The purpose of my goal is to determine which types of bread will grow the most mould.
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Transcript of Name of Lesson: Watch These Numbers Grow - Weebly · Name of Lesson: Watch These Numbers Grow ......
Name of Lesson: Watch These Numbers Grow
Topic: Primary Algebraic Thinking Lesson #12
Approximate time: 3 sessions
Gifted Standard and element(s):
G2CG1. Students will reason logically using induction, deduction, and abduction.
a. Explore and develop critical thinking skills through the process of convergent thinking.
d. Solve problems using logical reasoning.
f. Develop verbal and nonverbal communication skills to convey logical reasoning.
Supports CCGPS:
5.OA.3 “Analyze patterns and relationships” fits but the specific element does not—it involves
two patterns and comparing corresponding elements of each, etc.
Writing Gr. 2: 2. Write informative/explanatory texts in which they introduce a topic, use
facts and definitions to develop points, and provide a concluding statement or section.
Language Gr. 2: 1. Demonstrate command of the conventions of standard English grammar
and usage when writing or speaking.
Language Gr. 2: 2. Demonstrate command of the conventions of standard English
capitalization, punctuation, and spelling when writing.
Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others.
6. Attend to precision.
7. Look for and make use of structure.
Essential Question(s):
How can I use the mathematical meaning of “equivalence” to solve problems?
How can I use variables to solve problems?
*How can I use patterns, rules, and relationships to solve problems?
Lesson Questions: How can I analyze a growing number pattern to determine its rule and to determine future or
missing elements in the pattern?
Lesson Summary: Students will analyze various number patterns, determine the next element or
missing elements, and then determine future elements by using its rule rather than expressing all
intermediate elements. Key idea: There are many strategies for analyzing patterns. These
strategies need to be logically and systematically applied until a solution is reached.
Assessment Description/Performance Task:
Constructed response Informal assessment
Performance task Selected response
Brief Description of Assessment: Teacher will observe groups as they explain various
patterns/rules to each other. The student sheet, “Number Pattern Analysis” has students complete
number sequences and explain their strategies and reasoning independently, both orally and in
writing.
Instructional Methods:
Hook/Activator: Do “Ready to Order” game with pictures that tell a story. (You may need to teach
this game first. One set of pictures is attached. If you have something else, feel free to use it.)
After completing the game, discuss how students determined the order of the pictures. A main
point of this discussion is that one must use all available clues to determine the logical sequence.
In order to do that:
use prior knowledge
look at what is happening in current picture for two purposes: to predict the effect
of the action AND to determine the cause of the action; then decide whether
another picture shows this effect or cause
periodically review the sequence to be sure the order is logical
Say something like, “Now that you have some experience with sequencing pictures, you will use the
same kind of clue-gathering and analysis techniques to determine missing elements in mathematical
sequences. We will be analyzing number sequences to determine the missing or next element, and
then thinking about our strategies for doing this and explaining them to others.” Remind students
of the definitions of the words “analyze” (study the parts of something), “metacognition” (thinking
about one’s thinking), and “explanation” (telling about something so someone else understands).
Teaching Strategy:
Write the following on the board:
1, 2, 3, 4, ______, 6, 7 . . .
Ask, “What number belongs in the blank? How do you know?” Most students will refer to
counting in some way. If no one suggests it, the teacher should lead students to the idea that it
is also “adding 1” to the previous number in the sequence.
Next example: 2, 4, 6, 8, _____, ______, 14, 16 . . .
What numbers belong in these blanks? Have students explain their reasoning. If no one
mentions adding 2 to any element to determine the next element, the teacher should lead them
to it.
Next example: 4, 7, 10, 13, _____, _____, . . .
What numbers belong in these blanks? Have students explain their reasoning. If no one
mentions adding 3 to any element to determine the next element, the teacher should lead them
to it.
Next example: 11, 12, 9, 10, 7, 8, 5, _____, . . .
What number belongs in the blank? Have students explain their reasoning. At some appropriate
point in the discussion, point out that there is not just one straightforward rule for this pattern. If
these have not been introduced by different students lead them to see these ways to explain it:
add 1 to get the next element, then subtract 3 to get the next, then add 1 to get the
next, and continue alternating these two operations
subtract two from the next-to-last listed element to get the next one
Brainstorm strategies to use when solving patterns involving numbers. This may be done
individually or in small groups. Have students record these in the “Numbers” column of the
“Pattern Analysis Tools” chart (begun during previous lesson). Add these strategies to the class
chart. If students have trouble doing this, continue with the next part of the lesson and revisit
after they complete “Number Pattern Analysis”.
Next, the teacher models writing an analysis, possibly using one of the patterns from
the beginning of class or one from “Number Pattern Analysis”. Focus on the critical
thinking skills of metacognition and explanation. This modeling should focus on
explaining one’s thinking in writing, including some strategies that did not work and
their results. This will be important when students complete the assessment. The most
effective way to do this is to show the pattern to the students and then “think out loud”
as you write or type something similar to the example below.
Example for modeling:
I first determined if this (the last example above) was a linear or growing pattern. There is no
repeated pattern unit, so it is a growing pattern. Next, I looked to see if the pattern was getting
larger or getting smaller. In general, it is getting smaller. I asked myself questions like, “Are all
of the numbers the same distance apart?”, “Is skip counting happening?”, “What is similar or
different about the numbers?”, and because it is generally getting smaller, “What is the difference
between each element?” The difference between the first and second elements, 11 and 12, is
“plus one”. The difference between the second and third elements, 12 and 9, is “minus three”.
The difference between the third and fourth elements, 9 and 10, is “plus one” again. The
difference between the fourth and fifth elements, 10 and 7, is “minus three” again. This looked
like a pattern. It seemed to be alternating between the two operations of adding one to an
element to get the next element and then subtracting three from that element to get the next. I
called this a “plus one, minus three” pattern in my head. I made sure that this pattern worked for
the whole sequence. It did, so the solution to fill in the blank would be “plus one”, or 6. Later I
noticed that you could also say that the number pattern was really two separate growing patterns
combined. One is to skip count down by two beginning at 11. The other is to skip count down by
two beginning at 12. These two skip counting patterns are combined and alternated to form the
entire pattern. That is, 11, 9, 7, … alternates with 12, 10, 8, …
Have students complete the sheet, “Number Pattern Analysis”.
Summary by the Learner: Have students choose a pattern from “Number Pattern Analysis”.
(Students may NOT choose the same pattern about which they already wrote an explanation.)
Each will orally explain to a small group how he/she knew what to write in the blank. The teacher
listens to group discussions, correcting any misconceptions the students do not correct.
Differentiation:
More capable: Have students come up with a minimum of 3 different ways to explain any of the
patterns on “Number Pattern Analysis”. (Example: For number 1, it could be counting by 5’s,
adding 5 to the previous, adding 6 and subtracting 1, etc. If students are REALLY being precise,
they would also name the beginning number.)
Less capable: Suggest specific strategies for completing any sequences the student finds
difficult.
Materials for this Lesson:
picture cards for sequencing (The ones provided are set to “grayscale”. If you want them to be
color, right click on the picture, choose “Format picture”, and then select “automatic” from the
“color” drop-down menu.)
“Ready to Order” dot lines
class set of “Number Pattern Analysis”
students’ “Pattern Analysis Tools” charts from previous lesson
class poster of “Pattern Analysis Tools” from previous lesson
Vocabulary for this Lesson: increasing
decreasing
sequence
analysis
metacognition
explanation
strategies
Name ______________________________________
Pattern Analysis Tools- Suggested answers
Number Shape Word
odd/even
counting by (multiples) increasing by same number
decreasing by same number increasing by a pattern (+1, +2, +3,
etc)
number of sides- increasing or
decreasing position- facing up/down/left/right,
etc. number of shapes in each element
arrangement of shapes in each element (if more than one shape
per element) color or shading of each
shape/element size or shape changes
number of letters
spelling pattern singular/plural
meaning of words (synonym, antonym, etc)
beginning letter alphabetical order
double letters number or position of vowels
ending letter rhyming
CCSD Version Date: May 2011
Name ______________________________
Number Pattern Analysis Use the strategies discussed to analyze each pattern. Then write the missing
element. Be ready to explain how you knew what to write.
1) 5, 10, 15, ______, 25, ______, ______, 40, . . .
2) 21, 19, 18, 16, 15, ______, 12, . . .
3) 122, 128, 134, ______, ______, 152, . . .
4) 48, 24, 12, ______, 3, . . .
5) 51, 40, 29, 18, ______, . . .
6) 2, 4, 8, 16, ______, 64, ______, . . .
7) 31, 35, 33, 37, 35, 39, 37, ______, ______, 43, . . .
8) 1, 8, 15, 22, ______, ______, . . .
9) 65, 50, ______, 40, 45, ______, . . .
10) 207, 208, 210, 213, 217, ______, 228, ______, 243, ______, . . .
11) 9, 11, 15, 17, 21, 23, ______, . . .
12) 1, 2, 5, 10, ______, 26, 37, ______ 65, . . .
13) 850, 800, 810, 760, 770, 720, ______, ______, . . .
14) 100, 90, 79, 67, ______, 40, ______, 9, . . .
15) 1, 2, 3, 6, 7, ______, 15, 30, 31, 62, ______, . . .
16) 11, 2, 16, 7, 21, 3, 26, ______, 31, 4, ______, 9, . . .
CCSD Version Date: May 2011
Choose one of the patterns above and write an explanation of your analysis and
solution. Focus on your thinking, and include any strategies you tried that did not work, as well as those that did.
Re-write your chosen pattern on the line.
___________________________________________________________________
Write the explanation of your analysis and solution below.
CCSD Version Date: May 2011
Name KEY
Number Pattern Analysis Use the strategies discussed to analyze each pattern. Then write the missing
element. Be ready to explain how you knew what to write.
1) 5, 10, 15, __20__, 25, __30__, __35__, 40, . . .
2) 21, 19, 18, 16, 15, __13__, 12, . . .
3) 122, 128, 134, __140__, __146__, 152, . . .
4) 48, 24, 12, __6__, 3, . . .
5) 51, 40, 29, 18, __7__, . . .
6) 2, 4, 8, 16, __32__, 64, __128__, . . .
7) 31, 35, 33, 37, 35, 39, 37, __41__, __39__, 43, . . .
8) 1, 8, 15, 22, __29__, __36__, . . .
9) 65, 50, __55__, 40, 45, __30__, . . .
10) 207, 208, 210, 213, 217, __222__, 228, __235__, 243, __252__, . . .
11) 9, 11, 15, 17, 21, 23, __27__, . . .
12) 1, 2, 5, 10, __17__, 26, 37, __50__ 65, . . .
13) 850, 800, 810, 760, 770, 720, __730__, __680__, . . .
14) 100, 90, 79, 67, __54__, 40, __25__, 9, . . .
15) 1, 2, 3, 6, 7, __14__, 15, 30, 31, 62, __63__, . . .
16) 11, 2, 16, 7, 21, 3, 26, __8__, 31, 4, __36__, 9, . . .
CCSD Version Date: May 2011
CCSD Version Date: May 2011
CCSD Version Date: May 2011
CCSD Version Date: May 2011
CCSD Version Date: May 2011