Math Routines: Ten Frames

Using Routines with Math Tools: Ten Frames

Routines in the math classroom are important for a variety of reasons. While some routines are just necessary for the organization and structure of the classroom (and teacher's sanity), other routines can build students' mathematical understanding and reasoning. In this series of blog posts on Using Routines with Math Tools, I will discuss various routines that can enhance the teaching and learning in the classroom. I will reference various articles and books that can support us in implementing these routines in our classrooms. However, many math routines are very simple in nature and can be implemented with very a little prep and resources.

What makes something a routine? In the book High-Yield Routines: Grades K-8, McCoy, Barnett & Combs describe a high-yield routine with the following characteristics:

• a structured activity that helps students gain proficiency with a range of concepts and practices
• offer access to the big ideas of mathematics and allow deep understanding of concepts
• give students opportunities to develop expertise with the eight Standards for Mathematical Practice
• offer opportunities for students to demonstrate their thinking and for teachers to gain insight into the thinking of their students

In my work with Kindergarten and 1st grade teachers, we are looking at a variety of methods, strategies, and tools that support students' learning around their sense of numbers, combinations of numbers, and how numbers relate to each other. So, let's engage in some mathematics by looking at routines with Ten-Frames!

Let's explore some routines with Ten Frames.

What is a Ten Frame?

A Ten-Frame is a 2 by 5 array. Most often you see it this way:

A ten-frame can be used to support the development of land-mark numbers of 5 and 10. Using a double ten-frame can be useful as students are working towards the number 20. Ten-frames can be used as a model and support counting and subitizing. And can be great tools to support students' strategies for addition, and subtraction. The routines I am going to share are not ones I have created and are probably being used in many classrooms. I enjoy the work of Marilyn Burns and find that it resonates with my understanding of teaching and learning. I use the book, It Makes Sense! Using Ten-Frames to Build Number Sense (K-2) as one resource to support my work with Kindergarten and 1st grade teachers. Some of the routines can be found in this book.

Ten Frame Routine: Look, Quick!

Overview:
In this routine, the teacher will show some counters on a ten-frame and students will look for groupings without counting. This routine builds students ability to subitize - to know a number just by looking at it.

Materials:
Ten-Frame, counters

Directions:
*Begin with modeling in the Introduction, Example 1, and Example 2 so that you set the stage for the routine. Students should become familiar with the ten-frame, counters, and the questions you are going to ask before beginning the routine. 

Introduction

• Show students the blank ten-frame. Ask:"How many squares are there?" Rotate the ten-frame and ask again. 

Model: Example 1

• To begin, tell students that you are going to place some counters on the ten-frame and they will need to determine the total amount of counters. You will need to place the counters on the ten-frame without students seeing - either students close their eyes or cover up your work until you are ready to show students the ten-frame with counters. 
• Example 1 - model the routine
• Place 5 counters on the ten-frame, possibly like this: 

• Reveal the Ten-Frame to students. Ask: "How many counters do you see?" 
• Ask students to whisper the number of counters. Then ask "How do you know?"
• Ask students if there is another way to see how the counters are grouped. Ask "How do you see the counters?"

Model: Example 2   (repeat the routine)

• Place 4 counters on the ten-frame - keeping it a secret from the students. 
• Reveal the Ten-Frame to students. Ask: "How many counters do you see?" Encourage students to look for groupings of counters. 
• Have students whisper the total amount on the count of 3. 
• Ask a student to share how he or she knew how many counters were on the ten-frame. 
• Record students explanations as a number sentence. 
• For example, 4 = 2 + 2 or 4 = 1 + 1 + 1 + 1. 

Now that students are comfortable with looking at the ten-frame and counters, introduce the routine, Look Quick! 

Ten-Frame Routine - Look Quick! 

1. Teacher places an amount of counters on the ten-frame (hidden from students). As you repeat the activity, vary the groupings of the counters. 
2. Give student 3 seconds to recognize the amount of counters. Cover/Hide the ten-frame and counters. 
3. Ask: "How many counters do you see?" Then have students whisper, on the count of three, the total number of counters. 
4. Ask students: "How do you know how many counters are on the ten-frame?" or "How did you see the counters?" 
5. As students share their idea, record the number sentence. For example, 4 = 2 + 2 (you can vary the equal sign at the beginning and end so that students don't development a misconception that the equal sign means the answer is coming.)  

I saw this routine done in a vary similar way on the Teaching Channel.
The Teaching Channel is a great place to go to see classroom lessons that support the learning of Common Core.

Check out the video in a Kindergarten classroom:  Quick Images: Visualizing Number Combinations

Ten Frame Routine: Make the Number

Overview:
In this routine, the teacher will quickly show some counters on a ten-frame and students will build what they saw with counters on their own ten-frame. This routine builds on students' ability to subitize and combines it with spatial reasoning.

Materials:
Ten-Frame, counters

Directions:
1. Give students a ten-frame and counters. Ask students to keep their counters off thei ten-frame mat until the routine begins.

2. Model: Example #1 Place 3 counters on the ten-frame. Leaving it in sight, have students build exactly what they see. Ask students to whisper how many counters they used. Then, have students turn and talk to their partner about what they built.

3. Have students clear their Ten-Frames.

4. Ten-Frame Routine: Make the Number! This time the students will only see the Ten_fRame & counters for 3 seconds. Place 3 counters in a different location on the Ten-Frame. Show students the Ten-Frame for 3 seconds, then hide the frame and counters. Ask students to use their counters and Ten-Frames to build what they remember seeing.

5. Lead the class in a discussion by asking questions:

• How many counters did you see?
• What did you build first?
• How did you know where to place the counters?

Students should have an opportunity to talk to a partner before discussing as a class.

6. Show the original Ten-Frame that you built to give students time to check their answer.

Resources & Digging Deeper

Hand Signals

Hand Signals can be very helpful with routines like the ones discussed above. Number Talks use hand signals as a silent gesture to show a students' response to the talk. Here is a poster that shows the hand signal and the meaning of the signal. 

Additional Resources for Routines with Ten-Frames:

• Article on Subitizing
• Illuminations: Ten-Frames 
• K-5 Math Teaching Resources - "Ten Frames and Dot Cards"
• North Carolina Lessons for Learning - Grade K   Grade 1

References: 

Conklin, Melissa. It Makes Sense!: Using Ten-frames to Build Number Sense. Sausalito, CA: Math Solutions, 2010. Print.

McCoy, Ann C., Joann Barnett, and Emily Combs. High-yield Routines for Grades K-8. N.p.: n.p., n.d. Print.

Shumway, Jessics F. Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3. Portland, Me.: Stenhouse, 2011. Print.

The Standards for Mathematical Practice (K-1): Part 2

Recently I have did professional development for teachers in our district that included a segment on the SMPs. The purpose for discussing the SMPs was for teachers to have conversations with grade-alike colleagues around the Mathematical Practice and think about the connections and application to their specific grade level  content standards. Teachers were divided into 8 groups, one group per mathematical practice, and asked to read and discuss the Mathematical Practice. Then, create a poster that describes and shows the SMP connected to content standards at the various grades levels represented (teachers were encouraged to use words, pictures, illustrations, etc). This would allow a snapshot of a possible continuum of how that mathematical practice grows and develops from grade level to grade level. After groups finished their posters, we did a gallery walk and pairs of teachers walked around to look at, discuss, and ask questions around the other SMPs,

Standards for Mathematical Practice: Kindergarten and 1st Grade

The Kindergarten and 1st grade teachers were able to discuss the SMPs and did a great job illustrating the Mathematical Practices. Here are their posters and some descriptors of what each SMP could look like at this level. 

SMP #1 Make sense of problems and persevere in solving them.

Grade K & 1: SMP#1

• make predictions about what the answer and determine a possible strategy that might help them solve the problem.

• choose a method or strategy to solve to a problem. 

• explain mathematical problems in their own words. 

• explain how their picture, model, or equation represents the problem. 

• draw on classroom experience with variety of concrete objects, models, and pictures so that he or she can adjust his or her strategy, as needed, when solving a problem.

• check their answer using a different method or strategy and ask themselves, "Does this make sense?" 

• listen to classmates to understand the approaches of others. 

SMP#2 Reason abstractly and quantitatively.

Grade K & 1: SMP#2

• make sense of quantities by repetitive experiences with a variety of objects, models, and situations. 

• decontextualize a given situation by representing it symbolically, including acting out a situation, modeling it, drawing a picture, using manipulatives, or other representations. 

• contextualize by referencing the real-world mathematical situation to support, plan, and adjust the strategy and solution.  

• think quantitatively by making meaning of numbers, referencing units, and flexibly using different models and representations. 

SMP#3 Construct viable arguments and critique the reasoning of others.

Grade K & 1: SMP#3

• understand and use previous learning when discussing mathematics. 

• explain his or her thinking, and justify his or her answer. 

• communicated explanations and justifications to others. 

• respond to the arguments of others.

• construct arguments using concrete models such as objects, drawings, diagrams, and actions.

• make hypothesis and conjectures that build on a logical progression of statements from prior learning and experiences while connected it to current learning.  

• analyze situations and can recognize and use counterexamples that demonstrate when a mathematical idea is incorrect or a general statement cannot be made.  

• reason about data through making plausible arguments that take into account the context from which the data arose. 

• compare two ideas or arguments and determine when the thinking is correct or when the  reasoning is flawed. 

• explain the flaw in the mathematically thinking or procedure. 

• listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

SMP#4 Model with mathematics.

Grade K & 1: SMP#4

• apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. 

• write simple addition or subtraction equations to describe a situation.

• identify important information required to solve the mathematical real-world problem and use tools as diagrams, tables, graphs, number lines and formulas. 

• interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

SMP#5 Use appropriate tools strategically.

Grade K & 1: SMP#5

• consider the available tools when solving a mathematical problem. These tools might include pencil and paper, base-ten blocks, linker cubes, other objects, ten-frames, counters, a hundreds charts, a number line, a ruler, etc. 

• decide when best to use a tool,  when a tool might be helpful, and recognize when a tool might not be helpful. 

SMP#6 Attend to precision.

• communicate precisely to others by using academic and mathematic vocabulary.

• explain their thinking, their mathematical expressions/sentence and their answers to classmates.

• specify units when measuring and refer to the corresponding quantities in a problem. 

• accurately and efficiently calculate addition and subtraction problems. 

SMP#7 Look for and make use of structure.

• look closely to discern patterns or structures. 

• notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. 

• look at the patterns of making ten, the basic structure of our base-ten system.  

SMP#8 Look for and express regularity in repeated reasoning.

• make connections between various counting experiences to develop a sense of numbers and their sequence, including noticing patterns within a counting sequence.

• recognize what happens to numbers when you add or subtract ten to a number, and developing an understanding of what happens when you add or subtract groups of ten to a number.

• look for and notice patterns when combining numbers.  

• evaluate the reasonableness of their results when solving problems.

Of course, these examples are not an exhaustive list of what each SMP could look like at the Kindergarten and 1st grade levels. 

Standards of Mathematical Practice Resources:

SMP Examples for Elementary Math
SMP Posters for Elementary
Standards for Mathematical Practices Progression through Grade Levels (K-12)