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Objectives for Today To translate the IL Math Goals (and
Standards) into friendly language and to review math content related to each
To suggest some math activities you could use in your IBL units related to the Math Goals
To allow you time today to integrate math activities related to some of the Math Goals into your IBL units
STATE GOAL 6STATE GOAL 6: Demonstrate and apply a knowledge and sense of : Demonstrate and apply a knowledge and sense of numbersnumbers, including , including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios numeration and operations (addition, subtraction, multiplication, division), patterns, ratios
and proportions.and proportions.
Number/Number SenseNumber/Number Sense
Official WordingOfficial Wording In a Few Short WordsIn a Few Short Words
A. Demonstrate knowledge and use of numbers A. Demonstrate knowledge and use of numbers and their representations in a broad range of and their representations in a broad range of theoretical and practical settings. theoretical and practical settings. Numbers by themselvesNumbers by themselves
B. Investigate, represent and solve problems B. Investigate, represent and solve problems using number facts, operations (addition, using number facts, operations (addition, subtraction, multiplication, division) and their subtraction, multiplication, division) and their properties, algorithms and relationshipsproperties, algorithms and relationshipsC. Compute and estimate using mental C. Compute and estimate using mental mathematics, paper-and-pencil methods, mathematics, paper-and-pencil methods, calculators and computers calculators and computers
ComputationsComputations
D. Solve problems using comparison of D. Solve problems using comparison of quantities, ratios, proportions and percents.quantities, ratios, proportions and percents. Ratios, Proportions Ratios, Proportions
and Percentsand Percents
A. Numbers by themselvesWhat students need to know and be able to do related to this standard
Count- for older students that is combinations and permutations (counting books display)
Read, write, order numbers and number words. Write a number using scientific notation. Write a number as a decimal, percent, fraction etc.
Know categories of numbers - Odd? Even? Prime or Composite? Is it a square number? Triangular number?
Do operations on a number. Can I raise it to a power? Find the square root?
Understand that you can break a number apart and put it back together
Have a solid understanding of place value Children should have a sense of how big a number is or how small
and what number makes sense in a scenarios.
Neil’s Numberless World
By Lucy Coats
35 48 40 6 8 80,000 110,000 30 1995
STATUS: On J uly 12,______ , the bald eagle was reclassified from endangered to threatened in the lower ____ states. I t remains unlisted in Alaska. DESCRIPTION:
The majesty and strength represented by the bald eagle are world renowned. The eagle is referred to as 'bald' because of the white plumage on its head. I ts yellow eyes and beak stand in contrast to its dark brown body. Eagles can reach flight speeds between _____ and 44 miles per hour.
SIZE:
One of the largest raptors, the bald eagle is 32 to _____ inches long with a wingspan of ____ to ____ feet. Males are smaller than females.
POPULATION:
_______ to _________ eagles exist in the wild; 4,500 breeding pairs in the lower 48 states.
LIFESPAN:
Over ____ years in the wild; longer in captivity.
Can you figure out where the numbers from the box on the left fit into the fact sheet on Bald eagles on the right? If you have good number sense you can fill in the numbers even though you may not know a lot about eagles. The answers can be found at http://www.kidsplanet.org/factsheets/bald_eagle.html Make a number fact sheet about your favorite topic for your classmates to solve.
•Individually read your Bald Eagle Fact Sheet and decide where each number belongs.
•Compare the individual decisions at your table and be ready to explain why each number makes sense.
•Whole Group Discussion
•There is a copy of the Bald Eagle Fact Sheet that can be used as a template for each teacher’s unit at Joan’s handout website.
Some possible activities for 6A
Do (or could) the students count anything in my unit? It could be people, birds in a given area, supplies, seeds, days of rain, possibilities of routes, etc
Could the students make “trading cards” for the subject of your unit? Birds, Foods, Planets, Countries, Famous People, (Presidents). The cards would have pictures of the subject on one side and their important stats on the other.
In a plant unit, students could count petals on each kind of plant and see if there is consistency among plants. Do some numbers come up more than others? (Fibonacci numbers)
Have students take part in the Classroom Feeder Watch sponsored by Cornell University
Create a counting book with facts and pictures similar to those displayed at this session. Bibliography of these books are at Joan’s handout website.
Have students create a number fact sheet on their topic. Fact Sheets could be used as a “hook” at the beginning of a unit, an assessment during a unit, or a product to produce. See Bald Eagle Fact Sheet sample
Websites related to 6A
Hardcopy handout and electronic copy at Joan’s website
Websites Related to Goal 6, Standard A Gateway to Educational Materials http://www.thegateway.org/
Website with Fact Sheets about animals http://www.kidsplanet.org/factsheets/map.html
Animal Facts http://www.zoo.org/educate/animalfacts1.htm
Animal Information http://www.seaworld.org/animal-info/index.htm
Welcome to the Wonderful World of Insects http://www.earthlife.net/insects/six.html
Classroom Bird Feeder Watch (Count) http://birds.cornell.edu/cfw/home.html
World Fact Book http://www.cia.gov/cia/publications/factbook/index.html
All Federal Agencies have Kids Pages with their Statistics at this central site http://www.fedstats.gov/kids.html
Internet Public Library – section on Presidents of the United States http://www.ipl.org/div/potus/
Websites Related to Goal 6, Standard A (cont.)
The Counting Game for PreK-1 http://home.earthlink.net/~cmalumphy/countinggame.html
A PreK-K site for counting http://math.rice.edu/~lanius/counting/
Count – On (click on Numberland to get the numbers 1-100 and facts about each http://www.counton.org/
Science Website for Children http://www.kapili.com/topiclist.html
Weather for K-5 Students - National Oceanic and Atmospheric Administration site http://www.education.noaa.gov/sweather.html
University of Michigan’s Weather and Animal web resources http://groundhog.sprl.umich.edu/site/links/links.html
Iditarod- education http://www.cabelasiditarod.com/2002/education.html
Enchanted Learning (multiple links for Science/animals and Soc Studies topics like States and Presidents http://www.enchantedlearning.com/Home.html
Early number concepts (delightful site for early primary) http://www.abc.net.au/countusin/default.htm
B-C. Computation
Combining numbers (add, subtract, multiple, divide) in and out of context. Students also need to decide the method they’ll use (mental, calculator, or pencil) and whether the answer needs to be exact or if an estimate will do.
Computation Strategies
Taken from Young Mathematicians at Work- Constructing Numbersense, Addition and Subtraction By Catherine Fosnot and Maarten Dolk
A “String” is a series of problems that encourage the use of a given strategy. When using strings, only write one problem at a time on the board or overhead and stop and talk about each one before adding the next.
25 + 25
25 +26
25 + 24
24 + 26
Splitting 28 + 44
20 + 8 40 + 4
60 12
10 + 2
70 + 2 = 72
14 X 15Individually think about what the answer to this problem is.
Be ready to share your answer and method of solving it.
We want to generate as many ways to solve this problem as we can.
Graph paper and scissors
14
15
= 7
30
Then 14 x 15 = 7 x 30
Computation strategy handout
What computations do (or could) my students do during my unit? Do they total costs? Divide materials among groups or people? Do computations related to measurements? Add distances covered each day of the race? Add and divide to find averages?
D. Ratios and Percents
In primary grades students should able to recognize, write, and show common fractions and percents such as ½, 1/3, ¼, and 50%.
In intermediate grades students
should have a good number sense about fractions, decimals and percents and realize that they are interchangeable names for the same quantity.
Some Possible Activities for 6D(ratios and percents)
Percentages: In my unit do the students figure percentages of something happening or look at the ratio of one quantity to another?
Fraction Sentences to Describe Data - Any graph that students look at or create can generate fraction sentences. I.E. if there were 31 people that were surveyed and 3 said they are raising chickens on their farm then the students could write that 3/31 (or about one tenth or 10%) of the farmers surveyed raise chickens.
Great New Fractions-Percents-Decimals Interactive Website that allows a student to change the numerator and denominator numbers and automatically the corresponding decimal, percent and picture is displayed. When you get to the site select “applet”
http://my.nctm.org/eresources/view_article.asp?article_id=2071
Scale Drawings: Any scale drawings (including maps) require ratios.
Some Possible Activities for 6Dratios and percents - continued
Ratios/percentsVillage of 100 - There are many websites related to Village of 100 but
this one gives the references to the agencies and sources of the datahttp://www.populationconnection.org/Communications/ED2002WEB/
WorldOneHundredDataMaster.pdf
Indirect Measurement: Classic measurement problem with one unknown. Height of a far away mountain or tree? The object to be measured may be in an inaccessible area like across a river. Also can find the height of tall objects using shadow measurements.
See “Shake and Peek” boxes in Probability section as simulation for counting and determining ratio of Males to Females
Fraction Kit with Microsoft Word demo
Fraction Calculators
STATE GOAL 7: Estimate, make and use measurements of objects, quantities, and relationships and determine acceptable levels of accuracy.
Official Wording In a Few Short Words
A. Measure and compare quantities using appropriate units, instruments and methods.
Measuring Instruments and Units
B. Estimate measurements and determine acceptable levels of accuracy.
Estimation
C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
Solving Measurement Problems
7A. Measuring Instruments and Units
Students should be able to use measuring instruments (rulers, scales, clocks,
thermometers, coins, etc.), appropriate units (non-standard and standard) and
realize their units have to be uniform in size.
A good book for money - The Go Around Dollar
Good book for introducing the necessity for consistent units when measuring is How Big Is A Foot. student work
Some Possible Activities for 7A
Make masking tape lines on the floor or wall to represent the length or height of various animals, plants, trees, etc so students can compare themselves to each line.
Snap together unifix cubes or centimeter cubes to represent the length of various living things being studied and then on post-it notes or index cards have the names of the various plants or animals and see if the students can put them in order and match with the names.
Find distances in the students environment (on their bodies, on the playground or distances between familiar landmarks in their town that would equal length or distances related to your unit topic. I,e, the distance covered in one day in the Iditarod is equal to the distance between our school and the Dairy Queen.
Activities for 7A (continued)
Measure objects related to your unit (i.e. seeds, plants) over time using scales, rulers, etc
Websites related to measurement Animated history of clocks
http://www.britannica.com/clockworks/main.html Metrics Matter http://tqjunior.thinkquest.org/3804/ Metric History Timeline http://library.thinkquest.org/J002831/
metrictimeline.htmDemo IPAC probes
In my unit do (or could) my students use any kind of measuring devices?
Non-standard or standard? Paper clips? Rulers? Timers? Scales? Thermometers? Protractors? Probes attached to calculators? Measuring devices attached to IPACs?
7B. & C. Estimating and Solving Measurement Problems
Students should be able to estimate measurements
Solve measurement problems (area, perimeter, volume, etc. using blocks, toothpicks, counting units)
Pe-rim-eter
Big Measurement IdeasBig Measurement Ideas
1.1. Relationship between area and perimeter. Relationship between area and perimeter. If one remains the same, does the other? If one remains the same, does the other?
2.2. Relationship between surface area and Relationship between surface area and volumevolume
3.3. Relationship between diameter and Relationship between diameter and circumferencecircumference
Area and Perimeter Task with graph paper and tilesClass Chart on Circles
Websites related to 7B & C
Story/history of Weight for primary students and estimation tasks
http://www.cyberparent.com/kidsdo/weight.htm An introduction to measurement for Primary
Students http://mathforum.com/varnelle/krods.html A collection of applets for measurement for 4th-10th
grade students http://www.mste.uiuc.edu/java/default.php An Applet that allows students to investigate the
relationship between area and perimeter. http://www.mste.uiuc.edu/users/carvell/rectperim/
RectPerim.html
Possible activities for 7B&C
Could my students determine the length, perimeter, area, volume or weight/mass of anything in the unit? Especially consider irregularly shaped objects.
Is there an opportunity to introduce my students to the relationship between area and perimeter? I.e. if I keep the perimeter constant, does the area stay constant? Fencing for a garden – is there a “best way?”
Brainstorm with your team on possible measurement connections to your unit
STATE GOAL 8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
Official Wording In a Few Easy Words A. Describe numerical relationships using variables and patterns.
Patterns and Representing them
B. Interpret and describe numerical relationships using tables, graphs and symbols.
Tables, Graphs and Symbols
C. Solve problems using systems of numbers and their properties.
Numbers and their properties
D. Use algebraic concepts and procedures to represent and solve problems.
Solve Problems using Algebra
Patterns and Representing them
Repeating PatternsGrowing patternsPower of patterns in all fieldsDo (or could) my students look at trends
or patterns of behavior or growth in my unit?
8B. Tables Graphs and Symbols
Describe numerical relationships using tables (1 tricycle- 3 wheels, 2 tricycles – 6 wheels) and graphs (plot points on a coordinate graph)
Write number sentences to describe scenarios, stories or relationships. “Each yard of fencing costs seventy five cents. So if I want to figure the cost of any length fence I could write.
F x .75 = C (cost) caterpillar exercise with pattern blocks
Activities and Websites Related to 8B.
Translate sentences from the nonfiction materials students are reading to number sentences.
Educational Java Programs (Click on “Biology” to use a mathematical model to look at the relationship of population growth of oak trees, to squirrels to their predators – hawks.) You can see side by side pictures of trees growing and the corresponding graph. http://www.arcytech.org/java/
Northwestern Mutual’s Longevity Game –http://www.northwesternmutual.com/nmcom/NM/longevitygameintro/toolbox--calculator--longevitygameintro--longevity_intro
8C&D. Solving Problems Using Algebra
Using variables in number sentences (could be boxes in the primary grades) is an algebraic skill
Understanding Equality Communitive, Associative, Additive identity Generalizing from specifics is algebraic
thinking Sorting activity
STATE GOAL 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space
Official Wording In a Few Easy Words A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
Shapes by Themselves
B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
Classify and Compare Shapes
C. Construct convincing arguments and proofs to solve problems
Construct convincing arguments
D. Use trigonometric ratios and circular functions to solve problems.
Trigonometry, (Triangles)
9A. Shapes by themselves
Think about 1 shape. Can the student draw or construct a given shape? Is it 2 or 3 dimensional? What is it’s geometrical name? How many sides and vertices does it have? What kind of angles are in the shape? Is it symmetrical? Concave? Convex, Open, closed? etc.
Nickname Math Name Diamond Rhombus Oval Ellipse
2-D shape names end in “gon” 3-D shape names end in “hedron”
9B. Classify and Compare Shapes
Think about more than one shape. Compare and contrast shapes. Are they congruent? Similar? Which has more sides? Categorize them
Pattern and Geometry Power Point
STATE GOAL 10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. Official Wording In a Few Easy Words A. Organize, describe and make predictions from existing data.
Organize and analyze given data
B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
Collect, organize, and analyze your own data
C. Determine, describe and apply the probabilities of events.
Probability
10A. Organize, Describe, and analyze GIVEN data
We have been given data about the sugar content of cereals on the top and middle shelves of the grocery store.
First, each of you have received a slip of paper that has the name of a cereal from the top shelf and the number of grams of sugar that cereal has.
Take the corresponding number of snap cubes and bring them with you as we gather together
Let’s review “Measures of Central Tendencies” from your data experiences
Talk with a partner about the meaning of the following words: Mode, Median, Mean, Range, Outlier
Can you create a set of numbers where the mean median and mode are all the same, all different? Be ready to share your sets of data.
Mode, median, mean can all be found with physical materials, paper and pencil calculations, and software programs. Students should have experience with all three.
Always have students write Always have students write about their dataabout their data
fraction/decimal/fraction/decimal/percent statementspercent statements
write statements they write statements they know for sure about know for sure about the datathe data
What seems to be What seems to be implied from the data?implied from the data?
What questions does What questions does the data raise?the data raise?
Would you do anything Would you do anything differently in collecting differently in collecting the data if you the data if you repeated the surveyrepeated the survey
10B. Collect, organize and 10B. Collect, organize and analyze your own data analyze your own data
Brainstorm all of Brainstorm all of the errors that the errors that students make students make when making a when making a graph. Be ready to graph. Be ready to share them with share them with the group.the group.
All graphs should have:
Overall relevant title for the graph Each axis titled (horizontal and vertical) Scale consistent on each axis Numbers on the axis should be written on the line
not between lines (like on maps) Zero marked or a place for zero on each axis A Key if it is a Pic-to-graph Independent variables go on the horizontal axis and
the dependent are graphed on the vertical axis. The appropriate type of graph for the subject. No
line graphs unless looking at rate of change.
Activities and Websites related to 10B
Students could design a survey related to issues from the unit, display results in a graph, draw conclusions, and make decisions/recommendations based on the findings.
Use Excel Spreadsheets to collect any numerical data such as temperatures over time, plant growth over time, weights and heights of animals, counts of populations at a given place or time in history. Etc.
