Head, Shoulders, Knees and Toes

posted by Debbie Lee

So far I have written about patterns that involved objects you can pick up and manipulate. Those are usually what we think of first when we think of patterns. Patterns, however, are so much more than that!

The old children’s song “Head, Shoulders, Knees, and Toes” is a pattern. You and the children can make up patterns using various forms of movement. Hop, twist, hands on shoulders; hop, twist, hands on shoulders is an ABC pattern of movements. If you want to keep the children seated on the floor or chairs, you can use less grand movements. Touch ears, pound on chest, flap arms is also an ABC pattern. The various movements are limited only by the various body parts that can be used and your and the children’s imaginations of what can be done with them.

 

HEAD PHOTO                                SHOULDER PHOTO

 

KNEES PHOTO

 

 

 

TOES PHOTO

Remember with all forms of patterns it is best to start with the simpler forms. Do ABAB patterns first; then progress to ABB, AAB, and ABC. If your children are starting to catch on, think about longer patterns such as ABBC or ABCD.

It helps when you are doing the patterns to describe them aloud and not just do the movement itself. This helps those who learn best through what they hear. You are reaching those who are more auditory learners and with this form of pattern you are also engaging young children who are kinesthetic learners and find it difficult to sit quietly.

Patterns do not always have to be a special time set aside just for math skills. If the children in your care are having troubles sitting still to listen to a book or do another sedimentary activity, take a quick break to do a movement pattern. Stand up, jump, clap, twist, jump, clap, twist for a minute or two and the children will find it easier to sit and you will have provided a quick “lesson” on patterns.

As with the other forms of patterns, don’t forget to have the children first copy your pattern. Once confident, have them extend the pattern. Do tap head, touch chin, hug self, tap head, touch chin…..what comes next? What comes after that? Have the children extend the pattern through at least two repeats so that they can show that they are truly understanding what the pattern is.

 

CHIN PHOTO                                        HUG PHOTO

 

 

 

 

Lastly, don’t forget to have the children create their own patterns. Have a child suggest a pattern, name it first by its movements and then by its type (ABAB, etc.). Then have the other children (and you!) copy it. Give each child a chance to create a pattern of movements to share with the others. You can also use this as an educational “filler” – for lack of a better word. When you have a few minutes to fill, have the children take turns creating patterns that the others can do. This makes these short periods of time between activities more than just ways to bridge activities but also gives these moments educational value.

As in past weeks, I encourage you to share in the comments section how you have been using movements to make patterns with the children you serve. Everyone has great ideas – share them!

The Attributes of Patterns

posted by Debbie Lee

Last week I wrote about patterns and using everyday household items to make them. Did you think of some items around your house you could use? I also wrote about simple ABAB patterns in a row formed by having two different elements (fork/spoon or red/green) that alternate. There are other ways to make patterns with everyday items though!

Elements of patterns are distinguished by an attribute. That can be WHAT an item is such as a spoon or a fork. It can also be by color, such as red or green. Those are easy visual ways to distinguish one element of a pattern from another. Don’t stop there! Again, start to think “outside the box.” Think positions!

You can use all of one type of item and make it into two elements just by altering the position. A soup can that is sitting upright, and then one sitting upside down, and then again one upright, and one upside (and so on) is also an ABAB pattern. What about a row of knives, one straight up-and-down and one diagonal, one straight up-and-down, one diagonal? That’s an ABAB pattern too. You can even have one knife straight up-and-down and two knives “crossed”, one knife up-and-down, two knives “crossed.” The possibilities are endless!

 

SOUP CAN PHOTO

KNIFE PHOTO

 

 

 

 

 

CROSSED KNIVES PHOTO

Don’t stop there! A row of cups sitting upside down with a small pebble sitting on top of every other one – that’s another ABAB pattern.   In other words, two items can be combined to make one of the elements and the second element can be just one of those items by itself.

 

CUP PEBBLE PHOTO

 

Once you start to think of positional patterns, the sky is the limit! Almost anything you can use to make a “regular” type of pattern can also be used in a pattern that includes positioning.

Now that you know lots of ways to make patterns – ABAB, AAB, ABB, ABC, etc. – where do you go? Besides the different types of patterns we’ve talked about, there are different pattern skills. The easiest is copying a pattern. To do this, a child is shown a pattern and copies it, laying the same items under the presented items.

 

PATTERN COPYING PHOTO

Once confident doing that, a child can move onto extending patterns. In this scenario, a child is presented a pattern and is asked what comes next, then places that item in the row, then is asked what comes next, etc. until at least two repeats of the pattern are completed.

PATTERN EXTENDING PHOTOThe last skill comes after much practice with patterns in their various forms. For this skill, a child is asked to create from scratch a pattern following one of the pattern types.

 

PATTERN CREATION PHOTO

Once the children you work with begin to become confident with patterns, continue to challenge them with new and different types. Then let them create patterns that you or other children in the group have to try to extend. As they use their imagination to create new patterns, their understanding of the concept of patterning grows and grows!

Let us know what you have done with patterns this week by sharing in the comments section.

 

Patterns – An Introduction

posted by Debbie Lee

From birth, the human brain is wired to recognize patterns. It is how infants are able to figure out the world around them. Because of this, young children can recognize patterns from an early age. We get excited when a child says “foots” even though, in English, that is incorrect. It tells us that the child has internalized the pattern concept that plurals have an “s” on the end. What they cannot do automatically is match the vocabulary of patterns to the concepts. Just the word pattern is something that must be shared by a more advanced peer or an adult. Children are not born knowing the words particular to their language (English, Cantonese, Urdu, etc.) The labeling of patterns as ABAB, ABB, AAB, ABC, etc. also need to help of a more advanced helper.

That is where the adults in a child’s life (and, yes, the more advanced peers also) can help a young child to identify, extend, and create patterns. There are all types of patterns in this world and it is important that children be helped to recognize them in all their different forms. This is so important because, besides being an important math concept, patterns are also a science concept. Scientists make discoveries when they notice patterns in what they are studying.

Probably the easiest and simplest way to start with patterns is to use real objects. Pattern blocks are great for this (see photo below) but they are not present in most homes so that means looking for something else. Here the possibilities are endless!! Look into the kitchen drawers. Use forks and spoons to make a pattern. Coins – pennies, nickels, dimes, and quarters – can also be used. Have a piece of paper and some crayons? Cut or tear the paper into strips. Color each strip a different color. Then cut the strips into squares. Use the various colored squares to make patterns. Have books and DVD cases? Those can be used to make patterns. It is not necessary to spend a lot of money to make patterns. It just requires a little “thinking outside the box.” If you have ideas for everyday household items to use, share them in the comments section.

 

FORK SPOON PHOTO

COIN PHOTO

PAPER SQUARE PHOTO

 

What are some of the different types of patterns? The simplest patterns are ABAB patterns. This would be fork, spoon, fork, spoon, etc. It could also be red, green, red, green, etc. An ABAB pattern has two elements that are placed alternately in a row. Because at all times we should be modeling important literacy skills, teach patterns that appear in a row as going from left to right, as the English language is written and read in that direction. You can progress to ABB or AAB or even ABC (three elements) as the child with whom you are working becomes comfortable with ABAB patterns.

I am challenging you this week to find various items in your house that can be used for making patterns. Then share your findings with the rest of this math learning community by telling us what you found in the comment section. I’m excited to read what

Researcher for a day: What kinds of animals live in the Amazon?

posted by Lindsay Maldonado

By day, I’m a researcher at Shedd Aquarium. I study people though, not animals – but, at Shedd, there are also a lot of people who do study animals. Some of these people are conservation research scientists or aquarists, who use math, and science, to help them learn more about the animals in their care, or animals in the wild. No matter who, or what, your subjects are, collecting data helps researchers collect information (i.e., data) that can provide answers to important research questions. For example, I might want to know how many visitors learned something about how they can help animals after their visit; or a conservation researcher might want to know how many seahorses live in a certain area of the world. So, to get us started, let’s pretend we are research scientists. We have our clipboard loaded up with our data collection sheet, some pencils, and our observation eyes. Now we’re ready to start collecting data!

penguin survey

Data analysis is one of the big ideas of early mathematics and can serve as a foundation for introducing other big ideas like sets, number sense, and counting — and, what better place to apply these ideas than at the aquarium with real living animals.

We have some important research questions to answer, so let’s get back into scientist mode. Today we want to know how many different animals live in the River Channel – and, we’re going to answer this question by observing animals (i.e., gathering data) and documenting what we see (i.e., organizing and describing data). These are all important steps to data analysis! If we want to know what animals live in the River Channel, we first need to make some observations. What do you see? A variety of animals live in the River Channel. How many animals do you see? Can you count them? I see 8 animals.

how many animals

Like the Amazon River, this habitat shows the diversity of animals that live in the river. What kind of animals do you see? I see turtles, stingrays, and fish.

kinds of animalsWe can sort the animals in the River Channel in a number of ways. First, we can sort by the attribute: type of animal. There are fish, turtles, and stingrays. Let’s put these animals on our graph. Representing data, in this way, is an important part of data analysis and allows us to interpret the data we collected.

blank graph

Let’s revisit our research question. We want to know how many types of animals live in the Amazon River. Through observation, we saw that fish, turtles, and stingrays live in the Amazon River so there are three types of animals in the River Channel. But how many of each live there? Let’s use our graph to help us organize our data. How many fish do you see? How many turtles? How many stingrays?

animals on graph

In what other ways can you sort these animals? You can use any number of attributes to sort the animals in this picture. We used the attribute of type (turtles, stingrays, and fish) but you could also sort these animals by size or shape. Observing animals at an aquarium is full of math possibilities. You can use data collection and data representation as the foundation for exploring the big ideas of early math. Keep exploring data analysis in the classroom. Try more data activities here.

Let’s sort this out!

posted by Dr. Bilge Cerezci

sorting rocksAt all ages, children classify intuitively to make sense of their world that seems largely out of their control. By 2 weeks of age, infants distinguish between objects they suck and those they do not. By 2 years, toddlers form sets with objects that are similar. In preschool, children begin to sort objects according to a given attribute and form categories. Many parents have likely walked into a room to see their four-year old putting their blocks or other toys in piles based on color or type. So why sorting is important you may ask. By sorting the objects around them, children start using their analytical thinking skills that is the lifeblood of mathematics. Studies have even been shown that by comparing objects to one another and understanding the relationship between set of objects, children engage in transitive thinking: A blue block is bigger than a red block and smaller than a yellow block. So, blue blocks need to go into a medium-sized block pile. Practicing sorting skills also provide children with models for organizing things in the real world, such as putting toys into the right toys boxes or putting the socks in a sock drawer and underwear in the underwear drawer.

Sorting Ideas

Helping children recognize math in the real world and finding everyday math activities at home is a great way for parents to reinforce young children’s sorting skills. Here are some of the sorting ideas you can implement in our home:

* Collect real-life objects such as rocks, marker caps, marbles, and buttons. Ask your children to guess which objects will together and which items will not. Ask the children to sort them according to different attributes such as; color, texture, type and etc.

* When it’s clean up time, ask your child to sort toys by attributes. For example, ask your child “Can you pick up all the toys that are the same color as this?”

* Encourage your children to name groups of things or activities. For example, at the dinner table, talk about attributes. You might say “2 people at this table wear glasses, 4 don’t.” or “3 have curly hair, 3 have straight.”

While you are doing these activities, use words such as “same,” “different,” “math,” “group,” “collection” and “set” as they apply and encourage your child them to use when they are describing their groups and comparing the groups they have created to one another. You may also ask your children questions such as, “Can you figure out what goes together?” “Can you sort these a different way?” “Why do these go together?” “Why do these not go together?” These kinds of open-ended questions will allow you to better understand your child thinking and push your child to be more precise in explaining their mathematical thinking processes.

Different children, different decisions

Children at different development stages are equipped with different mathematical abilities. A younger child will likely require less categories (sorting by two attributes) while an older child often can handle three, four or more. What you use for sorting also depends upon the age and ability of the child, as well as their interests. Some materials may be more challenging to sort for younger children (e.g., visually ambiguous materials) while others too simple and even boring for an older child (e.g., colored unifix cubes). Using real-life objects and situations to provide sorting experiences is always beneficial for all-around learning for all age groups. The bottom line is to know your child’s abilities, interests and to meet them where they are at, so you can just give them the right amount of challenge without underwhelming or overwhelming them.

Focus on Attributes!

posted by Dr. Bilge Cerezci

As she sits on the floor, a three-year old starts stacking blocks with various shapes and sizes. After some experimentation, she realizes that it is hard to build a tower if a block lays on its curvy side.

 

What does this 3-year-old discover about shapes?

From an early age, young children notice different shapes have different characteristics, even if they don’t know their names yet. They realize that some shapes have points while others have none. They also discover some shapes have flat sides while others don’t. Traditionally, we teach children the names of basic two-dimensional shapes: circle, square, triangle and rectangle and assume that being able to name these shapes indicates a higher level of geometrical understanding. Unfortunately, this can be any further from the truth. In reality, young children need your help to focus on attributes of shapes rather than overall appearance. For example, as you build a block tower together, encourage your child to pay attention to defining attributes of the each shape you are using. You might say, “I see you are stacking up the blocks that have flat sides. Look, all of its sides are flat. How is this one (i.e., cube) different that this one (i.e, half circle block)?” As you continue with the activity, encourage your child to use her fingers to trace and feel the shape. Give them a plenty of time to feel the shapes, count the sides and even ask them to find an item in your home to that resembles that shape.

As children manipulate various three-dimensional shapes, they will eventually build deeper understanding geometrical shapes such as flat faces of solid (three-dimensional) shapes are two-dimensional shapes.

There are many ways to encourage and help your child to learn about shapes. Here are some of the games you might play with your children at home:

* Drawing shapes in sand or foamshapes in shaving cream

* Walking around shapes drawn or taped on ground

shapes on the floor

* Making shapes with bodiesbodies making shapes

Shapes are all around us and it is easy to play games like these at home, outside and elsewhere. Most importantly, make sure to have fun while doing it.

Number Sense: Make it Real!

numbers opaqueposted by Dr. Bilge Cerezci

Young children are motivated to explore mathematical concepts they encounter in their everyday interactions with the world. Through these interactions, they develop a range of informal understanding of numbers including ideas of more or less and one-to-one correspondence. For example, a child as young as two knows if she gets more or less crackers than her friend next to her. She also exhibits her basic understanding of one-to-one correspondence when she insists on getting a cookie because her brother had one and she had none. Such intuitive understandings of number sense may help lay the groundwork for later understandings of numerical equivalence and operations, such as addition and subtraction. While serving as important building blocks, such understanding does not necessarily help young children explicitly examine and interpret their experiences in mathematical forms. So, how do we help young children make connections from these informal knowledge around numbers to a deeper, more concrete understanding of numbers?

Helping children recognize math in the real world and finding everyday math activities at home is a great way for parents to reinforce young children’s developing number sense. For example, when you are setting your table for breakfast, ask your child to join you. You can ask them how many plates do you need to set the table or whether you have enough eggs for everyone or not. While they are taking the plates from the cabinet, encourage them to count. When young children practice counting, they’re also learning one-to-one correspondence. A child that understands one-to-one correspondence knows that 4 plates equals 4 or that 5 eggs equals 5. To help them practice this concept, give your children large groups of objects to count. For example, you are making a strawberry cake for dessert and you only need 10 strawberries. You may ask your child to help you figure out whether you have enough strawberries or not. As they are practicing this skill, children may count some of the strawberries twice and/or skip counting some of them. Therefore, it is important to closely observe your child as she is counting. When she is double-counting some of the strawberries, does she realize what she has done? Does she self-correct? In such instances, resist the temptation of correcting them. Instead, ask her to double-check her answer and give them enough time to check their work and self-correct their mistakes. If she is struggling, provide them with some strategies she can use(e.g., moving strawberries to a different pile as she counts).

Taking this kind of approach not only allows children to see math as fun, but also helps them see numbers as useful tools that they can use to make sense of the world around them. While doing these kinds of activities, the most important thing you can do is to help your child see math is something that makes sense and it is practical and enjoyable. This will help your youngsters to build a strong understanding of math and develop a love of learning math that will last a lifetime.

square blocks

The Early Math Experience Matters

posted by Dr. Bilge Cerezci

Traditionally, mathematics education has not been considered developmentally appropriate for young children (Battista, 1999). Math is abstract while young children are deemed to be concrete thinkers, and some cognitive developmental work done in the mid-twentieth century has been used to suggest that young children’s mathematical ideas develop on their own timetable, independent of environmental factors like teaching (Piaget, 1969). Over the past two decades, however, a growing body of literature has indicated that many mathematical competencies, such as sensitivity to set, size, pattern, and quantity are present very early in life (National Research Council [NRC], 2009). magnetic numbers plus symbolsYoung children have more mathematical knowledge, such as an understanding of number and spatial sense, than was previously believed. For example, research suggests that young children have a basic understanding of one-to-one correspondence even before they can count verbally (e.g., pointing to items in a collection and labeling each with a number) (Mix, 2001). Further, young children also enjoy exploring spatial positions and attributes of geometric shapes by building towers with blocks and cubes and by manipulating various materials, such as puzzles and two- and three-dimensional shapes (Clements, 1999; Clements & Sarama, 2008). They also demonstrate emerging awareness of measurement, when they begin to notice and verbalize similarities and differences in the size, height, weight and length of various objects and materials (Clements & Sarama, 2008). In addition, research also suggests that 3 and 4 years-old children engage in analytical thinking as they collect and sort materials by various attributes (e.g., color, size, and shape) and in algebraic thinking as they copy the patterns they observe in their surroundings and create their own patterns by using pattern blocks and other materials (Epstein, 2003; 2006). In fact, as research points out, most children enter school with a wealth of knowledge in early mathematics and cognitive skills that provide a strong foundation for mathematical learning (Clements & Sarama, 2009; Ginsburg, Lee, & Boyd, 2008; Mix, 2001).

There is also new evidence that achievement in early mathematics has a profound impact on later success. For example, Duncan and Magnuson (2009) examined the mathematics achievement of children who consistently exhibited persistent problems in understanding mathematics in elementary school and analyzed it in comparison to children who had stronger early math abilities. The results of the study revealed that 13% of the children with persistent problems are less likely to graduate from high school and 29% of them are less likely to attend college than those who had stronger early mathematics abilities. In other words, the initial differences in mathematics skills in early years may lead children to remain behind their more knowledgeable peers not only in primary grades but throughout their formal schooling (Geary, Hoard, & Hamson, 1999).

Studies also showed the predictive power of early math skills compared to other academic skills, such as reading. Lerkkanen, Rasku-Puttonen, Aunola and Nurmi (2005) investigated the relationship between mathematical performance and reading comprehension among 114 seven-year-old Finnish-speaking children during the first and second years of primary school. The results suggested that the level of mathematical knowledge children have before schooling is very important because these skills are predictive of their subsequent reading comprehension. In other words, early mathematics skills predict not only later achievement in mathematics but also later reading achievement. Similarly, Duncan and colleagues (2007) conducted a meta-analysis of 6 large-scale longitudinal data sets to examine the relationship between early learning and later school achievement. Of them, two were nationally representative of U.S. children, two were gathered from multi-site studies of U.S. children, and last two focused on children either from Great Britain or Canada. The researchers focused on the relationship between school-entry skills (i.e., reading achievement, math achievement, attention, internalizing behavior problems, social skills, and anti-social behavior) and later math and reading achievement while controlling for children’s preschool cognitive ability, behavior, and other important background characteristics such as, socioeconomic status, mother’s education, family structure and child health. Their meta-analysis revealed that only three of the six sets of school entry skills and behavior are predictive of school achievement: math, reading, and attention. Further, early math skills were consistently a stronger predictor of later achievement compared to reading and attention (Duncan, et. al., 2007). Consistent with the educational attainment analyses (Duncan & Magnuson, 2009), early math achievement was found as the most powerful predictor of later school achievement (Duncan, et. al., 2007).

Even though young children are natural mathematicians (NRC 2009) and capable of developing some complex mathematical ideas (e.g., addition) and strategies (e.g., sorting by multiple attributes to analyze data), it is also true that they do not become skilled in mathematics without adult guided rich and intentional interactions with those foundational math concepts. This month, we are going to focus on three of these foundational math concepts (e.g., number sense, sorting and geometry) and how you can provide your youngsters with rich and engaging math experiences that offer for opportunities and structures for the development of deeper math understandings.

Silly Putty Recipe Card

Math Morning Meeting

posted by Stephanie Forsman

Each morning, my class has a Morning Meeting that consists of a Morning Message, a Greeting, a Share, and an activity. It is a great way to start the day, reinforces our sense of community, and sets the expectations and goals for the day.  These meetings last anywhere from 15 to 30 minutes. While I cover many topics during these meetings, my favorite topic is math. I love a Math Morning Meeting!

I have an interactive Morning Message (a message written on chart paper with an area for the kids’ responses) that the children work on during morning arrival and then later talk about during Morning Meeting.  Anything from identifying and giving the monetary value of coins to measuring various line segments with a ruler using both inches and centimeters, we try to either reinforce what we are working on in math or cover a topic that isn’t heavily hit upon in our curriculum. For example, when working on multiplication facts, I will put up problems that are related and share a pattern.

3 x 3 =

3 x 6 =

3 x 12 =

3 x 24 =

I have a problem for each of the children and one that I use as an example.

For Morning Meeting, we sit in a circle and begin with a Greeting. In keeping with our Math topic of the day, we play Match Card Greeting. I give each child a card on which I’ve written part of an equation. For example, one child gets a card that says “3 x 6”; and another student gets one that says “= 18.” The children move around trying to find the match for their card. When the children find their match, they greet each other. A simple “Hello” or “Good morning” is fine. I always keep a big stack of Index cards on hand for games such as this and this greeting can be adapted and/ or modified for almost any concept; addition, subtraction, shape recognition.

After the Greeting and the children are settled back into a circle, we do a Share. Share can be anything. Topic driven, partner share, a prearranged share in which one student shares something they’ve experienced or an object brought in from home.  During a Math Morning Meeting and when we are working on a specific skill, I will announce a topic for an around-the-circle sharing. Since we are working with multiples of “3”, I will refer back to the Morning Message and ask the children what they notice. “I am definitely seeing a pattern with not only the answers but the problems. Who else is noticing what I am noticing?” The children take a minute to think and then I will start to entertain answers. The children get so excited to share what they notice and there are usually so many extensions and directions I can go based on their observations, that I usually have to jot down notes and table some of their observations for another time.

Since we are working on multiples of “3”, we will play an adapted game of “Ruof” called, “eerht” which ends up sounding like “earth.”  Three spelled backwards. The children stand in a circle for this game. The children count off and on every multiple of “3”, they say “eerht”  1, 2, eerht, 4, 5, eerht… If the they say the multiple of three or make some other mistake, they sit down and the count off starts again.  I play this game for every multiple up to 12 and have even played this game using square and prime numbers. The children love it and challenge themselves to see how high they can count.

After the activity, the children sit back down and we end our Morning Meeting with a heads up about what we’ll be working on during math that day, pretty obvious given our Morning Meeting work and ask if there are any questions, comments or concerns.

Math Mornings Meeting are so beneficial and bring so much enthusiasm to the math that is happening in your classrooms. By 9:15 am, we’ve already had a good 20 minutes of math, the children had fun practicing their math facts, and their minds are warmed up and thinking about math for the rest of the day. I highly recommend the book, Doing Math in Morning Meeting, 150 Quick Activities That Connect to Your Curriculum by Andy Dousis, Margaret Wilson, Roxann Kriete. The book contains math-themed ideas for all four Morning Meeting components: greeting, group activity, sharing, and morning message. Have fun!

Click here to see the link to the book below.

 

 

Baby Brains and Math- People and Number

Did you know that infants as young as 6 months old, have a rudimentary understanding of number? When babies hear two voices they will look for two people and when they hear three voices they will look for three people.  This was discovered in a study that presented infants with pictures of two and three people.  When the infants heard two voices, they looked at the picture with two people on it and when the infants heard three voices, they looked at the picture with three people on it.

Fascinating!  We have always believed that human beings are hard-wired for language from birth and before.  Perhaps, we need to rethink our ideas about baby brains and math.