For those of you who have missed my previous posts on visual routines and counting routines, I am doing a series of posts on number sense routines from this fabulous book:
This post is on Playing with Quantities: Making Sense of Numbers and Relationships
The sentence in this section that stood out to me the most was: "The base ten numeration system and the concept of place value are crucial components of students' number sense development. Therefore, it is essential that students understand the number ten and play with grouping of ten." (page 80)
Why do playing with quantities routines?
The purpose of these routines is to encourage students to play with quaitities, decomposing and composing them, as well as think about how the base 10 place-value system works. In some ways, this seems to be the most important (I don't want to devalue the other routines though) category of routine - only because I see time and time again students struggling with place value.
The Ten Wand
This is by far the cutest routine in the book! The ten wand is made up of unifix cubes (2 different colors). Shumway talks about how she introduced it in her school by dressing up as the Queen of Ten on the 10th day of school (and again on the 20th and 30th). The Queen of Ten was very clumsy and her wand would always break. The students were given the job of figuring out how to put the wand back together by finding sums of 10. This routine is great for students getting comfortable with: combinations of 10, part-part-whole relationships, commutative property, and using the 5 and 20 structure.
I was sort of wondering if this could be used at a math work station? I'll be working on that!
Ways to Make a Number
This routine is very much like "Name Collection Boxes" from Everyday Math. What I love though about the way she explained it, is she breaks down how we as teachers should be looking at our students' work. We want to look for the math in what they are doing so we can push them to think about numbers in increasingly more sophisticated ways. Here are some of the big ideas she says to look for:
- Decomposing a number into expanded notation (If the number is 470, a students may write 400+70+0 with lines drawn from each addend to each digit).
- Various groupings of ones, tens, hundreds, and thousands (If the number is 124 - a student could draw: 1 flat, 2 longs, 4 cubes; 12 longs and 4 cubes; 1 flat, 1 long, and 14 cubes)
- Using a pattern (if the number is 50: 49+1, 48+2, 47+3, 46+4...)
- Interesting ways of thinking about numbers using coins, pictures, subtraction, tallies, multiplication, etc.
- Showing a variety of ways to think about a number
This may sound no different than "ways to make a number," but it is! The idea behind this routine is to help students expand their thinking about a given number in relation to different situations and scenarios.
For example, let's say the number is 50. Some questions Shumway suggests that we as teachers pose to are students are:
When is 50 big?
When is 50 small?
When is 50 a lot?
When is 50 very little?
Make 50 using three addends.
Make 50 by subtracting two numbers.
Divide 50 in half.
Divide 50 into four equal parts.
What other ways do you think about 50?
**What is 50's relationship to 10? to 100? (Shumway makes a point to discuss how valuable it is to relate numbers to 10 and 100 as it will facilitate a deeper understanding of magnitude, the number line, and seeing differences.)
What is 50's relationship to the age of your mom? to your age?
**How much is ten groups of 50? (Shumway talks about how talking about groups of numbers is a great way to establish understanding of the base 10 system....ten groups of 22 is 220 and one hundred groups of 22 is 2200...)
To extend this routine, Shumway talks about having students come up with number stories to match equations to match the equations students came up with in response to things like "make 50 using three addends." If a student came up with 20+20+10, a number story could be: I had 20 red beads on my necklace, 20 blue beads on my necklace, and 10 green beads on my necklace. How many beads in all? I also wonder if this extension could be turned into a math work station?? Ideas?
Mental Math Routines
I am so glad Shumway included a section about mental math routines. I am always looking for ways to get my students away from relying on things like the number grid and their trusty fingers :) So, mental math routines aren't anything other than just posing a problem to students (at the carpet - preferably in a circle, but doesn't have to be) and telling them to give a thumbs up when they have found the answer. The most important part of this routine is helping students to verbally and symbolically represent the strategy or strategies they used to find the answer. Process over Answer!!! This is where things like turn and talk, active listening, and think alouds are so important! Shumway gives a great progression of possible mental math problems to use. Side note - she says it's important to give a context to problems (number story) in k-1 and even for much of 2nd grade, but by the end of 2nd and for sure in 3rd - they shouldn't need a context anymore.
- Making Ten (6+4 or 16+4)
- Counting on or Counting back (58-4 or 99+3 or 78-10)
- Decomposing Numbers into Tens and Ones (10+17, 36+20) - this would also be a good time to try a number string (36+10, 36+20, 36+22...)
- Using Ten or Compensation Strategies (9+11...changing the 9 to a 10 by adding 1 and changing the 11 to a 10 by subtracting 1)
Aren't these great routines? I loved this chapter!
That's it for now! Let me know any questions or comments or suggestions!!!