as I discuss chapter 8.



Chapter 8: How Do I Design Purposeful Multiplication and Division Number Talks in the 3-5 Classroom?

The number talks presented in this chapter are organized by operations and strategies.  A rationale for helping students develop each strategy is presented and specific instructions are given for their implementation.  

Even if you are not using number talks, this chapter does an exceptional job of illustrating essential strategies for multiplication and division.

First, Parrish stresses the importance of using number talks that focus on fluency with small numbers BEFORE moving on to using those that focus on computation with greater numbers. Number talks with small numbers help students focus on strategies rather than the magnitude of numbers and foster confidence.  In this chapter, specific number talks are presented to bring about the use of specific strategies, but it is also understood that students will share other methods.  "The ultimate goal of number talks is for students to compute accurately, efficiently, and flexibly."

Multiplication Number Talks


Repeated Addition or Skip Counting:  Specific number talks are not presented for this strategy because the goal of number talks is to move students beyond additive thinking to multiplicative thinking. Praise students for using this type of thinking, but don't forget to make a connection to multiplication.

Making Landmark or "Friendly " Numbers: It is important to remember here that if an adjustment is made to one of the factors, an adjustment must also be made to the product.

Examples:

6 x 21
6 x 20 = 120
120 + 6 = 126

3 x 19
3 x 20 = 60
60 - 3 = 57

Partial Products: This strategy requires the breaking up of one or both factors into addends using expanded notation and the distributive property.  This strategy can be used with any multiplication problem.

Examples:

6 x 23
6 x (20 + 3)
6 x 20 = 120
6 x 3 = 18
120 + 18 = 138

6 x 31
(3 + 3) x 31
(3 x 31) + (3 x 31)
93 + 93 = 186

Doubling and Halving:  This strategy can be used to make problems with multiple digits easier to solve.

Example:

8 x 35
8/2 = 4
35 x 2 = 70
4 x 70 = 280

Breaking Factors Into Smaller Factors:  It is important to expose students to number talks that lead to the use of this strategy to help students understand the associative property.

Examples:

6 x 21
3 x 2 x 7 x 3

32 x 8
4 x 8 x 2 x 4

Division Number Talks

Repeated Subtraction or Sharing/Dealing Out: Specific number talks are not presented for this strategy because the goal of number talks is to move students beyond removal to multiplicative thinking. Praise students for using this type of thinking, but don't forget to make a connection to multiplication.

Partial Quotients: When the partial quotient strategy is used, students are able to understand the value of each digit in a number being divided.  No longer is there the "goes intos" thinking based on single digits without an understanding of each digit's value. When I taught fifth grade, this strategy along with the use of base ten tools helped students understand the concept of addition and set aside a series of memorized steps they had previously used. 

Here is a great post by Tara, the Elementary Math Maniac, all about teaching the partial quotient strategy--Teaching Division with Partial Quotients: Moving from Concrete to Abstract Models.

Multiplying Up:  Students build upon multiplication they know until they reach the dividend.

Example:

12 x 35

12 x 10 = 120
12 x 10 = 120
12 x 10 = 120
12 x 2 = 24
12 x 2 = 24
12 x 1 = 12

12 x 35 = 420

Proportional Reasoning: Division is considered from a fractional perspective.  Halving and halving or thirding and thirding can be explored with the number talks included.  Some number talks include: 800/40 and 144/6.

I hope you find the overview of each strategy helpful, if you have not purchased a copy of the book.  I highly recommend you do!

Please feel free to share your comments, ideas, or experiences related to chapters 6 and 7.  We would love to hear your thoughts!

AND don't forget to stop by this coming Sunday for our Makin' It Math mid month linky!

Have a fabulous Friday--

Number Talks Book Study -- Chapter 6

Welcome back to our book study of Number Talks by Sherry Parrish.  The study is sponsored by Tara, the Elementary Math Maniac.  She is right on schedule, so if you want to read a discussion of chapters 7 & 8, feel free to visit her blog!

I have changed our schedule just a bit:

• Today I will be discuss chapter 6 of Number Talks. 
• This Thursday I will discuss chapters 7 & 8 of Number Talks.  
• Sunday we come to you with our Makin' It Math mid-month linky. 
• Then, I will wrap up our Number Talks book study the following Wednesday with a discussion of chapter 9. 

We hope you will stop back and join us on the above dates!

To read past book study posts, visit our Number Talks Book Study Archive!

Chapter 6: How Do I Design Purposeful Addition and Subtraction Number Talks in the 3-5 Classroom?

The number talks presented in this chapter are organized by operations and strategies.  A rationale for helping students develop each strategy is presented and specific instructions are given for their implementation.  

Even if you are not using number talks, this chapter does an exceptional job of illustrating essential strategies for addition and subtraction.

First, Parrish stresses the importance of using number talks that focus on fluency with small numbers BEFORE moving on to using those that focus on computation with greater numbers. Number talks with small numbers help students focus on strategies rather than the magnitude of numbers and foster confidence.  In this chapter, specific number talks are presented to bring about the use of specific strategies, but it is also understood that students will share other methods.  "The ultimate goal of number talks is for students to compute accurately, efficiently, and flexibly."

Addition Number Talks

Making Tens:  Making ten is an essential strategy and should be a default strategy used by fourth and fifth graders. If this is not the case, Parrish suggest the use of the second/third grade making ten strategies presented in this chapter first. Once you see students using the making ten strategy in default, it is safe to move on.  Being able to make tens is foundational for further understanding.

Example:
8 + 5
(8 + 2) + 3
10 + 3

Making Landmark or "Friendly" Numbers: This strategy requires the understanding that compensation can be used---taking from one addend and adding to another without changing the sum.  When students make a landmark/friendly number, they understand that by doing so the numbers become easier to "work with", as we say in our classroom.  Parrish suggests giving students plenty of time to explore and experiment with the use of this strategy and why it works.  Start by having students prove their thinking with tools.

Example:
25 + 26
(25 + 5) + 21
30 + 21

Doubles/Near Doubles: Selecting numbers that are close is important here.

Example:
39 + 39
40 + 40 = 80
80 - 2 = 78

Breaking Each Number Into Its Place Value: Use numbers that do not have an obvious relationship to one another.  This will encourage the breaking apart  of numbers into their values and adding them mentally from left to right.

Example:
18 + 31
(10 + 30) + (8 + 1)
40 + 9

Adding Up in Chunks: Parrish suggest that students should be using this strategy midway through the second grade year.  "Adding up numbers in chunks builds upon adding multiples of ten by encouraging students to keep one number whole while adding chunks of the second number." 

Example:
45 + 38
45 + 30 = 75
75 + 8
(75 + 5) + 3
80 + 3

In helping my second graders develop all of the above strategies with "small" numbers, I have found it important to continuously explore and discuss the efficiency of each strategy.

Subtraction Number Talks

Removal or Counting Back:  A sequence of problem for use with this strategy are not presented.  Parrish discusses how this is naturally a strategy students will use.  Most important--the discussion of when the strategy is efficient and inefficient. 

Adding Up:  When choosing equations to encourage the use of this strategy--choose minuends and subtrahends that are far apart and frame them in a context that implies distance.

Example:

60 - 18

Our class has collected 18 cans for the food drive.  Our goal is to collect 60 cans.  How many more cans do we need to collect to meet our goal?

I have found it especially helpful to model mental thinking when adding up using an open number line.   

Removal: Creating a context of removing an amount from a whole is important here.  Parrish suggests encouraging students to keep the minuend intact and remove the subtrahend in parts.

Example:

60 - 18

You saved up 60 Muppet Bucks earned for exceptional effort and behavior.  You cashed in 18 bucks.  How many bucks do you still have saved?

Place Value and Negative Numbers: What's important? You CAN "take a bigger number from a smaller number".  Starting with problems that have a difference of -1 is suggested.  The following example shows a sequence of problems that can be used to illustrate this strategy.

Example:
Start with 4 - 4, move to 4 - 5, 4 - 6, and then 4 - 7

Adjusting One Number to Create an Easier Problem:  This strategy involves the adjustment of the minuend or subtrahend to make a "friendlier" number.  It is important to keep in mind when this is done that an adjustment to the answer must be made.

Example:

60 - 29
60 - 30 = 30
30 + 1 = 31

Keeping a Constant Difference: The difference/space between the minuend and subtrahend remain constant when the minuend and subtrahend are adjusted by the same amount.

Example:
25 - 8
27 - 10 = 17

I hope you find the overview of each strategy helpful, if you have not snatched up a copy of the book yet.  It's a phenomenal resource!

Please feel free to share your comments and/or take-ways from chapter 6!  

AND-- Just a reminder that this is our last day for collecting question for Sherry Parrish's Q & A!

Here are the questions we have so far:

What suggestions do you have for the implementation of number talks as a building?  Steps for beginning? Unforeseen obstacles?

Do you ever use number talks with missing addends?

I teach fifth grade, and I have not used number talks.  None of my colleagues before me have used number talks.  Where do I begin?

Please share any question you have! Simply send them to guidedmathadventures@gmail.com.

Looking forward to a discussion of Chapters 7 & 8 this coming Thursday!

All the best for a wonderful week--

Number Talks Book Study -- Chapters 5

Hello from snowy Illinois!  Today we continue our Number Talks book study sponsored by The Elementary Math Maniac. We move on to a discussion of chapters 5.  Originally, I had planned to discuss chapter 6 as well, but I will be lumping chapter 6 with chapter 7 in next Sunday's post. Both chapters focus on designing purposeful number talks in the 3-5 classroom.

To read past chapter posts, visit the Number Talks Book Study Archive!  

It feels a bit funny saying this is an excellent chapter because they're ALL wonderful.  But, this chapter brought back memories of teaching third and fifth grade for many years and provided for a huge amount of self-reflection and assessment of days gone by.  At the same time it serves as affirmation for my current practices and fuel for the future.

I have spent the majority of my years teaching 3-5 grade students, moving to second grade four years ago. I have to say I loved my days at 3-5, and parting ways was not due to a growing dislike for the age, burnout, our a need for change due to becoming stagnant.  My decision to move grade levels was actually due to what I noticed about my fifth grade students year after year--a lack of conceptual knowledge in mathematics that was accompanied by a series of memorized steps to get an answer.  Did I move to second grade because I was tired of taking them "back to the basics"? No! Was I frustrated by what was done before they got to me? Honestly, yes.  Did I play the blame game? At times. Is this where it stopped? No.  I have been blessed to be surrounded by outstanding educators during the 20+ years I have been at this, and I can't say a focus on procedures without the depth of understanding was intentional by my students' previous teachers, but I do believe it came with a lack of understanding/knowledge--and, yes, I was in the same boat many years ago myself.  What is most important? Self-reflection and a commitment to continuous growth. Chapter 5 has something for everyone, whether you teach 3-5 or not!

Chapter 5: How Do I Develop Specific Addition and Subtraction Strategies in the 3-5 Classroom?

Chapter 5 begins by outlining five number talk goals for 3-5:

Number Sense: Number talks help to develop number sense by---asking students to assess the reasonableness of a solution, having students make estimates BEFORE choosing a strategy to solve an equation, and requiring students to justify their solutions. These behaviors place emphasis on understanding, not on the memorization of steps/procedures. Parrish's discussion of the importance of students' abilities to estimate is almost identical to that shared for K-2.  Just recently, I have experienced the power of having students make estimations before selecting a strategy.  I began using number talks with my students about a month ago, but most recently I began our number talks with some estimation.

With my second graders, I asked students to answer 2-3 questions and justify their thinking.  For example, Is 50 a reasonable solution? Could the sum be 100? and we moved to more general questions such as, About how much is each addend? What is a good estimate of the sum?

How has this helped?  The number of incorrect solutions has reduced considerably with 1-3 solutions being shared, and students who had not previously shared began to share (their thinking being recorded for all to see "up on the board").  Asking students to estimate before finding a solution creates the mindset for reasonableness.  Below you can see a number talk without (left) and with estimation BEFORE (right).

Place Value: I think this quote says it all, "The true test of whether students understand place value is if they can apply their understanding to computation." Place value should be a focus for understanding and application at ALL levels.

Fluency: As shared in a previous K-2 post, Parrish states, "Fluency is knowing how a number can be composed and decomposed and using that information to be flexible and efficient with problem solving." When students have fluency with composing and decomposing "small" numbers they begin to understand that this can also be done with greater numbers.  This is foundational for understanding that making landmark/"friendly" numbers makes mental computation easier. Such fluency is essential at all levels and is strengthened with the use of number talks.

Properties: Parrish stresses how number talks foster students' use of their own strategies and their thinking can be directly linked to mathematical properties.  This in turn creates opportunities for students to apply properties while understanding their meaning.  Can you see the use of any properties in the strategies recorded in the following number talk?

Connecting Mathematical Ideas: Whenever possible, help students to understand that mathematical concepts are related. Some examples Parrish shares,  How can addition be used to solve subtraction problems?  How are arrays in multiplication related to division?

Chapter 5 goes on to overview the use of an open number line and part-whole box.

Open Number Line: If you are not familiar with open number lines, I highly recommend this introduction by Jeff Frykholm--Learning to Think Mathematically with the Number Line. It comes from his book of the same name.  Click here to learn more and view a sample lesson.  The open number line is a strategy many of my students use to model their thinking.

Also, Dreambox is a wonderful resource for using the open number line on an interactive whiteboard/computer--Teaching Number Sense Using the Open Number Line.

Part-Whole Box:  This visual helps students understand the relationship between parts and a whole.  Part-whole boxes are ideal for use when solving word problems with the unknown in different positions (start unknown, change unknown, and result unknown).

Download a simple part-whole box here!

Parrish continues by stressing the importance of using real-life contexts, discussing efficiency, and anticipating student thinking (as presented for K-2 in chapter 3). 

Finally, three common addition strategies, and five common subtraction strategies, are shared.  These illustrations are great for helping teachers anticipate the strategies their students will use and how to record them.

We would love to hear your thoughts about chapter 5, so feel free to leave a comment!

AND, keep those questions coming! Sherry Parrish, the author of Number Talks, will be doing a Q&A after the completion of our book study!  We will take questions through this coming Sunday--so don't hesitate to ask! You may send questions to guidedmathadventures@gmail.com. Thanks go out to Sherry!

Lastly, stop back this Sunday for Chapter 6 & 7!

Have a fabulous week--