Compare Problems and the Common Core

Are your students good at compare problems?

My first and second graders (and sometimes third) often struggle with this concept.  Here is a peek at the Common Core Standards that specifically address compare problems

First Grade
CCSS.Math.Content.1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.¹

Second Grade

CCSS.Math.Content.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.¹

CCSS.Math.Content.2.MD.A.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

CCSS.Math.Content.2.MD.B.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

CCSS.Math.Content.2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems¹ using information presented in a bar graph.

Third Grade

CCSS.Math.Content.3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

CCSS.Math.Content.3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

As you can see there are a LOT of common core standards that address the importance of being able to do compare problems, especially comparing distances!

Here is a fun and easy way that I help my students with comparing lengths.  It has great tie-ins to science and we can go off on huge tangents about force, friction  etc but in this post, I am going to focus on the math related questions I ask during this lesson.

It is a VERY engaging lesson, so I usually save it for those hard to plan for, full of wiggle days like the day before a vacation or holiday or the days leading up to summer vacation.  I have done this lesson or a similar one with a few tweaks in first grade up through sixth grade.  I will be showing you pictures of a second grade lesson and at the end will give you some ideas about how I adapt it for older and younger kids.

The set up:
I use unifix cubes snapped into groups of 10 and alternate colors going down the track.  I use a binder as a ramp.  In the picture you see a 1 inch binder but I have used smaller and larger binders depending on how far I want the balls to roll (I also use matchbox cars in some cases).  I often use a long sheet of paper that is about 12 inches wide underneath so that there is less friction and the balls go farther.  I line both sides of the track with unifix cubes to ensure the balls stay on course.  

A look at the set up

I set the track up ahead of time or have a kid help me set it up.  Having a kid help who needs some more work with groups of ten is a great way to kill two birds with one stone.  I also write the name of the ball on a sticky note ahead of time so we are ready to record their distances. 

My collection of balls/marbles for this particular lesson.  I go to the teacher in our school who loves science the most and she can provide me with 9 different balls in under 2 minutes.  If you don't have an impressive ball collection check with people who love science.  Better yet get them to co-teach this lesson with you for a great science/math double whammy!

Then we establish some rules together.  We talk about things like where we will release it, how to release it (no pushing) and how we will decide how far it went.  Then we start rolling.  As each ball is rolled, I have kids figure out how far it went and record it on a sticky note.  (this is a huge focus when I do this with K and 1 kids.  Counting tens and ones and writing the numbers is exactly what they need practice with)


The first two balls we rolled were the steel ball and the large marble.  We stop and ask how much farther did the marble go than the steel ball?  Kids give me a ready signal when they are ready.  They then turn and talk with a partner about what their answer is and how they know they are right.  This lets me hear a lot of answers all at once and gives me a good idea about who should share with the whole group.  I often ask a kid to explain their partner's answer to me.  This gives them practice looking at a problem a different way and ensures that they are actually listening when their partner is talking. 

Our first two balls went 91 and 103 cubes.  We pay attention to these labels.  Notice how we move the balls to the outside of the track but leave them in the same place they landed.  This supports kids who need to use the cubes as a visual model when answering my questions.

We keep rolling balls and the kids quickly take over generating compare questions.  They get very excited to figure out how much one ball "beat" the other ball by. 

One section of our track got REALLY crowded this time!   

When all the balls have been rolled, I finish up with some compare questions.  I also often ask questions like how much farther would the ping pong ball have to have gone to get to 100?  This is similar to asking how much farther did one go than the other but can sound very different to kids.

HERE IS THE VERY IMPORTANT PART!!!!!
We just spent half and hour working as a whole group doing some really fun and exciting math that gets at the big idea of compare problems.  I want this fun and excitement to continue so I preserve our game board by having a few students help me turn it into a number line. Check it out!

I have kids make a mark at the end of each unifix cube, alternating colors every 10.  This turns our race track into a number line that I can put on the board and talk about with students few times the following week.

I have a few students help me to make marks where each unifix cube is and we then take the sticky notes and show where different balls went.  We do this right on that long piece of paper we used as the race track.  Now I have a record of our work and we can talk about it and answer questions about it the next day and the day after.  It is a great way to keep talking about compare problems. 

The next day, I met with 6 kids that I noticed were struggling a bit with the whole group lesson.  We sat right in front of our number line record and talked about what happened and how much farther some balls went than others.  They got more practice doing compare problems using a visual model (the number line) to help them.

The day after that, I created a written practice sheet that had compare questions on it about how far various balls went and used it as a station in our math rotation for that day.  I was doing some end of the year assessments and had several workstations set up around the room.  This one was a big hit and kids kept the excitement they had about doing this activity and were happy to be digging back into it.  Their very favorite part was writing their own questions for their partner to answer about what happened. 

Using this activity with K/1 kids

Since I had all of this stuff out, I also used it in K and 1 this week.  With these younger students, I did do some compare problems but the students relied heavily on the cubes to help them figure out the answer.  My focus shifted a great deal to multiple ways to figure out how far the balls went.  Some kids in this age range always go back to zero and count forward.  Others are able to use a previously placed sticky note and count on from there.  Having these discussions with kids was very valuable!  Also we focused on writing numbers up to 120 and what each part of the number means.  Example: When a student wrote 82, I could ask them what the 8 in the number meant and how they could see the 8 in the cubes.  This led directly to the seeing that there were 8 groups of ten or eighty.  I also wanted the marbles to go a bit farther so I had the "start point" be at the top of the binder.  This ensured a lot of the balls were falling in the 100-120 range which is where these kids need the most practice at this stage.

Using this activity with older kids

By changing the value of the cubes, you can easily extend this game into fractions and/or decimals.  I have used it for decimals by making each group of 10 cubes worth 1 unit.  Then each cube is a tenth and you get a lot of great connecitons that way. The compare problems become a matter of adding up or subtracting decimals.  GREAT PRACTICE!  Very visual and supported by the materials

When I want to work on fractions with this idea, I often snap either 8 or 12 cubes together to make 1 unit.  This gets kids into thinking in eighths or twelfths and their related fractions.  It also gets kids thinking about fraction addition and subtraction in a fun and supported way.  Next time I do this with fractions or decimals, I will take a lot of pictures and write a post about it.  It is a great experience to give your students!

How do you help your students with compare problems?

Meeting Common Core Problem Solving Standards with Water Themed Picture Problems

I recently was using my water themed problem solving pictures in first grade and I thought I would talk some more about why I created these problems.  (They are available for FREE at my Tpt store: the link is on the bottom of this page!)

My students always need more practice with subtraction type problems at the end of grade 1 and beginning of grade 2.  This set includes a lot of those type of compare problems.  (see glossary table 1 in common core for more information)

I love whole page picture problems when working with small groups or the entire class.  They are very engaging and are good at pulling all students into the problem.  Here is a peek at a few of the problems (I print these in color on a full sheet of paper)

I also made them so that you can print them for student work pages.  The picture takes up about a fourth of the page and the rest of the space is white space for students to show their thinking and solve the problem.

All 12 problems can be printed as full page color illustrations or has student work pages

I also included a student work page that has a picture and asks students to write a story problem to match the picture.  This gets at a deeper understanding of the math required to solve the problems

Students write a story problem to match the picture

I always have kids who want to make up their own problems so I also included a blank background in the set so that kids can illustrate and write their own problems.  This also gives the class even more problems to solve!

Students illustrate and write their own problems

My students love these problems.  If you think your students will love them too, head on over to my Tpt store to grab your set for FREE!  If you use them and love them, be sure to follow me on Tpt so that you will see my newest products and freebies!

Looking for more themed problem solving for your first or second grade students?

Check out my Ant problems

A set of 10 problems that meet CCSS for grades 1 and 2 with a cute ant theme!

I also have penguin problems

Aligned to CCSS for grade 1.  Includes all problem types first graders are expected to  master under the Common Core

Data Standards Common Core Style Second Grade

One of my favorite Common core standards is this data standard that runs from grade 2- grade 5.  I have already posted about how I addressed this data in standard in grade 4 and grade 5 if you want to check them out!  

Here is the standard for second grade

CCSS.Math.Content.2.MD.D.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Compared to the grade 4 and 5 standards, this seemed like a piece of cake!  

Off to a bad start

So I decided that since it was so nice and sunny outside that we would go outside and collect some fun data.   We measured how far each second grader could do a feet together forward hop.  After a few practice hops, each student had their official measurement done by hopping the length of a yard stick (actually 2 yard sticks end to end).

Although the hopping was a lot of fun, the results were disastrous when we went back into the classroom and tried to construct a line plot.  The problem was that the results ranged from 31 inches to 72 inches.  Also only 2 people jumped exactly the same distance.  We did learn together that a line plot is not a good choice to display such data.  I wanted to quickly save the lesson so we measured each kid's height to the nearest inch instead.  MUCH BETTER results.

A line plot showing the heights of second graders constructed during a whole group lesson

A strong finish

The class results based on height look much better!  Their is enough spread and variation to make it interesting but small enough to keep it manageable.  Here are some questions we came up with that could be asked about our line plot

How many kids were measured?

What is the most popular height in second grade?

How tall is the tallest student? (this is great because when kids look at line plots without ever having constructed one themselves, they will often look for the tallest column of x's and respond with 51 inches.  Even after building this as a group I still had kids that went there.)

How tall is the shortest student (another question easily answered wrong.)

How much taller is the tallest student than the shortest student?

This was a good first look at line plots with my second graders.  I need to make sure we do a few more lessons like these before the end of the year.  

Any suggestions on good measurement data to use for second grade line plots?

Combinations of 100 and the Common Core

We have been hard at work in second grade this year on combinations of numbers that make 100.  Having students who understand how to combine numbers to reach 100 expands their repertoire of strategies for solving addition and subtraction problems.  It makes them much more fluid in their reasoning around operations and place value.  Having this concepts supports a huge chunk of the common core standards for grade 2.  Here are the main standards this supports

Use place value understanding and properties of operations to add and subtract.

• CCSS.Math.Content.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• CCSS.Math.Content.2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
• CCSS.Math.Content.2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
• CCSS.Math.Content.2.NBT.B.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
• CCSS.Math.Content.2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.¹

Here is a peek at some of the activities, routines and manipulatives we use to support this important idea.

Base 10 Pieces

We use our base 10 pieces and a deck of cards from 1-100 to make a simple practice game for students who are learning about combinations of 100.

Kids flip over a card and find what goes with that number to make 100.  Once they place the number of pieces they flipped over the 100 mat, what is left is what they need to get to 100.  Kids start noticing patterns right away and some move quickly away from needing to use the manipulative while others spend a lot of time at the concrete stage with the manipulatives.

 

I will sometimes do this as a warm-up, a math center or even as a whole class activity.  Sometimes we use record sheets and other times we just share our answers orally.

100 Bead String

Another manipulative to work on combinations of 100 that we use often is our 100 bead strings.  We purchased some plastic lanyard material and beads from the craft store and made a set of bead strings.  We alternated colors every 10 beads so that the groups of 10 would be highly visible.   We use some of the same routines/games with the 100 bead string that we do with the base 10 pieces

This student has pushed 41 beads to the left and uses the beads on the right to figure out what goes with 41 to make 100

Sometimes we use record sheets.  My students like to make their own on an individual white board.

A simple game where students flip a card and find out using the bead string or base 10 pieces or mental math what goes with that number to make 100.

And we extend it to subtracting from 100

Almost the same game as above but instead of thinking about the missing addend, the students are thinking of subtraction.

Are your students fluent with combinations of 100?  What experiences do you provide for kids to practice this important skill? 

Check out this lesson on how my students apply this skill to three digit subtraction.
Here is a fun, free app to work on combinations of 100!
Need a computer activity to work on combinations of 100?  My students love this one!

First and Second Grade Common Core Standards for Fractions

I have been working hard with my first AND second graders on fractions over the last week.  Here is a look at the Common Core standards for grades 1 and 2 around fractions

CCSS.Math.Content.1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

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.

Yup.  The fraction standard is found in the geometry section and it is all about partitioning into equal sized pieces.  It also gets to the HUGE idea that the pieces do not have to be congruent to be equal.  Notice what is not there?  There is nothing about using symbolic notation.  Awesome!  I have found that using the numerals 1/2, 1/2, 2/3, etc do nothing to promote understanding of fractions and actually hurt kids when they learn them to early.  Seeing the numerals for 1/2 and 1/4 at an early stage lead a lot of kids to reason that 1/4 is larger than 1/2 because 4 is bigger than 2.  This is called improper whole number reasoning and our instruction can really reinforce it if we are not careful.

Because of the move to the Common Core standards, I was not happy with the materials we had been using around fractions, so I decided to create some of my own.  I really wanted kids to use the language and words of fractions and stay away from the symbolic notation.   After creating things and tweaking the way I used them, I couldn't be happier with the results!  Both the first and second graders did a great job on the assessment and they have this amazing conceptual understanding of fractions. 

 Here are some highlights from our week of fractions!

Playing Fourths or Not Fourths (Scoot Version)

Have you played scoot games with your students?  They are so much fun and a very engaging way for kids to practice all kinds of skills.  For this game, I spent some time making a set of 18 cards where some show fourths and others show things that sometimes kids think are fourths.  We looked at a few of these pictures as a class and really talked about how we knew something was fourths.  Then the kids headed out to play scoot using these cards.  They rotate around the room with their record sheets and fill in fourths or not fourths (some used the word fib instead) When they finish, I pair them up with another person who is done and they have a "math talk."  This is where they compare answers and anywhere where they disagree, they go back to that card and try to come to a consensus.  This brings up some great conversations and is a place where a lot of math learning can take place.  

2 kids compare record sheets while playing the scoot version of fourths or not fourths.  The kids changed the rules slightly and made it fourths or fib.  

  When most kids had finished their math talk, I brought them back to the discussion circle and we further discussed two cards that caused a lot of discussion among pairs.

2 of the fourths or not fourths cards that caused a lot of discussion between kids.  These cards really get at the idea that the pieces do not have to be the same shape, but have to bee the same size.  

Talking about these two cards and having kids construct arguments to support their thinking really got at the big idea behind fractions.

Formative Assessment on Fourths

I ended the class period with a quick formative assessment sheet on fourths.  This let me see who got the big ideas and who needed a little more help.  There were a few kids who didn't seem to have it and I met with them for about 15 minutes in a small group at the beginning of class the next day.

A quick formative assessment check in that kids do on their own.  This lets me see who has the big ideas from today's lesson and who needs more instruction.   

I really love the question on the bottom of the page that says "How do you know you are right?"  This really lets me see what their ideas are around fractions.  Check out some of these responses

This kid really understands what it means to be one fourth!

Here is another one

And one more

This kid has been exposed to some symbolic notation around fourths and uses it in his response

Second Graders need to move onto thirds

With the second graders (and a few first graders who were ready for the challenge), I made up another set of cards almost exactly like the the last set.  These have thirds or not thirds.  We played scoot and used them for warm ups and such.  We used a similar record sheet and process.  Here were the 2 cards that were brought to the rug for our final discussion at the end of the game.  Notice how the pieces are eight oriented differently or not congruent.  Many kids still had disequilibrium around these 2 cards.  We again had a great discussion and had kids had to construct arguments and try to prove their thinking to their classmates.  

The 2 cards from the thirds or not thirds deck that prompted the most discussion.

We also followed up this scoot game with some formative assessment.  

The students in my class did very well identifying which shapes had one third shaded.  They did not do so well at shading one third of the picture.  We spent the next day doing a lot of practice with partitioning squares, rectangles and circles into thirds.  With some extra practice, all of the second graders got much better at this. 

We finished off the week with a quick assessment to see how students have progressed in their fraction understanding.  I made up 2 different assessments.  One was for grade 1 and the other for grade 2.  The kids did fairly well and we will continue to use some of the other worksheets I made up for extra independent practice or homework.  We put the cards from the fourths or not fourths game into a math center for extra practice during partner work time as well.

The materials I made for this unit turned out great!  I have posted the entire unit including games, worksheets, answer keys and assessments on Tpt.  Click here to check it out!

The entire fraction unit aligned to grade 1 and 2 common core standards is available on Tpt.  Click here to check it out!

I posted Fourths or Not Fourths as a freebie on Tpt.  Click here to check it out!

Click here to grab this freebie from my Tpt Store!

How do you teach fractions to first or second graders?  

You might also be interested in
A great book for introducing fractions
More fraction work with second graders
Paper folding fractions with first graders
Fraction You Tube songs and videos

No Prep Differentiated Fraction Game

This morning I was working with some fifth graders who needed some intervention in the area of fractions.  The Common Core has a great deal of expectations for fifth graders around conceptual understanding of fractions and fraction operations.  I grabbed my 2 sided counters to create a quick game for these intervention students.  After about 20 minutes, I had the intervention students join the other students and we invented level 2 and level 3 of the same game to work on fraction operations.  I love low prep games that get kids working on important concepts without requiring the teacher to spend hours prepping materials.  Kids make their own record sheets!!  You can get your whole class started on level 1 and then introduce levels 2 and 3 as pairs need.  Or pick just one level if your kids are in a specific place!

For all levels
-Play in pairs or groups of 3
- Each pair/group needs 12 2 sided counters
- Each person needs a piece of scrap paper or a small whiteboard and a pencil or marker
- Each game has 5 rounds. If pairs/groups finish one game and were fluent, move them onto the next level, otherwise have them play another game at their current level.

Level 1

The kids who needed more work really needed some more conceptual development around equivalent fractions.   Here is a look at a record sheet from round 1

Shake the counters in a small cup and drop them.   Sort into red and yellow. Record as many equivalent fractions that you can find  using the counters.  We made the rule that you couldn't split the counters into pieces therefore the largest denominator possible was 12.  When both partners are done round 1, switch record sheets.  Check your partner's fractions.  If you agree with them, circle them.  One point is scored for each correct fraction.  The winner is the person with the most points at the end.

I love level 1 for 4th graders and intervention/early 5th graders because it can be very hands on and there is a great deal of visual support.  Take a look

This student is proving to their partner how 4/12 is the same as 1/3 by moving and re-grouping the counters

Now the same pair is showing how 4/12 is also equal to 2/6 by moving and re-grouping the counters

Now if you change the number of counters in this game, think about all the different equivalent fraction practice kids would get!  Changing the number of counters is a great way to keep the game fresh.  It would make a great math center!

Level 2

The fifth graders are also working on adding fractions.  For level 2 I had them each take 5 turns and record one fraction each time.  Then they had to find the sum of the 5 fractions they rolled.  This was great because even though the recorded some in twelfths, some in thirds, some in halves, etc, they had just practiced finding equivalent fractions and were able to quickly convert between equivalent fractions in order to find the sum of 5 different fractions.  Take a look at a record sheet from level 2

I loved that they were finding the sum of 5 different fractions and that the sum often went over 1 and sometimes even over 2.  It was a great way to practice (with hands on materials as a back-up) a lot of the skills that fifth graders are required to have.  Each student played several games on level 2.   

Level 3

This level was for my advanced students and some students who had been exposed further to fraction operations.  They had to shake and drop the 12 counters and figure out what fraction of the counters were red.  Then then had to come up with equations that equaled that number.  In round 1, they had 1 equation, round 2 required 2 different equations all the way up to round 5 which had 5 different equations.  I LOVED this version because they had the answer and had to come up with the problem.  Depending on their comfort level, the equations varied quite a bit in complexity and uniqueness.  Here is a peak at 2 different record sheets from this level.

A record sheet from level 3.  Notice each equation got circled as their partner checked it.  The partner circling the equation meant that they agreed

Another record sheet from level 3

I love activities like this!  No prep required, minimal materials and completely differentiated to meet kids below, on and above grade level.  The best part is that the kids really think everyone is playing the same game.  Because the materials are the same and some of the rules, they don't see how much they vary in difficulty.  This series of games will become a math center during Guided Math time later in the week!

How do you differentiate learning for your kids?

If you want to see how I use these same counters with K-2 kids, check out this post or this one

Frog and Flower 10 Frame: My first link up with Maniac Monday

Have you checked out the Classroom Freebies blog?  It is truly amazing how many great freebies they post each week.  I am linking up this week with their Maniac Monday to offer a set of FREE frog and flower 10 frames.  (as you can see from the pictures, I also use them as 5 frames and 20 frames)

I use these as 5 frames with my K kids, especially those who struggle

Here a first grader is practicing combinations of 10

I put a full 10 frame on top of a partial one and instantly have 20 frames.  I use these with kids  in grades K-2

I have many ideas about how to use 10 frames in the classroom to improve numeracy and additive reasoning.  Check them out!


Click Here to get your freebie!

Here are a few other things I use during my various frog units in grades K-2 and ANOTHER FREEBIE!

Here is a fun spring themed version of I have....who has that works on number recognition of numbers between 100 and 120

A fun way to work on using the <, >, and = symbols

A bingo game that works on matching numerals to base 10 pictures.

Here is a post about how I use the frog theme to work on equality

s

Here is a version of I have who has that works on number recognition to 100

Here is another freebie offered at 2 levels to work on addition fact doubles. 

Happy spring!

Guest Post on Minds in Bloom

I have a guest post up over on Minds in Bloom.  I talked a lot about how to meet a common core data standard.  It is a great post, click here to check it out!

A Quick but effective game for pairs of 20

Yesterday, I wrote about a game and lesson I did with K and 1 kids around pairs of 10.  If you haven't seen it you may want to start there.

Today, I was working with a group of intervention second graders and decided to extend the pairs of 10 game to the pairs of 20.  I wanted to review the idea of compensation but the focus today was more on all possible combinations of 20 and how the combinations of 10 can help you with the combinations of 20.

I started by giving them each a small handful of two sided chips (pennies would also work!) and having them figure out how many I gave them and how many more they would need to have 20.  (I always underestimate.  This gives them one more chance to practice a combination for 20).  Once everyone had 20 chips (actually today we did pairs) we put our chips in a cup and shook and dropped.  We then sorted into yellow and red and had kids count how many of each color and write an equation to match.

20 two sided chips.  

Sorting the chips into yellow and red and counting them up.  This led to a lot of practice with counting by 2's and counting by 2's then adding one more when the numbers were odd.  A very nice side benefit because that is another skill this group has been struggling with.

A look at the record sheet of one pair.  Record sheets are great to bring back to the whole group to have kids share things they noticed.  

 After playing for about 10 minutes, I pulled the group back together and told them I wanted to share what happened when I was playing.  I gave them examples such as I had 8 red chips, how many were yellow?  OR I had only 3 yellow chips, how many were red?  This is a great way to use the context of the game to help kids think about missing addends.  I wrote a question on the board and asked kids to write an equation that went with it.

I wrote this question on the board and asked kids to find an equation that went with it.  As you can see in the picture, they came up with 13 + ___ = 20.  Then one little boy said, I actually got 20 - 13 but I think they are the same thing.  This led to a great discussion about fact families and the relationship between addition and subtraction.  

The kids in this group really understood the idea of compensation and how an equation like 12 + 8 is related to an equation like 13 +7.  They were readily able to demonstrate this with the materials so we moved on from here and talked about how the make 10 facts helped us with the make 20 facts.

I still had 5 minutes left so I asked if any group played the game long enough to find all the possible equations.  The whole group was not sure but one little boy was convinced that there was no way they had enough time.  They started sharing different equations and one student decided to organize the equations so that we would know if we had them all.  Check out his work below!

One boy's list of the combinations of 20.  Writing this list out himself really helped him process what he had learned and pull together all of the little pieces of knowledge we used in this game.  

As the kids were lining up at the end of class, one little boy noticed that the 2 numbers were either both even or both odd.  He said, "it is just like when we were playing if the number of red chips was even so was the number of yellow chips." What a great notice for the end of class.  I took a picture and wrote his idea down so that we can explore it more and he can prove why it is true to his classmates next week.  If only I had 15 more minutes with these kids today......

Are your students fluent with combinations of 20?  Can they extend what they know about combinations of 10 to combinations of 20 or even 100?