Everyday Objects/Experiences to Inspire Math and Science Learning
Math and Science Concepts Found in Everyday LifeGrades K-3 ECEL 517 Photojournal Angelique Kenney October 4, 2010
One Dozen Eggs
A. Eggs in a Carton I get my eggs from a chicken farmer who lets his hens run around a yard. I know they love their hens because I have heard them talk about them. The beautiful brown eggs have a deep orange yolk and are little nutritious gifts. I love the simplicity of eggs in an egg carton. They are neatly organized in two rows of six. The design of the egg carton has been around for many years, and has stood the test of time. I thought that the two rows of six eggs, could be a jumping off point to examine all the different number combinations that can equal 12. After various lessons, including word problems, playing with addition/subtraction; multiplication and division, I would imagine that this learning would be reinforced each time they see a carton of eggs in their kitchen.
B. Math content/concepts Eggs in an egg carton are an example of a real life array (2 X 6). An array is, according to thefreedictionary.com, a rectangular arrangement of quantities in rows and columns, as in a matrix. Eggs in a carton are a real-life example of a familiar quantity that can be used to talk about addition/subtraction. Arrays can also be used to introduce learners to multiplication and division. An egg carton can also be used To practice counting by 2’s To talk about half of something To frame math questions in word problems. Eggs in a carton can also be an early introduction to some algebraic concepts such as A*B=B*A, i.e 2X6=6X2; 2 rows of 6 equals 6 columns of 2 (Commutative Property)
B. Core Curriculum Standards Core curriculum standards: Grade 1 Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Understand and apply properties of operations and the relationship between addition and subtraction. Add and subtract within 20
C. Using this image to teach Math concepts. An egg carton as a focal point can be used over several classes. Ask students what they observe about an egg carton. As a class, count the cups, demonstrate counting by twos, notice that there are two equal sides (an even amount). Divide students into pairs and pass out empty egg cartons with marbles or some type of counter that they are to pretend are eggs. Each pair is given a sheet with word problems (that are reviewed by the teacher ahead of time). The word problems will be asking such questions as “When your family has finished half the eggs, how many eggs are left?”; “Your mom likes making scrambled eggs with 4 eggs, how many times can she do this before she runs out of eggs.” “How many rows of six are there? How many rows of two are there? Is it the same amount?” etc. Bring students back to the rug and discuss their findings. Have student pairs report and demonstrate their findings. Discuss the concept of an array and explore how the arrangement can illustrate multiplication i.e. 4 rows of 6 dots, makes altogether 24 dots (or simpler amounts for First Grade), and show or ask students to draw or find other examples. Introduce the term “dozen”: Latin for 10+2 primitive grouping, poss. Possibly drawn from 12 cycles of moon for 1 cycle of sun *.
D. Bloom’s Taxonomy Create and apply: What other even groupings can we find with 12 counters? What other arrays can be arranged with 12? Understand-Describe-Explain “What we know about the number 12” can be done individually or as pairs or in a group and return as a class to make a 12 poster. Have groups explain new 12 facts for the class.
A. Why is it that sometimes you wake up and your car and the grass is all wet but it didn’t rain? This is something that most kids have noticed at some point or other and is something that happens in their everyday life that can be used to explain the (all-important) water cycle. The water cycle is an important thing to understand, especially as concern over access to fresh water and water pollution threaten the planet and the humans on it. There is a limited amount of water on the planet and it is the same water that has been here for billions of years. Our planet is approximately 70 percent water and interestingly our bodies are approximately the same percentage water! The different states of water liquid, solid and gas are fairly tangible examples of the different states of matter. In addition, condensation can also be a way to begin a unit on weather.Studying the water cycle is a subject area that would constitute a whole unit. The photograph of the dew-covered car, would serve as an organic start to this unit and a phenomenon with which generally non-city children could relate. (Many city kids do not have cards nor lawns..!)
B. Science concepts related to water condensation The water cycle is comprised of various processes, including evaporation, condensation (most often in the form of clouds), precipitation and transpiration. Understanding that there is a finite amount of water which just gets recycled through these processes is enlightening. I have heard it described such as Cleopatra could have been drinking the same water as you have in your glass now! A discussion of the water cycle, also allows for a discussion on different states of matter, as water(H2O) in our natural world takes on all three states. The dewy car can also be used to discuss weather/meteorology, as only certain weather conditions can create this phenomenon. (Warm air rising to meet colder air.)
B. NJCCCS Science standards 5.4.2.G.1 Water can disappear (evaporate) and collect (condense) on surfaces 5.2.2.a.2 Identify objects as solids, liquids or gases. (Matter exists in several different states; the most commonly encountered are solids, liquids and gases. Liquids take the shape of the part of the container they occupy. Solids retain their shape regardless of the container they occupy 5.2.2.B.1 some properties of matter can change as a result of processes such as heating and cooling 5.2.4.b.1 Many substances can be changed from one state to another by heating or cooling. 5.4.2.G.1 Water can disappear (evaporate) and collect (condense) on surfaces
C. Teaching the Water (Hydrologic) Cycle Almost this entire unit can be taught using hands-on experiments. This will certainly help students to retain the information they are learning. As a hook, students can start the unit with an experiment. A classic is the clear giant plastic bottle terrarium. (This experiment demonstrates how a finite amount of water cycles through the terrarium environment, just as the planet’s water does the same thing. ) Kids can predict what they think will happen, if they cannot water the plants. (Although, it may be decided to use this experiment after some learning has happened and when the students can make an educated guess as to what may happen. (Evaporation) Another experiment that clearly shows that this happens: On a hot day, have students put paper cups of water out in the sun. Marking with a black marker where the water was filled. Look at the end of the day to see what happened (evaporation/changing from liquid to gas). (Condensation). Demonstrate condensation with boiling water and a metal spoon. (Just like the car!) Do same experiment with a cotton ball-cotton ball represents our atmosphere which is more absorbent. (Precipitation) When the cotton ball gets too full, water drips, just as what happens when the clouds get too heavy. Reviewing clouds and the different varieties makes sense. Students can use index cards to draw/write the different phases of the water cycle. Studying the Water cycle makes sense in the spring, when rain/condensation is a regular occurrence. The class can also be divided into groups with each group focusing on one of the processes and each group presenting it’s findings from research done (recommended websites can be made available.). A class poster made by the students to illustrate the water cycle can be displayed on the board. Observational weather journal including precipitation and amounts, clouds and what types, can be kept for the month and a graph detailing the monthly weather. It is great if you can have a “science lab” set up in the room.
D. Bloom’s Taxonomy Using experiments and the Scientific Method(s), students develop many of the skills described in Bloom’s Taxonomy. At the end of the unit, build the terrarium, ask students to predict what will happen in this experiment. Students will have to apply what they know about Earth’s water system to hypothesize what will happen in the terrarium. With their terrarium projects students have the option to discuss how a warmer planet may affect our water supply and explain their answer.
A. Symmetry In taking the time to closely observe the world around us, one begins to note how some items are symmetrical and others are not. You may be aware of order and balance when looking at a symmetrical object. These sensations are a link to the beauty of Mathematics in our world. Taking a moment to realize that the beauty of a butterfly or a field of ferns may be due in fact, to its’ symmetrical properties, can both enhance our observation skills as well as teach us to appreciate the properties of objects around us. Knowing and understanding the basic concept of symmetry is a way to see how Math connects with our day to day surroundings. Symmetry is also such a distinctive element in the art, architecture and design that we see in our world. Often when symmetry is taught in school we see it with classic geometric shapes, but by showing naturally occurring symmetry in nature, we really begin to understand how ubiquitous it is.
B. Symmetry There is something that draws the eye to a shape that is symmetrical. A sense of order, balance that we as humans are (generally) drawn to, makes the study of symmetry so appealing to young people. Although there may be an intuitive attraction to objects which are symmetrical, once students are aware of the concept, they begin to experience the ability to classify objects and initiate the beginnings of critical thinking skills as they learn to observe and draw conclusions about the world around them. Many educators value the teaching of symmetry as a way for students to directly (and fairly easily) connect math learning to the world around them. Art, Design, Engineering, Architecture, etc..All require an awareness of symmetry and understand it’s importance (even if you are choosing NOT to be symmetrical.) These fields are all becoming increasingly important as we are increasingly valuing creativity in solving many of the problems of the planet. Symmetry is a concept that is fairly easily grasped and and entice students who may not normally think of themselves as “mathematical”. Being able to determine whether an object depicted in a picture is symmetrical requires the viewer to take an abstract step of imagining the object being folded, or of a line running through it. This is not necessarily initially that easy, but it is a skill thatwill aid students in being able to visualize more and more complex steps in a process.
B. Math standards Grade 1, Geometry: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes. (symmetry can be included in the list of attributes) Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. (While partitioning, students become aware of whether and where a particular shape is symmetrical or not.)
C. Teaching symmetry Teaching symmetry can be approached in several ways. Starting with the Line of Symmetry, which can be visualized and manipulated as a fold, is the clearest way to determine whether an object/picture is symmetrical. Students can be given standard geometric shapes such as squares, triangles, hexagons, etc.. in the form of pictures that can be folded or a line(s) can be drawn. Playing with manipulating the shapes to see whether and where the item is symmetrical will help in visualizing this later when it may not be possible to fold something. Also, being able to draw the line(s) with a ruler can help determine whether the shape is actually symmetrical. The teacher can show on the board, but would want to physically show how when it is folded both sides are exactly alike. Another complementary approach is to seek out shapes in our every day world that are symmetrical. Looking at the photograph, can illustrate this fact. A scavenger hunt in the school yard with cameras would be an activity which would encourage observation and critical thinking skills. Also looking at “all-about books” especially of insects, other guide books, perhaps of famous buildings, would also expand their symmetrical boundaries! A look at the human body would reveal what aspects are symmetrical and which are not. Examples of art/architecture which are symmetrical will help to make the connection to one of the major uses for symmetry in the man-made world.
D. Bloom’s Taxonomy Encourage students to look closely to see whether there is more than one line of symmetry in the picture. By showing students various two dimensional items of increasing complexity, they have to evaluate and apply their learning to determinewhether the items are symmetrical. Shift from two-dimensional to three dimensional objects and apply what is known about two-dimensional symmetrical shapes to evaluate and analyze whether the three-dimensional shape is symmetrical.
Iris DeLoach Johnson, Sarah Katherine Bomholt. Teaching Children Mathematics. Reston: Dec 2000. Vol. 7, Iss. 4; pg. 208 http://symmetryinquiry.blogspot.com/2007/03/why-teach-symmetry.html http://www.innovationslearning.co.uk/subjects/maths/activities/year3/symmetry/shape_game.asp
A. What are these rocks in my woods?I This is similar to how I would introduce the picture to the students I have a favorite walk I take sometimes 2-3 times a week. It is near my house and I feel a strong connection to the rocks and trees in this patch of woods on a cliff overlooking my town, with NYC in the distance. I often imagine what it was like 200 plus years ago, while this country was fighting for its independence from Britain. I think that this overlook would be a very strategic point for whichever army controlled it. (I imagined that George Washington and his army, who spent sometime in New Jersey, would use it to spy on the British (Tory) controlled New York city. I also like to think a lot about this dark grey/blackish rock, that makes up this mountain range. I haven’t seen rock like this in too many places. It is especially visible along the cliff line. It’s not smooth, in fact, it’s pretty chunky and uneven, but it seems less from weathering but from the way it was formed. Along the actual cliff the rock goes straight up and down with ridges along it. I have often wondered to myself what the geologic history of this mountain is and specifically what kind of rock it is. The other day when I was in the woods on one of my regular visits, I paid a little closer attention and thought that I would make some careful and detailed observations. The rock seems almost bubbly. It is dark, really almost black in color and it has no sparkles in it like some other rocks do. The color is “uniform”, that is it is really only one color. It seems to cover the entire ridge-line. The rock is really hard and doesn’t chip off. It is like walking on a really rocky trail, except it is one giant rock! After taking the time to closely “observe”, I started walking home. While I was walking I started to try and make an “Hypothesis” about what I thought this might be. The shape reminded me of thick liquid in the way it had big bubbly type rocks and that it black and basically all one continuous rock. I wondered about whether it could be ancient lava. I also wondered if the ridge was formed by a glacier, as I know that a glacier can shear off the side of a mountain.
A. Connecting to the earth under our feet, the trees above our head and the sources of water in our vicinity makes a whole lot of sense to me. By taking the time to name these things, we develop respect and understanding and a connection to them. Inspiring wonder and curiosity is what makes a great teacher and fosters life-long learners. Learning how to look closely and make connections in your observations make us all amateur scientists. I think that as “earthlings” we should have some understanding of how the mountains, streams, forests, deserts were formed and how the planet is constantly changing and evolving. These are aspects of science that we constantly see. When you have a basic understanding of erosion or planetary evolution or the knowledge of what that tree or generally how old it is you pass everyday going to school, this is Science that has some relevance. The experience of knowing facts about the places about you, is exciting, increases your confidence about learning and allows you to share your knowledge easily. I use this example of the curiosity about the rocks, because it was real. I don’t see this as an introduction to the primordial planet per se, but to introducing the idea of questioning and learning about the world around you.
B. Science concepts Taking an interest in learning about the Earth and it’s flora. Knowing and understanding the history of how our planet is evolving. Being able to know and use academic/scientific terms and names. Developing observational skills and then applying what you see to make a prediction/hypothesis about what you are observing. Making the connection to what we see and may not notice, as really pretty fascinating. i.e. Look at that tree, see how wide the trunk is? I would guess that this tree is over 100 years old. Wow, what has that tree “witnessed” in the past 100 years?
B.Science concepts My example is an introduction to the beginnings of scientific inquiry. First of all noticing the natural world around you. Taking closer look and making notes (in your head or on paper.) Researching what is already known Using the research to learn more and apply the correct terms or names to the object of interest. Making an hypothesis about the object. Seeing whether this hypothesis is correct. Being excited about your learning!
B. NJCCCS/Science standards 5.1.P.A.1. Who, what, when, where, why and how questions form the basis for young learners’ investigations during sensory explorations, experimentation and focused inquiry 5.1.P.B.1/2 Observations and investigations from young learners understandings of science concepts. Experiments and explorations provide opportunities for young learners to use science vocabulary and scientific terms. 5.4. Earth Systems Science: All students will understand that Earth operates as a set of complex dynamic and interaconnected systems, and is a part of the all-encompassing system of the universe/From the time that Earth formed from a nebula 4.6 billion years ago, it has been evolving as a result of geologic, biological, physical, and chemical processes. 5.4.4.C.2. Earth materials in nature include rocks, minerals, soils, water and the gases of the atmosphere. Attributes of rocks and minerals assist in their identification.
C. What are these rocks in my woods? Questions that I would use with my photograph to inspire curiosity in my students: Do you have a special place that you ever wonder about? A favorite tree? A pretty rock you found, a special sea shell? Invite them to bring in examples or pictures of these things. What do you observe about this thing? Introduce descriptive terms. I wonder how was this mountain formed? What is thehistory of this area? How can I look closely (observe) this rock so I can take a guess (make an hypothesis) about how this rock came to be here?
C. Creating an environment of scientific inquiry in the classroom By modeling a curiosity about the natural and historic world: looking, watching, thinking, guessing and then researching, I hope to inspire my students to do the same. Provide opportunities for students to observe the (natural) world around them and encourage them to think and guess what they are seeing. Although much of the information related to how the mountain was formed would be difficult for young students to fully grasp, it is an initial introduction to the concept that there are natural processes. It is possible to give a basic introduction to the three different types of mountains, with fairly crude, but effective visual aids: One website suggests breaking the class into three groups and assigning each group the task of demonstrating one of the three processes. I think doing something of this nature would further cement the learning for the students. (http://artsedge.kennedy-center.org/content/2082/) In a general capacity, make available plenty of non-fiction research books or “all about” and guide books for students to look up information. Schedule guided inquiry activities with the students in the schoolyard. Each with his or her own personal discovery journal. This discovery time should be on a regular basis, 10 minutes once a week to make observations, do crayon rubbings of leaves, which can be followed by vocabulary used to describe leaves, which in turn can be used to aid in identifying trees from the “all-about” books; birdfeeder observations with basic vocabulary words to aid them in identifying birds and collecting rocks, observing and describing the rocks with basic vocabulary to aid them in identifying the types of rocks, to name a few of these types of activities. Cameras can also be used to document what they find and pictures kept in their journal.
D. Bloom’s Taxonomy Give students several different varieties of rocks/ leaves to observe. There can be several the same and several different varieties. The students can do an activity like a crayon rubbing for the leaves or drawing the rocks, which would force them to closely observe them (part of their Discovery Journal). Ask the students to organize and apply what they have observed when looking at the rocks or leaves. See if they can evaluate the objects and put them into piles based on whether they are the same type. For instance, you can put similar species, such as White Oak and Pin Oak, in contrast to Maples, Pines, Locusts, etc.. To see whether they can make the connection that although they are not exactly the same shape, they are a related species. Have them describe their piles and report on why they think the rocks or leaves are the same type.
(Text of voice-over)From the first slide Doing this project, several things came to mind. The importance of modeling in teaching; The importance of nurturing children’s natural curiosity The importance of connecting “real life” to their studies and specifically in the STEM areas. How we as teachers can help make that connection and in the process support the idea that learning takes place all the time and not just in the classrooom. And through teacher modeling that even adults are constantly learning new things, including DIY technology.
Voice-over text I went home and spent some time trying to find some history of this little mountain ridge in New Jersey. I learned that this was the First mountain range of the Watchung range (there is a second and even a third.) I was right that Washington’s army had used this range to spy on British and Tory troops in Manhattan and moving through New Jersey towards Philadelphia. The rock it turned out to be from an ancient lava flow from an eruption that happened just after the continental break up of Pangea! Various other geologic activity happened including a flood basalt that filled the Newark basin, “which cooled into blocky trap rock”. The basalt did not erode like the sedimentary rock that filled the basin subsequently and is what is exposed now at my little mountain. My guess about the rock being lava proved to be correct and in the process I learned about the different types of lava. However, I was incorrect about the ridgeline, but learned that this rock is called traprock.