Exploring Magnitude While Playing with Number Lines

 

Number lines are a great tool for helping young children develop an understanding of magnitude—the idea that numbers have a size and that numbers can be compared to one another.

Children may be able to count to 20, but that doesn't necessarily mean they understand how the numbers relate to each other. They may know that 8 comes after 7, but do they understand that 8 is close to 10? Or that 15 is farther from 10 than 12 is?

A number line can help make these relationships visible.

Start Simple

 

We can begin with a simple number line:

0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10

 

Rather than just using it to count, we can ask questions such as:

• “Where would 6 go?”
• “Which number is closer to 5 ... 3 or 8?”
• “What number is between 4 and 6?”
• “Where would you put 9? How do you know?”

These questions encourage children to think about the size and location of numbers, rather than just reciting the number sequence.

Estimate!

 

One of my favourite ways to use a number line is to give children a line with only the endpoints marked.

0 ____________________ 10

Ask:

“Where do you think 5 would go?”

Children have to think about where the middle of the line is.

We can then try:

0 ____________________ 20

“Where would 5 go now?”

This helps children see that the position of a number depends on the numbers at the ends of the line.

 

Use a Floor Number Line

 

A floor number line gives children the opportunity to physically experience number.

“Stand on 4. Move forward 3. Where did you land?”

We can ask children to predict where they will land before they move. This connects counting and movement with the idea that numbers have a position and a distance from one another.

Look for the Thinking

The important part isn't whether children place a number perfectly. We want to hear how they decided where it belongs.

“Why did you put it there?”

“What were you thinking about?”

“How do you know?”

Number lines give children a visual way to see that numbers aren't just a list of words we say when we count. Numbers have size, and numbers have relationships with other numbers.

Helping children develop this sense of magnitude is an important part of building strong number sense in kindergarten.

Spider Math

 "Oh look! There's a spider on the school! 

Maybe he's coming to learn too!"

Autumn always brings with it many treasures. Recently my students have been curious about the many creepy crawlies they have been discovering in the yard. Although spiders can be scary for some, they serve a big purpose in our local ecosystem as they eat insects and also are a source of food for others. Exploring them together also helps those who are scared or reluctant learn to see them in a new way. 

I always look for ways to incorporate children's interests into our activities, specifically math. Here five spider math ideas for you to use with your little ones!

1. Which One Doesn't Belong - encourage children to examine and describe these collections of images and articulate which they believe doesn't not belong in the group and their reasoning why.

  

2. See, Think and Wonder - this thinking routine asks children to carefully examine something and clearly describe what they see, articulate their thinking about the object, and express curiosity through wonderings and questions related to the subject. This picture of an intricate web might be an interesting prompt for discussion.

3. Spider Survey - ask children to record their names on a t-chart that indicates whether or not they like spiders. Calculate and interpret the results of the survey with children. Click the image to access the printable.

 

4. Spider Subitizing - use this printable with children to explore different ways of representing a number. Write a number on the spider and ask children to brainstorm and record many different ways of showing the number (e.g., tallies, dots, ten frames, word). Click the image to access the printable.

5. Spider Symmetry - use this printable with children to explore the concept of symmetry. Encourage children to draw the missing half of the spider and web as best as they can. Explore symmetry in photos of real life spiders!Click the image to access the printable.

Cultivating a Mathematically Rich Learning Space

It's almost Labour Day! This time of year always fills me with hope. Although it's sometimes sad to be leaving the fun and comforts of summer - spending time with my children, sleeping in, enjoying the back yard with my pup - it's exciting to think of the possibilities of another school year. Like a blank canvas waiting to be painted our classroom evolves and changes over time as the children and I learn and explore together. 

As we head back into the school year many educators are working thoughtfully to create environments that are rich with math possibility. In Reggio Emilia the environment exists as the 'third teacher' inspiring, supporting, and extending children's learning in rich and complex ways. I have been contacted by many educators asking for advice on how to best set up their classroom and routines in order to create as many opportunities for authentic math as possible. This has inspired today's blog post - how to cultivate a math rich learning space for children at the beginning of another school year.

I thought it would be easiest to create this as a 'math check list' with points to read and consider. When I reflect upon my own math pedagogy and practice, these are what I think stand out as mathematically meaningful for the educators, children and families that share our space. Although this check list isn't all inclusive, I thought it might spark some ideas to support and inspire as we enjoy the final weeks of summer and return soon to our classrooms with open eyes, minds and hearts.

1. Make math a part of every space in the classroom and child's school world. In the classroom are there math tools and materials available for use beyond a 'math center or math shelf'? Do children see how math relates to every subject in the space (e.g., how materials are sorted and stored on the toy shelf, how measurement is used when children decide on a size of paper to use for their project)? Can they translate math tools and ideas into other spaces in their immediate school world (e.g., see how math relates to their walks in the hallway or work in the gym)?

2. Ground and build math concepts into known objects for children. When introducing, extending or innovating a math idea is it organic and natural to the child's explorations and world? For example, it is more natural to engage children in an exploration of measurement if they measure things in their immediate world using the stick they are playing with, instead of using a standardized ruler (e.g., "Can you find something the same length as your stick in the yard?", "What is taller than your body?").

3. Use available math moments with children. In our classroom we have a large block of uninterrupted play each day. It's sometimes challenging to manage children, materials and activities during center time. However I try to engage with children as much as possible in the activities, and take on the role of 'play partner' together with them. When I am actively playing I am able to closely observe what they are saying and doing, helping me to identify and extend the rich math learning that is organically occurring (e.g., helping children to recognize why their tower keeps falling, using math terms when they equally share the play dough, introducing math ideas as they discuss how many cars are in their parking lot).

4. Become a math role-model for children, families, and colleagues. Even if math isn't your favourite subject, how do you discuss it within your school and classroom? Are you excited by new activities and resources? Do you demonstrate a growth mindset? When mathematical situations arise with children that you aren't sure of, can you use these opportunities to showcase positive thinking and problem-solving? Share your new math learning with others - suggest articles and books you're reading and post these throughout your classroom to enhance documentation displays. 

5. Find the math in everything. Many educators plan forward by choosing curriculum and programming expectations and then building activities to fulfill these. Try back-mapping activities from time to time; embrace child-centered, organic experiences and then deconstruct them in order to identify the rich math concepts and curriculum expectations that they utilize. You'll be surprised to find that math happens in almost every experience children have in the classroom.

6. Try looking at life through a mathematical lens. When planning invitations for learning in your classroom see what math you can sneak in as well. Changing one or two elements of the experience might be enough to engage children in rich math. It reminds me of how I used to sneak veggies into my children's meals - a little can go a long way!

7. Collaborate mathematically with colleagues. Share new ideas and resources informally. It's easy and effective to create math invitations and activities and share these within your school or division. If every educator plans one or two activities and these are shared, children will benefit from many rich and interesting games and activities without the burden of planning and preparation it would take one educator to accomplish the same.

8. Record and celebrate your math moments. Help children, families, and colleagues recognize that math happens everywhere in the classroom by creating a documentation display with photos, anecdotal observations and connections to curriculum. This bulletin board can be built over the course of the school year as artifacts of learning are continually added by staff and students. Keep sticky notes nearby and invite observers to record their own ideas and share them by posting the notes within the documentation.

9. Engage families in joyful math with children outside of school. Consider ways that you can promote and extend math for children after school. Encouraging families to play math games and activities together with their children will not only provide children with additional meaningful math moments, but it may help older family members reconcile their fear or dislike of math.

10. Build your collection of math stories, songs and games. Children love to sing, dance and play games. Ask colleagues to share their favourite games and activities, and use these to help with transitions and other 'math moments' throughout the day. Quite often the words in songs can easily be improvised to match something happening in your classroom, and many rich storybooks have mathematical elements and problems embedded within them that can inspire children.

These are just a few of the ways in which I cultivate a rich math space with children. I'd love to hear from you! Share your math ideas in the comments below, and consider following my Instagram @McLennan1977 for regular ideas from my classroom!

Easy St. Patrick's Day Math Ideas

St. Patrick's Day is a fun holiday that helps jump start the spring season! Here are a few easy to plan math activities for children!

1. Shamrock Subitizing- Write different numerals in the center of each shamrock and encourage children to place dominoes with the corresponding number of pips in each leaf.

 

2. Estimation/Counting Jars - Fill jars with a variety of different seasonal loose parts. Encourage children to estimate how many objects are in each jar. They can then use a variety of math tools (e.g., number grid, ten frame, hundreds chart) to count the total objects. These can then be recorded on a paper for comparison.

3. Rainbow Numbers - Provide children with a variety of numbers and encourage them to explore these in different ways (e.g., sorting by colour, ordering, create number combinations).

4. Colour and Coin Sorting - Recycled marker caps can become 'pieces' of the rainbow. Add fun play coins and seasonal pots to the tray and encourage children to sort, count, and pattern with the loose parts.

5. Roll and Record - Here is a fun template that can be used by children to support many math explorations! Children can roll and subitize a die and colour in the corresponding number of shamrocks. Two children can each roll and colour in shamrocks using their own colour and try to get 4 in a row. Children can colour the shamrocks in using different colours to create patterns. The possibilities for this template are endless!

Get the free printable here: Shamrock Printable

 

6. Which One Doesn't Belong? -  Show children pictures of different shamrocks and ask them to articulate which picture does not belong. 

Get the free printable here: WODB Shamrocks

7. Gold Coin Count - Add dice, coins, number lines and writing materials to this game board and encourage children to create and play their own treasure games!

Get the free printable here: Gold Coin Count

8. Find the Gold Coding - Draw the path needed to get from home to the pot of gold! Use arrows to display direction of movement.

Get the free printable here: Gold Coding Mat 

 

 

 

Ten Easy Holiday Math Activities

The holidays are such a lovely time of year to spend with children! However the last few weeks before the winter break can be hectic. Here are ten easy to assemble activities that can infuse playtime with math by capturing the magic of the season! Many of the seasonal loose parts included in these photos were found at the local dollar store. Enjoy!

1. Count the Presents - offer children mini presents (or other seasonal trinkets including bells or ornaments) and number cards. Encourage children to match the corresponding number of objects to the cards. Children can also place presents on a laminated ten frame and write a corresponding addition or subtraction sentence using a dry erase marker.

2.  Holiday Sensory Bin with Mini Boxes - fill a sensory bin with seasonal trinkets and treasures. Add mini present boxes and encourage children to fill the boxes with different objects. Children can then use a hundreds grid to count how many objects fit in each box!

 

  

3. Catapult the Gingerbread Man to Safety - help mini Gingerbread Men land to safety over the river by firing them using catapults made from clothespins attached to blocks using elastics. This activity works fine motor muscles too!

4. Cookie Cutter Bell Count - display a collection of bells in a tray with a variety of seasonal cookie cutters. Challenge children to fill one cutter with bells and use a hundreds grid to count how many it holds. Which cutter holds the most? Least?

5. What's Inside the Presents? - fill different holiday boxes with loose parts. Encourage children to shake one at a time and estimate how many objects might be inside. They can then open the box and spill the objects out. Each object can be placed on a number grid and counted.

6. Fill a Tree with Trinkets - children can explore the concepts of area and perimeter by filling or outlining wooden trees (or other seasonal place mats or shapes) with a variety of bead strings, ribbons or small objects.

7. String a Pattern - secure a number of green pipe cleaners to a sturdy cardstock or cardboard base in the form of a tree. Encourage children to string beads to 'decorate' the tree using different patterns. Children can also count how many beads they use for each section.

 

8. How Many Elastics? - children can wrap a number of elastics around cookie cutters until they are filled. Encourage children to count how many times they wrap each elastic. For an added fine motor challenge have children remove the elastics one at a time.

9. Gingerbread House STEM Challenge - provide children with magnet shapes and challenge them to build an intricate gingerbread house. Ask them to search the room for various loose parts that will attach to the magnets and 'decorate' the house (e.g., here the staples in mini bows attract to the magnets).

10. Holiday Guessing Jars - fill glass jars with seasonal loose parts. Encourage children to estimate how many objects are in each jar. The objects can then be shaken out and counted using math tools such as number grids and ten frames.

 

 

Looking for a book to support holiday math learning? Check out my book Holiday Math! 

 

 

Virtual Bird Count

“There is an unreasonable joy to be had from the observation of small birds going about their bright, oblivious business.”
 Grant Hutchison

 

Colder weather and light snow this week have inspired new observations during outdoor play and exploration. The children have noticed birds hiding in the trees. It's been fun to watch them flit from branch to branch, observe their tracks in the snow and identify their different calls. I hoped to continue with these observations indoors. I introduced Cornell's live bird cam and invited children to spend time observing the animals that visited the different feeders. The children were enthralled with the quick, happy little birds as they flew in and out of the frame and gobbled up the seed.

The next day I asked children to predict which birds they thought might be at the feeders. We spent time drawing our guesses on a graphic organizer. I wanted to capitalize on the children's interest in the birds and integrate math and literacy into the experience. I also displayed posters from our library that had illustrations of common North American birds to be used as reference.

As the children observed the feeders they tracked what they saw on their charts. After ten minutes of watching we calculated and shared our results. Blue jays appeared the most!

This is an easy to implement activity that brings the outdoors inside! Click here for a free printable Bird Count tracking sheet children can use to record birds.