Infusing Math into Inquiry Based Units 4th-6th

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Infusing Math into Inquiry Based Units 4th-6th

• Joan Barrett
• Madison County ROE
• jbarrett_at_madison.k12.il.us

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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

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STATE GOAL 6 Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. Number/Number Sense STATE GOAL 6 Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. Number/Number Sense
Official Wording In a Few Short Words
A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings. Numbers by themselves
B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers Computations
D. Solve problems using comparison of quantities, ratios, proportions and percents. Ratios, Proportions and Percents
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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.

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Neils Numberless World By Lucy Coats
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• 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 teachers unit
  at Joans handout website.

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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 Joans 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

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Websites related to 6A

• Hardcopy handout and electronic copy at Joans
  website

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B-C. Computation
Combining numbers (add, subtract, multiple,
divide) in and out of context. Students also
need to decide the method theyll use (mental,
calculator, or pencil) and whether the answer
needs to be exact or if an estimate will do.
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25 25 25 26 25 24 24 26
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Splitting
28 44
20 8
40 4
12
60
10 2
70
2 72
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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
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14
7
30
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Then 14 x 15 7 x 30
Computation strategy handout
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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?
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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.

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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?art
  icle_id2071
• Scale Drawings Any scale drawings (including
  maps) require ratios.

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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
• Fraction Calculators

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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

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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.

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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.c
  om/clockworks/main.html
• Metrics Matter
• http//tqjunior.thinkquest.org/3804/
• Metric History Timeline
• http//library.thinkquest.org/J002831/metrictimeli
  ne.htm
• Demo IPAC probes

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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?
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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

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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
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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/R
  ectPerim.html

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Possible activities for 7BC

• 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

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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?

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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

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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 Mutuals Longevity Game
  http//www.northwesternmutual.com/nmcom/NM/longev
  itygameintro/toolbox--calculator--longevitygameint
  ro--longevity_intro

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8CD. 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

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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 its 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

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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

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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

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Lets 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.

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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

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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.

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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.

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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.