Flipped Hundred Chart

Helping children conceptualize numbers and find meaningful ways to think about their relationships is a goal in our kindergarten classroom. We encourage problem solving and working with number strategies in daily number talks, and are always on the lookout for interesting ways to compliment the rich math learning opportunities we are observing in the children's play.

Recently I became a member of the National Council of Teachers of Math (NCTM https://www.nctm.org/). A highlight of membership is that I have access to the journal Teaching Children Mathematics, which is filled with research-based articles outlining interesting and developmentally appropriate practice for the early years. In the December 2017 (24, 3) issue there is a fascinating article by Jennifer M. Bay-Williams and Graham Fletcher called A Bottom-Up Hundred Chart? In this piece the authors challenge educators to consider the potential for enriching children's learning if the popular math tool is flipped upside down.

 

Click here for a downloadable copy!

Bay-Williams and Fletcher share that a flipped hundred chart makes sense because when children use the chart to solve equations, the language they use to describe direction on the chart matches their understanding of the operation - if adding the number appears to get taller, bigger and greater as physically modeled when children track the addition sentence by moving up on the chart and if subtracting the number appears to shrink, moving downwards and getting smaller by descending the chart (e.g., if a child is solving 13 + 12 s/he would first point to the thirteen, move upward one space and then to the right two). The authors also suggest a number of different activities for exploring the chart including cutting one into a 'number puzzle', encouraging children to find mystery numbers, and assigning children a number and challenging them to find all the number's 'neighbours'. These activities are great ways for children to physically and mentally manipulate the chart, helping them to become more comfortable working with the numbers.

After reflecting upon our math program I have created five additional activities that I believe will continue to challenge children and encourage them to strengthen their understanding and confidence working with the numbers 1 - 100.

Guess my number!

Display a flipped hundred chart and mentally think of a number that the children will have to guess. Give children one clue at a time to help guide them to your number (e.g., my number is less than 50, my number doesn't have a 6 in it, my number is odd). The children can consider the clues and cross out the numbers that don't follow the clues. With additional clues more numbers will be crossed off the chart until children guess the correct one. Reverse roles and invite the children to think of a number and give the clues to you!

Pentomino Trace

Our children love to manipulate pentominoes - using them to fill frames and trays and solving intricate puzzles. Children can also be encouraged to use them as tracers, matching them to the chart and outlining the numbers contained within. Once a collection of numbers has been traced, encourage children to find something that all numbers have in common (e.g., they each have a 4 in them; they are all greater than 36). Tip - ensure your flipped hundred chart is printed to the same size as your pentomino set to ensure an accurate match.

Dry Erase Number Write

Our children love to write with dry erase markers. Create a variety of 'missing number' flipped charts, laminate, and invite the children to practise filling in the missing numbers.

 

Click here for my downloadable copy!

Flipped Hundred Chart Coding

We spend a lot of time coding in our classroom and see potential for incorporating coding directions and spatial reasoning into exploring the flipped hundred chart. Display the chart and determine a starting number. Provide children with a series of verbal or written coding directions as they move from the starting number and reach the end number. Once the final number is determined encourage children to create an statement or equation that describes the relationship between the two numbers.

Start at 3.

Move up 4.

Move right 5.

The number is 48!

 What do you know about 3 and 48? (48 - 3 = 45, 3 + 45 = 48, 3 + 5 + 40 = 48)

Roll, Subtract and Race!

Use an enlarged copy of the flipped hundred chart as a board game. Two (or more players) can use recycled board game pieces and place them on the starting point 100 spot. Each player takes a turn rolling one die and moving their player backwards on the chart (or 2 to make the game more difficult). Students can be encouraged to think in equations (If I start at 100 and roll 5, 100 - 5 places me on the 95 spot). First player to move off the board into the 0 spot wins!

What other ways can children learn with the flipped hundred chart? 

Feel free to share other ideas in the comment section below or tweet #flipped100schart!

Exploring Math in an Inquiry-Based Kindergarten Program

Math has become a great interest for me due to a school wide focus on improving children’s interest in and attitude towards math. I was introduced to the work of Sherry Parrish regarding ‘number talks’ and felt it was a strategy that could easily be implemented into a play-based, inquiry-based FDK program. I have been fascinated by Jo Boaler's work on Mathematical Mindset. After learning about and implementing a focus on number talks and making math meaningful and engaging for children, I noticed huge gains in children’s computation and fluency as well as the time they spent during free play working with math tools and strategies. This was incredibly motivating for me.

Positive Growth Mindset

As a child I disliked math. I felt I wasn’t ‘smart enough’. My reading and current practice with number talks and growth mindset has shown me it’s not about how ‘smart’ you are, but how hard you work and persist with any given activity. Just as important are teachers' mindsets towards math and math learning. We need to truly believe that any child can succeed at math and create a supportive environment where they feel free to take risks and aren't afraid to make mistakes. Low floor high ceiling tasks will provide entry points for all learners and ensure we are able to differentiate to high degrees when needed for those children who are learning at different rates and require a different challenge (see an example here). I want to help children change their mindsets towards math and discover that there are many different ways to analyze, interpret, and solve a math problem. Math can be an enjoyable activity and is hugely relevant to our lives. I also wanted to continue to positively change my own mindset towards math as an educator and parent. To see some of the extensive work we have done on growth mindset please visit other entries tagged with this label.



Our Program

Children’s early learning experiences have a profound effect on their development. Early interactions directly affect the way connections are made within the brain. To give each child the best start possible our kindergarten program provides a variety of learning opportunities and experiences that challenge and engage children while building confidence - providing foundations in cognitive, physical, emotional, and social development. In our kindergarten class, we want each and every child to enjoy coming to school and to see learning as fun, exciting, and meaningful. We explore lots of teacher-guided and child-initiated opportunities that appeal to each child’s learning style. We want to help develop life long learners! Reaching each child’s potential while supporting learning development is the main goal of our kindergarten program.

                 

Gradual Release of Responsibility in a Playful Math Environment

The goal in a playful environment is for children to be comfortable and confident applying mathematical strategies in authentic problem-solving situations. An educator helps children become successful by first introducing the ‘big ideas’ of math in a whole group situation and then providing numerous opportunities for children to practise using the tools, terminology and strategies in authentic contexts during small group time and the open play block. For example, during circle time the educator might introduce a ten frame, demonstrate how to use it for various purposes (e.g., subitizing, counting, recording, adding) and then encourage children to independently use the ten frame in small group activities and play.

Here is a sample math lesson where children are considering what they observe and wonder in a growing shape pattern:

Authentic Math in an Inquiry Model

In emergent programs educators aim to embed rich math resources and opportunities throughout the room and not just in a defined ‘math centre’ in order to encourage organic exploration. The children are investigating and finding solutions to questions or problems generated in the social interactions they have during playtime. Teachers can bring these inquiry-based topics and authentic queries to the whole group for extensive discussion, specifically highlighting math and computation when applicable. Because children are highly invested in solving these problems they will be more likely to work together to brainstorm various strategies for arriving at solutions that meet the needs of many learners.

Finding the balance in emergent practices also means that the teacher carefully selects developmentally appropriate activities that capture children’s interests while still fulfilling curriculum expectations. Interesting materials can be placed in the classroom and the teacher can ask questions or suggest challenges to entice children into exploring these further. An emergent kindergarten program creates natural opportunities for purposeful computation by:

• providing children the freedom to explore self-directed areas of interest 
• introducing interesting and challenging materials for children to use independently and with teacher guidance
• emphasizing a child-centered problem-solving approach when difficulties arise
• using organic materials and loose parts in place of commercial products
• honouring children’s questions and providing guidance when needed

 

Documentation 

Young children show their understanding by doing, showing, and telling. They come school with a wide variety of experiences, interests, strengths, and needs. We will observe, listen, and ask questions in order to assess the achievement of each child. This information will then be used to determine instruction so the diverse needs of each child are met.

Observation is the most important assessment strategy that we use in the classroom. Since students spend much of the day interacting with others in various learning centers, we will spend a lot of our time observing children in action and recording these observations.

In our classroom we will create a portfolio for each child – it will contain pieces of “work” from throughout the year. This includes samples of writing, drawn pictures, photos of the child engaged in the classroom, recorded notes from observations of them in action, recordings of student/teacher conferences, and pieces of artwork. Portfolios can be viewed by parents anytime, and will be shared during parent-teacher conferences at report card time. Portfolios are also sent home on a regular basis and parent feedback is encouraged through the use of a parent observation sheet. See a copy of our reflective prompts page to families here.

Environment as the Third Teacher

We start the beginning of the school year with empty walls. Working together we slowly create documentation displays that reflect our questions and explorations using artifacts of learning (e.g., photos, artwork). Effective documentation “draws others into the experience - evidence or artifacts that describe a situation, tell a story, and help the viewer to understand the purpose of the action” (Seize, p. 88). As the year progresses our walls honour learning by sharing the children’s journey helping them to feel valued, respected, and encouraged to take greater risks in their work with others. This work then inspires the children to reflect upon what they have done to help consolidate learning and use this as a reference or inspiration for future explorations.

Seitz, H. (2008). The power of documentation in the early childhood classroom. Young Children, March: 88 - 93.