Navigation Menu

All rights reserved
Growing Grade by Grade 2016

Showing posts with label number sense. Show all posts
Showing posts with label number sense. Show all posts
How To Have Fun AND Build Number Sense: Play "No More"!

How To Have Fun AND Build Number Sense: Play "No More"!

     Do you want a no-prep math activity that you can use with almost any grade-level? Do you like to feel confident that you're building strong number sense? Would you like to know you're creating a smooth segue into pre-algebra? If so, let's play "No More"!
     When I say "no prep", I mean it! Simply stroll to the whiteboard or SmartBoard and sketch this:
     Next, pick a number. I typically use the day's date at the beginning of the year, but you can pick any number. Write the number at the top.
     Now, challenge students to call out as many different ways as they can think of to "express" that number. 

     This is a beautiful way to get used to identifying just what a mathematical expression is - another way to say a number. I always make an ELA connection here, explaining that I can refer to a child, say Jayden, with different expressions. I can refer to Jayden as, "Jayden", "Mr. Williams", "the boy closest to the door", "the guy in the red shirt", "one of my students", etc. In the same way, we can refer to numbers in just as many ways.

     As you get started, students will typically share fairly simple expressions although some students are ready for more advanced examples:
      Help students by adding some expressions yourself. Remind students that they can use the word form of a number, the short word form, Roman numerals, decimals, and fractions.
     My students often hang out with the easiest expressions they could think of, like addition. As you notice one operation being used a lot as in the example below, write the operation in the "No More" column. This means that there can be no more addition used in expressions for the rest of the game! Yikes! Kids really start to slow down and think!
     They may head for the relative safety of, say, subtraction. Let them go a while, then lower the boom. No more subtraction!
     Continue playing for a few minutes, usually 2 - 5. Once you eliminate the third operation, you're really cooking!

      You get the idea. You're guiding students to think deeply about how to create a number and they're understanding the difference between expressions and equations.

      Consider adding this to interactive math notebooks, assigning it as a warm-up, and letting kids collaborate before they share. I'd love for you to try "No More" and let me know how it works for you!
Read More
Growing Grade By Grade
16 Comments
One Of The Best Number Sense Games Of All Time: Contig

One Of The Best Number Sense Games Of All Time: Contig

     Every teacher on the planet should learn the math game Contig!  Read the details here and consider adding it to your collection of go-to math activities. 

Why Contig?

I recommend this game for any class:
  • it's awesome at building number sense
  • it's easy to prep and play 
  • each game is fresh and new 
  • you and your students can adapt it to your own needs as you go 
  • it works beautifully in centers, small groups, or as whole-group fun 

The Gameboard

     You can download a free copy of the game board here. There is also a Contig, Jr. for younger students. Here's the game board for grade 4 and up:

The Materials

Materials are simple. For each pair of students, you need:

  • a laminated Contig game board
  • 3 dice
  • a different colored dry erase marker for each player

How To Play  

1)  Roll three dice. Use the numbers just as they are. For example, if you roll 2, 4, 6, they cannot be 24 or 62... just 2, 4, 6. 

2)  Add the three numbers. That sum is your starting number. Cross it off the board. This is the only time that you are required to do anything specific with the numbers you roll.
3)  Look at all of the numbers surrounding the number you marked off. These are your target numbers. If your starting number is 12, your target numbers are 3, 4, 5, 11,13, 19, 20, 21. You do not have to mark them, as I have in blue below. This is just to show you what is allowed.
4)  On each turn, roll three dice. The player can perform any operations in any order on those three numbers as long as the result is one of your target numbers. If you rolled 3, 5, 6, you could say: 3 x 6 - 5 = 11. Cross off 11. 
5)  Notice that your new target numbers are 2, 3, 4, 5, 10, 13, 18, 19, 20, 21.
6)  Continue rolling 3 dice on each turn. Perform operations to produce one of the target numbers. Notice that your target possibilities increase with each new number. Continue to play for a specified time or number of turns, whatever works for you.

     Once students are confident about playing the game, they typically start asking to change the rules. That's great! This type of mathematical discussion is powerful. I always ask students to predict how their suggested change will affect the game. Common changes that kids suggest are:
  • Use 4 or more dice.
  • Treat your starting roll like any roll; instead of just adding, perform any operations.
  • Use only multiplication and division.
  • Use one of your dice as an exponent.

One Last Connection

     If students ask about the name, Contig, I love to make this ELA connection. I tell them it comes from the word contiguous, then ask if that sounds like a word they've heard before. They typically respond, "Continuous". I agree and say contiguous means continuous and touching. That refers to the target numbers that need to be touching, or contiguous to, the numbers you choose.
  
    I hope you'll give Contig a try. I love it so much that I created a version to send home with my students. It's a great homework activity. You can find it in my store here.

     Best wishes and I'd love to hear how Contig works for your students!

Read More
Growing Grade By Grade
123 Comments
Powerful Number Sense: Where's The Math In The Date?

Powerful Number Sense: Where's The Math In The Date?

     

     I'm a math teacher so I'm always looking for activities that build number sense. My criteria are simple: I want activities that are fun, engaging for a whole class, no-prep, and quick. Sound impossible? Try "Find The Math In The Date". I'll bet you love it as much as I do!

      I write the day's date at the top of my whiteboard every day. I generally use the M/D/YY format. However, when we want to "Find The Math In The Date", I quickly change it to MM/DD/YYYY. You'll see why below.

      Our goal is to use the digits in the date to make any and all mathematical statements that we can. These are usually equations but can be a number fact that is commonly known or can be proven. The only rules are 

 1) you can use the digits in any order you wish 
2) you can only use the digits that are actually in the date.

     We generally spend 2-3 minutes playing, but you can adjust as needed. You can write student contributions on the board as you go, have students come up to write, or just let listen and affirm.

      As soon as I ask, "Where's the math in today's date?" hands start flying up. You might want to require about 30 seconds of thinking time to give everyone a shot.
Number sense math in the date

      Let's see what we heard on February 25, 2017 or 02/25/2017.
Number sense math in the date game
2 + 5 = 7
7 + 1 = (2 + 2) x 2
2 + 2 + 5 = 2 + 7
5 x 2 = 2 + 1 + 7
25 - 20 = 7 - 2
(We have a 20 to use, but you could also use the first 0 and 2, if needed.)
2 x 5 = 10
 There are 725 students in our school. 
Valentine's Day was 11 days ago. That's 7 + 2 + 2.

     You'll be amazed at the math connections that your students can make! 

      You can modify this game to address your students' needs.
  • Have students work on it independently for a few minutes, maybe as a warm-up, giving students even more time to think. 
  • Use it as a center if you're doing center work one day. 
  • Have students use their own birthday as the date. Once they write a good number of equations/facts, they could swap with a partner and share.
     Give this fun, no-prep game a try. I'd love to hear how it works in your classroom. Also, let me know what number sense activities are a hit for you!


Read More
Growing Grade By Grade
4 Comments
The Hundreds Chart With A Twist: A Powerful Math Tool

The Hundreds Chart With A Twist: A Powerful Math Tool

    

     Most primary and many elementary teachers use a hundreds chart as a powerful tool in their math classes. It can help students master so many concepts: counting, skip counting, one-to-one correspondence, patterns, basic facts,...the list goes on. In addition, the visual and kinesthetic components of a hundreds chart are powerful tools in developing number sense.
     I've used hundreds charts for years in 5th grade.  My kids especially like the activities where I ask a question or present a problem, they put a chip on the answer, and it makes a self-checking picture at the end - much more fun than a skill worksheet.

     Several years ago, it dawned on me that the traditional hundreds chart, starting with the one (1) in the upper left-hand corner, might seem backward to some children.  It certainly did to me!  

     Starting in the upper left corner and moving down to add, or moving up to subtract is contrary to our language and our algorithms. Of course, algorithms are not our primary focus in math.  However, we often physically move down for subtraction and up for addition.  Most importantly, our language should match our math.  We say, “Add up the numbers”, “low numbers”, “one step forward, two steps back” and “count down”!   One day, I sat down and developed this chart to help my students connect what they hear with what they see and do.

     This chart starts with 1 in the lower-left corner.  It allows students to move up the board as they count higher or add.  They subtract and move down the board, more in line with algorithmic directions.  

     This “upside-down” hundreds chart is just what many of my students needed to develop number sense and see how our number system works with our algorithms!    

How to use the “Different Hundreds Chart”:

     Begin by providing a cube or game piece for students to move when finding numbers.  As students become more confident, they may move a finger to find sums or differences.

      Start with easier tasks, such as adding/subtracting tens. Here are some sample directions.

1.     Add/Subtract 10:  Call out a beginning number for everyone to mark.  Help students see that if they add 10, they will move directly up one line, a full ten spaces.  If they subtract 10, they move directly down one line.  Challenge students to add/subtract 20 or 30 and see where they land.  Try these:
         ➤Start at 50.  Add 10.  Add 20.  Subtract 10.  Add 20.  Where should we be? 90.
         ➤Start at 60.  Subtract 20.  Add 30.  Subtract 10.  Subtract 10.  Where should we be?  50

      Next, explore the patterns of adding/subtracting elevens and nines.

 2.    Add/Subtract 11: Once students are confident with tens, help them discover that adding 11 moves directly up and to the right one space.  Subtracting 11 moves directly down and to the left one.  Try these:
       ➤Start at 40.  Add 11. (Students will have to move to 51.)  Add 22.  Add 11.  Subtract 22.  Add 33.  Where should we  be?  95.
       ➤Start at 35.  Add 22.  Subtract 33.  Add 11.  Add 11.  Where should we be?  46.

3.     Add/Subtract 9: Continue with 9s.  Adding  9 moves directly up one line and to the left one space.  Subtracting 9 moves directly down one line and to the right one space.   Try these:
         ➤Start at 25.  Add 9.  Add 18.  Subtract 9.  Add 27. (Students will have to move to 70.)  Subtract 9.  Where should we be?  63
         ➤Start at 46.  Subtract 9.  Subtract 9.  Add 27.  Add 9.  Where should we be?  64

4.     Now, you can challenge students to follow a series of mixed additions or subtractions and see if everyone lands on the correct number.  Try these:
          ➤Start at 45.  Add 10.  Subtract 11.  Add 20.  Add 9.  Subtract 11.  Where should we be?  62
          ➤Start at 12.  Add 30.  Add 11.  Subtract 9.  Add 11.  Where should we be?  56

     You can get this Little Different Hundred Board as a freebie right here.  

 Please download, try it out, and let me know what you think.  I'd love to hear your feedback! 
 
Read More
Growing Grade By Grade
0 Comments
Subscribe to: Posts (Atom)
[name=Pat McFadyen] [img=https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhczE6mtgjdS5V3nWcCULBmAKHizsGN444Azjfc-ELJU4pYOVxAuVvcVGE029uyMOPBP-AUR_CJvQrMIVFpWzqAbwkwZ4EKslxl_weBhSbNsjgReTTdZq0IiCYvyyzXomhRuka_TgZ-Wd_Z/s1600/Pat.jpg] [description=My purpose is to support YOU and your students with practical solutions and curriculum materials that teach, play, practice, and assess.] (facebook=https://www.facebook.com/GrowingIn5thGrade/)

Follow @georgialoustudios