Post date: May 28, 2017 2:37:27 PM
Social media and the internet can be a great way of getting an insight into how other teachers are working with maths in their classrooms. As you might know, I'm a firm believer in the importance of explicitly teaching children a range of strategies, be they for problem solving or mental calculation skills. And, anytime I delved into mental calculation strategies online, one initiative kept coming up: number talks.
With number talks, a number of names also kept coming up, including Cathy Humphreys, Ruth Parker and Sherry Parrish all of whom have done a lot of work in this area and published a number of books. After reading and watching a lot of YouTube videos, I decided to invest in Sherry Parrish's book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5. I wasn't disappointed that I had! The book is laid out in a very practical way with lots of examples and ideas for teachers to use with their classes.
In this post, I am going to give you more information about number talks, tips on how to use them with your class and share with you a whole suite of number talks resources.
What is a Number Talk?
According to Maths Perspectives Teacher Development Centre "A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation".
Short: They should only take 5 to 15 minutes; they are not intended to replace current curriculum or take up the majority of the time spent on mathematics.
Daily: they are most effective when done everyday, although aiming for two-three times a week should also yield effective results.
Typically, the children are presented with a calculation, which they are then asked to solve mentally. Individual children then share their strategy, which the teacher records on the board.
To get a better flavour for what number talks entail and rather than me re-inventing the wheel, I recommend you first to do either, or both, of the following:
Read the Number Talks Overview from Maths Perspectives Teacher Development Centre
Watch one of the video clips that are featured in Sherry Parrish's book (this is part of a longer clip, of Sherry showing a classroom clip, from the DVD that accompanies her book)
What does a Number Talk look like?
Sherry Parrish recommends the following structure (take a look at the video clip to see this in action):
The teacher presents a number sentence to the class; the students are given thinking time to mentally solve it.
The students start with one fist to their chest; they make a "thumbs-up" on their chest to show that they have found an answer. They then use the remaining time to try to think of another way/strategy which they then indicate by putting up a thumb and a finger, and so on.
The teacher asks a number of children to volunteer their answers and all given answers are recorded on the board.
The teacher asks a child to “defend their answer”/”explain their strategy”.
All strategies are recorded on board by teacher, using visuals where possible.
The children agree on the "real" answer.
In Sherry's book the number sentences suggested are also presented as a number string; this is a string of number sentences/expressions that are related to, and scaffold, each other eg:
20 + 20
19 + 19
19 + 21
19 + 17
She also recommends that teachers start with small numbers so that the students can learn to focus on the strategies instead of getting lost in the numbers.
In Kindergarten and the beginning of Grade One for the US, Sherry recommends using images instead of number sentences. These are images of ten/five frames, rekenrek (number rack) and dots to which the children are asked:
How many counters/beads/dots did you see?
How did you see them?
How many more needed to make five/ten/twenty?
This encourages the children to subitise (i.e. to tell a number at a glance) and in particular to develop their ability to conceptually subitise i.e. recognise that there are 6 counters/beads/dots because they have seen a a group of 3 and a group of 3. These again are organised into strings, in that every group of 3 or 4 images are related and should be used together in the same session.
Sherry Parrish's book has hundreds of number strings and images for Kindergarten to 5th grade. And because of the popularity of these resources, many teachers have already produced powerpoints which feature the number sentences and images from her book. I downloaded these myself for my own ease of use but found that because they were intended for US grades, I needed to reorganise and re-structure some of them to align them to our classes and curriculum. I also collected other suitable number talks from other sources and am currently creating some of my own. Below, are my suggestions for the different class groups and links to download the resources.
Number Talks Resources for Infants
I have taken the resources for Kindergarten and broken them up into two folders, Junior Infants (numbers to 5) and Senior Infants (numbers to 10). Each of the folders has a READ ME FIRST document; you should do this!
These folders are then further divided into sub-folders: frames, rekenrek and dots. From each folder, do the activities for the numbers as you teach them in class e.g. after doing the number 3 in class do the frames set for number 3, the rekenreks set for number 3 and then the dots set for number 3.
When all numbers for that specific class have been introduced, you can do the mixed number talks that cover all the numbers; these are a collection of slides that are a combination of the sides for each individual number. Senior infant teachers might also like to do the mixed number talks for junior infants, as revision at the start of their year.
In each of the non-mixed sets, usually each group of 3/4 slides are designed as a number string and intended to be used in a single session. This will be explained on the first slide if relevant.
Show the image to the children and ask
How many counters/beads/dots did you see?
How did you see them?
How many more needed to make five/ten?
Then ask children to explain how they saw that number eg "I saw 2 and 2 and then 1 and that’s 5", "I saw a group of 4 and 1 and that’s 5".
Connect the child’s thinking to a number sentence by circling the dot arrangement(s) the child describes and by writing a matching number sentence ie 2 + 2 +1 = 5, 4 + 1 = 5
Click here to access the Number Talks folder for Junior Infants
Click here to access the Number Talks folder for Senior Infants
Number Talks Resources for First & Second Classes
For these classes, I have renamed the Grade One folder as First Class and the Grade Two folder as Second Class (while not all of the maths contents of these US grades corresponds exactly with our first and second class curriculum, the number talks resources here do).
The First Class folder is further divided into sub-folders, each of which deals with one of four addition strategies:
Doubles & Near doubles
Within each of these sub-folders, there are different sets of slides of images (ie once again these are frames, rekenrek and/or dots) or slides of number sentences. As there is a substantial number of slides for this class, it is not necessary that every slide is covered, nor is it necessary to complete all or most of a strategy eg counting all/on, before moving onto another strategy. A teacher might decide to complete all the frames images in each strategy and then re-do the strategies but this time looking at the number sentences. However, it is recommended, and is more logical that you go through the strategies in order ie only explore benchmark/friendly numbers once the children are comfortable with the corresponding activities in the making tens folder.
The subtraction number talks are first introduced in Second Class and thus this folder is divided initially into addition and subtraction. The addition folder contains different slide presentations of number sentences only, each of which deals with one of six addition strategies:
Doubles & Near doubles
Breaking each number into its place value parts (also known as partitioning)
Adding up in chunks (also known as sequencing)
The subtraction folder also contains different slides presentations, each of which deals with one of two subtraction strategies:
Adding up (also known as complementary addition)
Removal (also known as deduction)
Within each of these slide presentations, there are three different categories, of increasing difficulty. Again, as there is a substantial number of slides for this class it is not necessary that every slide is covered, nor is it necessary to complete all or most of a strategy, before moving onto another strategy. A teacher might decide to focus on the slides in category one or two of each presentation/strategy and then revisit each strategy later in the year but this time focus on category two or three respectively. However, it is recommended, and is more logical that you progress through the strategies in order ie only explore benchmark/friendly numbers once the children are comfortable with the corresponding category in the making tens folder.
Click here to access the Number Talks folder for First Class
Click here to access the Number Talks folder for Second Class
Number Talks Resources for Third to Sixth Classes
In the final section of her book, Sherry Parrish has a section of number talks for Grades 3-5. These grades would loosely align themselves with our third to sixth classes, but not as closely as how the junior end grades and classes align. As a result, I felt it necessary to go through the number talks and try to organise them so that they would better align with our senior classes. To this end, I put together a table of how I'd suggest the Grade 3-5 talks could be divided among out 3rd-6th classes. This table is included on the document titled READ ME FIRST and the table may be used to aid a whole school approach to number talks. In this table, the categories of each number talks set is divided among suggested classes:
• Based on the suitability of the content for the curriculum of each specific class
• So as to avoid unnecessary repetition, while also facilitating beneficial revision (ie for the Making Tens strategy I've suggested that 3rd class do category 1 and 2, and then that 4th class can revise category 2 again before moving onto category 3)
Some other suggestions:
As with the previous classes, the operations should be done in order ie Addition, Subtraction, Multiplication, Division (as relevant to the specific class) and then, within each operation, progress through the strategies in the order on the table. If there is a second category of number talks to do, then this cycle can be repeated using the second category for the 2nd half of the school year.
Where two categories of the same strategy has been suggested for a class, (eg I have recommended that 3rd class do Making Tens, Category 1 and 2) it is not necessary for these categories to be done back-to-back and may even be preferable if the class did Category 1 early in the school year and then category 2 in the second half of the school year). In a similar way 4th class could do Making Tens, Category 2 in the first half of the school year and Category 2 in the second half. Differentiation: a weaker group may need to stick to the first category and/or use a category assigned to a lower class eg 4th class doing Category 1 instead of 2 or 3.
It is not necessary to do all the slides within each category. Differentiation: a weaker group may need to stick to the first category and/or do it again for the second half of the year meaning they may do all the slides in that category
As there is only a small number of number talks here for 6th and, to a lesser extent, 5th class, I am currently developing more resources to suit those classes. Check back for these.
Click here to access the Number Talks folder for Third to Sixth Classes
My Own Number Talks Slant
I'm no number talks guru by any means but I'd like to also share with you some of my own practice and ways I have been using number talks.
Number talks are recommended to use as an Oral & Mental starter for the 5-15 mins at the beginning of the main maths class. Initially, I found that I was going over time when I started these with a class and that if I tried to stick within 15 minutes that I wasn't getting to do all of the calculations in a specific number string. However, as time went on, I found that the sessions went much faster, as both the class and myself got more familiar with the structure.
It is suggested that number talks would be a daily activity at the start of each maths lesson; however I feel that sometimes, depending on the content of the main lesson, there might be a more appropriate or relevant starter activity. Number talks form an excellent suite of ideas that could be dipped into any day, irrespective of the content of the main lesson, but teachers should not be under pressure to do them everyday; choose what you think is best for you and your class depending on the content of the main maths lesson on that particular day.
I found that the number talks sessions worked equally well with whole classes, infants to sixth, and with smaller groups, (eg as part of a learning support slots, either within the class as a station in team-taught lesson or in withdrawal sessions). The small groups are particularly useful for the children who might be reluctant to volunteer their ideas in a whole class situation and gives them the opportunity to develop their confidence to ultimately contribute in a whole class setting. Learning support teachers could also use the number talks to pre-teach groups so they would be more confident and willing to contribute to a whole class number talk with their class teacher. For example, if a learning support group in 4th class were due to start category 2 of a specific strategy with their class teacher, their learning support teacher could revise category 1 with them in advance and/or use some of the category 2 strings or compose new number talks based on similar numbers.
I found that class participation levels and the "quality of the talk" both rise if the children have already encountered specific mental computation strategies in class. Where classes had been explicitly taught mental calculation strategies, eg doubles, making a ten, friendly numbers, compensation, constant difference subtraction etc they were more likely to explain their thinking using the correct mathematical terminology.
In the number talks videos, the children are often seen sitting together on the floor. As the children in my school wouldn't be that familiar with this seating arrangement, I just worked with them in their usual seating places as I didn't want the change of scene to detract and distract from the focus of the number talks.
While I initially used the fist and thumbs up system advocated by Sherry Parrish, when collecting answers, I often got the response "I had the same answer as Jack". So I returned to my preferred tool of mini-whiteboards, (to maximise on participation and honesty regarding answers) but insisted that they were not to be used at all for working out, all of which was to happen in the heads. Rather, the MWBs were only to be used to record the answer.
As mentioned earlier, It is suggested that the teachers use smaller numbers than that with which the children are more familiar, so that the children can focus on the strategies rather than the numbers. While I agree with this logic, I also feel there is an argument in favour of showing a relatively unfamiliar calculation to a class when the the aim is to introduce a new concept to see how the children might tackle it themselves. For example, I recently used a selection of the number sentences opposite (no images, just the number sentences on a MWB) as part of my number talks in a first class to introduce addition of 2-digit numbers to 1-digit numbers with renaming, before they had encountered how to do this with the traditional written method. In this way, the children were able to appreciate that they we able to calculate these type of number sentences already, using their own preferred strategies, before being asked to use the more formal way. Depending on the range of possible answers given at the beginning, I have also asked the children to identify any unreasonable answer from those suggested and explain why they think so. This in turn encourages them to use their estimation skills e.g. to justify why given answers are too big or too small, or unreasonable for another reason.
As I mentioned earlier, while number talks are still not a widespread practice, they are gaining traction, and any search of the internet will yield many Number Talk related results. These are some of the links that I would recommend as a starting place.
Number Talks & Operation Maths: If you are an Operation Maths user (or are considering this programme) you might already recognise how number talks and Operation Maths are a perfect partnership for each other. This post outlines how they both support each other.
Assorted docs and info: this is another of my number talks folder, this time with supporting articles and information. It might be useful to dip into over time
Number Talks Build Numerical Reasoning: Sherry Parrish's article from NCTM Teaching Children Mathematics magazine
Getting started with Number Talks: a great article for general info and organisational tips
On Your Marks. Get Set. Number Talks: An article from Graham Fletcher with lots of links
Number Strings: A site where teachers, can find new strings, post their own strings, get feedback and discuss the pedagogy of number strings
There are other resources and images available freely on the internet that are similar to, and work very well in conjunction with, Number Talks:
Splat! resources made freely available here by Steve Wyborney. While officially not a number talk, these excellent visuals are alternative images that can be used as number talks. Play the powerpoints on your class IWB and use MWBs for the children to respond.
Unit chats: from Math4Love and based on the idea of various representations for one whole unit, these images support the topic of fractions.
Dice Chats: Using dice images, these can help support the introduction and development of the concept of multiplication as repeated addition.
I would also strongly recommend that you consider purchasing Sherry Parrish's book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5. Not only does it have all the number talks mentioned earlier, but it also includes a breakdown of each strategy, instructional tips and includes a DVD of video clips of teachers conducting number talks in their classes. I'm already planning to make Number Talks: Fractions, Decimals, and Percentages be my next purchase.