Infusing Math into Inquiry Based Units 7-12

1. Infusing Math into Inquiry Based Units 7-12 Joan Barrett Madison County ROE jbarrett@madison.k12.il.us

2. 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

4. 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 including decimals • Children should have a sense of how big a number is or how small and what number makes sense in a scenarios.

5. 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.

6. M2T2 Website for Numbersense • http://www.mste.uiuc.edu/m2t2/resources.html#numbersense • M2T2 handouts of Sears Tower and Gateway Arch

7. 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. • 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, Sears Tower, and Gateway Arch samples

8. Websites related to 6A • Hardcopy handout and electronic copy at Joan’s website

11. 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.

12. 25 + 25 25 +26 25 + 24 24 + 26

13. Splitting 28 + 44 20 + 8 40 + 4 12 60 10 + 2 70 + 2 = 72

14. 14 X 15 Individually 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

15. = 14 7 30 15 Then 14 x 15 = 7 x 30 Computation strategy handout

16. 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?

17. D. Ratios and Percents 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.

18. 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.

19. Some Possible Activities for 6Dratios and percents - continued Ratios/percents Village of 100 - There are many websites related to Village of 100 but this one gives the references to the agencies and sources of the data http://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

21. 7A. Measuring Instruments and Units • Students should be able to use • appropriate units for the task • measuring instruments (rulers, scales, clocks, thermometers, calibers, probes that are attached to calculators or handheld computers, etc.), • Demo Probes with handhelds

22. Some Possible Activities for 7A • 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.

23. 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.htm Demo IPAC probes

24. In my unit do (or could) my students use any kind of measuring devices? Paper clips? Rulers? Timers? Scales? Thermometers? Protractors? Probes attached to calculators? Measuring devices attached to IPACs?

25. 7B. & C. Estimating and Solving Measurement Problems • Students should be able to estimate measurements • Solve measurement problems (area, perimeter, volume, etc.) • Pe-rim-eter

26. Big Measurement Ideas • Relationship between area and perimeter. If one remains the same, does the other? • Relationship between surface area and volume • Relationship between diameter and circumference Area and Perimeter Task with graph paper and tiles Class Chart on Circles

27. Websites related to 7B & C 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

28. 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

30. Patterns and Representing them • Repeating Patterns • Growing patterns • Power of patterns in all fields • Do (or could) my students look at trends or patterns of behavior or growth in my unit?

31. 8B. Tables Graphs and Symbols • 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

32. 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

33. 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, etc. • Generalizing from specifics is algebraic thinking • Sorting activity

35. 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/or faces 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” • Demo Microsoft Draw for Irregular shaped polygons

36. 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

38. 10A. Organize, Describe, and analyze GIVEN data • We have been given data about the sugar content of cereals on the top and middle and bottom 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

39. 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. What other questions could you pose to assess you students’ statistical understanding • Mode, median, mean can all be found with physical materials, paper and pencil calculations, and software programs. Students should have experience with all three.

40. Always have students write about their data • fraction/decimal/percent statements • write statements they know for sure about the data • What seems to be implied from the data? • What questions does the data raise? • Would you do anything differently in collecting the data if you repeated the survey

41. 10B. Collect, organize and analyze your own data • Brainstorm all of the errors that students make when making a graph. Be ready to share them with the group.

42. 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.

43. 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.