Embed Size (px)
Citation preview
Language Discovery Camp is for ESL newcomers that have been in US schools for two years or less. These students will learn about early American history, biology, and math-related language skills and critical thinking skills. Teachers will seek to engage students in learning through project-based activities. Students will learn key social and academic English through content area topics.
Language Discovery camp was developed based on the findings from the Carnegie Panel on Adolescent EL Literacy (Short and Fitzsimmons, 2007: http://www.adlit.org). The panelists provided the following recommendations for educators:
Integrate listening, speaking, reading and writing skills into instruction from the start.
Teach the components and processes of reading and writing.
Teach reading comprehension strategies.
Focus on vocabulary development.
Build and activate background knowledge.
Teach language through content and themes.
Use native language strategically.
Utilize technology with existing interventions.
Motivate adolescent ELs through choice.
Although the summer camp is for newcomers, these ELLs are not a homogeneous group. Newcomers can be refugees, immigrants, or recent arrivals.
Some of the newcomers are well-educated and know more about math, science, world history and geography than their peers who have been educated in American schools. These students have high literacy skills in their native language and benefit from a program focused more on reading comprehension and vocabulary.
Another group of newcomers may be Students with Interrupted Formal Education (SIFE). These students experienced limited or interrupted formal schooling in their home countries. SIFE students often need intensive interventions to catch up on basic skills. These students require educators to assist in building their background for content lessons.
Some ELLs may come with exceptional educational needs, not unlike many other students in American schools. These needs may not have been identified yet because of the challenge of distinguishing between a learning disability and a language proficiency problem. These students will require educators to provide various instructional supports, in addition to assisting in building background for content topics.
1
Social Studies Vocabulary Pre-Test
Draw a line to match a word with a picture
Ancestors
Voyage
Feast
Immigrants
Leader
Laws
2
Colony
Social Studies Vocabulary Post-Test
Complete these sentences using one word from the box.
Ancestors, voyage, laws, leader, immigrants, feast, colony
1. The president is the ______________ of a country.
2. My ______________ come from Italy.
3. The ______________from England to Provincetown took 65 days.
4. We celebrate Christmas with a ____________________.
5. Millions of _______________ came to America from Europe in the
19th Century.
6. Congress passed several new ___________ on the environment.
7. When the English came to America in the 1500's, they lived in a
_______________.
3
4
5
6
7
8
9
10
11
12
13
14
Biology Vocabulary Pre/Post-Assessment
Student: ______________________________ Date: _________
Match the words to the right definitions.
A. cells ( ) any of the RNA-rich cytoplasmic granules that are sites of protein synthesis
B. organelles ( ) the final stage of mitosis and of the second division of meiosis in which the spindle disappears and the nuclear envelope reforms around each set of chromosomes
C. cytoplasm ( )a chemical that is found in the air, that has no color, taste, or smell, and that is necessary for life
D. chromosomes ( ) an optical instrument consisting of a lens or combination of lenses for making enlarged images of minute objects;
E. ribosome ( ) a cell that is formed when an egg and a sperm combine : a fertilized egg
F. bacteria ( ) a cell formed by the union of two gametes; broadly : the developing individual produced from such a cell
G. protists ( ) any one of the very small parts that together form all living things
H. amoeba ( )a part of the body (such as the heart or liver) that has a particular function
I. microscope ( ) an aggregate of cells usually of a particular kind together with their intercellular substance that form one of the structural materials of a plant or an animal
J. euglena ( ) to end or disappear or cause (something) to end or disappear
K. telophase ( ) any of the rod-shaped or threadlike DNA-containing structures of cellular organisms that are located in the nucleus of eukaryotes, are usually ring-shaped in prokaryotes (as bacteria), and contain all or most of the genes of the organism
L. oxygen ( ) many, multiple, more than two
M. identical ( )any of a large genus (Amoeba) of naked rhizopod protozoans with lobed and never anastomosing pseudopodia, without permanent organelles or supporting structures, and of wide distribution in fresh and salt water and moist terrestrial environments; broadly : a naked rhizopod or other amoeboid protozoan.
N. zygote ( ) being the same
O. organ ( ) any of a genus of green freshwater flagellates often classified as algae
P. multicellular ( ) a specialized cellular part that is analogous to an organ.
Q. tissue ( )the stage of mitosis and meiosis in which the chromosomes become arranged in the equatorial plane of the spindle
15
R. dissolve ( ) consisting of or existing in two corresponding or identical parts or examples, being the same as another
S. metaphase ( ) any of a diverse taxonomic group and especially a kingdom (Protista syn. Protoctista) of eukaryotic organisms that are unicellular and sometimes colonial or less often multicellular and that typically include the protozoans, most algae, and often some fungi (as slime molds)
T. split ( ) a cell that carries messages between the brain and other parts of the body and that is the basic unit of the nervous system
U. blastocyst ( ) to make a copy of, to produce something that is the same as or very similar to something else, to cause (something) to happen again in the same way
V. neurons ( ) Group of microscopic, single-celled organisms that inhabit virtually all environments, including soil, water, organic matter, and the bodies of multicellular animals.
W. reproduce ( ) to break apart or into pieces especially along a straight line, to separate or divide into parts or groups, to separate or divide into groups that disagree
Y. zygote ( ) the modified blastula of a placental mammal having an outer layer composed of the trophoblast
Z. duplicate ( ) the organized complex of inorganic and organic substances external to the nuclear membrane of a cell and including the cytosol and membrane-bound organelles
16
Biology Vocabulary Assessment A
Student: ______________________________ Date: _________
Match the words to the right pictures.
duplicate split chromosomes cells neurons Identical microscope organ oxygen
_____________________________ ______________________ ______________
___________________ ________________ ___________________
____________________ ______________________ _______________________
17
Biology Vocabulary Assessment B
Student: ______________________________ Date: _________
Match the words to the right pictures.
organelles cytoplasm ribosome bacteria protists
amoeba euglena telophase zygote
______________________ ___________________________ _________________________
_______________________ _________________________ _______________________
______________________ ____________________________ ____________________________
18
Biology Vocabulary Assessment C
Student: ______________________________ Date: _________
Match the words to the right pictures.
multicellular tissue dissolve
metaphase blastocyst reproduce
___________________ ______________________ _________________________
___________________________ ________________________ _________________
19
Biology
Goal: Provide a foundation in key vocabulary and concepts of living organism structure and functions.
Week 1: SWBAT: Use key vocabulary to discuss plant and animal cells. Compare and contrast animal and plant cells verbally and in written form using a graphic organizer. Create a model of a plant cell or animal cell by collaborating with a partner. Present orally the parts of the cell and function of each part.
June 23 June 24 June 25 June 26
Essential Questions:What do you know about the body? What is Biology?Introduce students to word parts in biology. (bio=life; logy=study of)Engagement Activity: Students will illustrate the body and label as many parts as they can with a partner.Now tell them to think of smaller parts. What are the words for the smallest parts of the body or life forms?TW show DE Engagement Activity: The Magic of Cellshttp://player.discoveryeducation.com/?guidAssetId=0e3f8a1e-2b67-437d-858a-ab88ad2e1a33
SW discuss what they learned about cells from the video and TW create a thinking map to demonstrate summarizing.
Exit Ticket: SW copy thinking map in a journal.
Essential Question:What are cells?
TW introduce key vocabulary from the article: The Building Blocks of Lifehttp://player.discoveryeducation.com/?guidAssetId=9392525e-d652-49fc-b8e4-c2ec426bdb3f
Key Vocabulary Words:Tier 1: house, blocks, small Tier 2: building, cells, living things Tier 3: plants, animals, microscope
TW do a think-aloud and model summarizing and clarifying. TW model taking notes or drawing pictures as a tool for summarizing.
SW partner read the next two paragraphs and practice summarizing and clarifying. SW take notes in journals.
Engagement activity:TW have students share key summary information by Snowballing. Snowballing is when students work in pairs to discuss key ideas. Then write down their ideas on a piece of paper and crumble the paper. SW toss the ball to the center of the room. SW select a snowball and read the info to the group.
Optional ActivitiesArticles:Cells and Organisms:http://player.discoveryeducation.com/?guidAssetId=b3a146d1-373c-4a00-8301-fef2d0f189fb
Cells:http://player.discoveryeducation.com/index.cfm?
Essential Question: What are the parts of a cell?SW share journal entries as the review of what are cells.
TW introduce plant cells by showing video clip : Plant Cells (7:12)http://player.discoveryeducation.com/?guidAssetId=a8258a12-ff4b-47b1-aed8-17989f765ab4Engagement Activity:TW have students review the parts of a plant cell by playing a matching game.After playing matching game, students will complete the plant cell diagram in the Oxford Picture Dictionary: page 104.
Discovery Education Video clip (6:23):The Cellhttp://player.discoveryeducation.com/?guidAssetId=03d549e7-c0a0-4dc6-831f-d01b21a11412Article: Discovery of Cells and Cell Theoryhttp://player.discoveryeducation.com/index.cfm?guidAssetID=f36fa6df-e53b-4bf6-ba08-336e18bedf46&productCode=DSCDiscovery Education Interactive Informational text: Seeing Cellshttp://player.discoveryeducation.com/?guidAssetId=0e3f8a1e-2b67-437d-858a-ab88ad2e1a33
Essential Question: What are the parts of a cell?
TW review key vocabulary from this week.
Discovery Education Video clip: Types of Cells (6:02)http://player.discoveryeducation.com/?guidAssetId=e6390cc7-8bfc-4b48-94e2-c89f0a4638ca
Articles:How Cells Workhttp://player.discoveryeducation.com/?guidAssetId=2114541b-d376-4204-ac1d-2752df14b397Formed for Functionhttp://player.discoveryeducation.com/index.cfm?guidAssetID=04b0c977-9be0-4478-a90f-0c0d22156b43&productCode=DSCDiscovery Education: Interactive TextFinding Cellshttp://player.discoveryeducation.com/?guidAssetId=7e513a53-1b00-4637-af32-88ea610472ab
Assessment: SW match, identify, or name at least one organelle in a plant cell.
20
guidAssetID=71c9da3a-6b6b-466b-a413-f3df11bea469&productCode=DSCExit Ticket: What are cells? Write an entry in journals.
Biology
Goal: Provide a foundation in key vocabulary and concepts of living organism structure and functions.
Week 2: SWBAT: Use key vocabulary to discuss plant and animal cells. SWBAT compare and contrast animal and plant cells verbally and in written form using a graphic organizer. SWBAT create a model of a plant cell or animal cell by collaborating with a group. SWBAT present orally the parts of the cell and function of each part.
June 30 July 1 July 2 July 3
Essential Question:What are the differences between plant and animal cells?
TW review parts of a plant cell using the matching game or Oxford picture dictionary. TW introduce key vocabulary of cell organelles: organelles, nucleus, cytoplasm, cell membrane, ribosome, Golgi complex, mitochondria, and chromosomes.
Engagement Activity:SW play DE sorting game: Here a Cell, There a cellhttp://player.discoveryeducation.com/?guidAssetId=3242fb1e-5517-43fc-9e86-b3fbacec41ce
SW use Oxford Picture Dictionary to complete animal cell diagram.
TW use a Venn Diagram to model comparing and contrasting plant and animal cells. TW model using sentence starters to compare and contrast. Please see resources for sentence starters.
Essential Question:What do organelles do? Review Tier 1 and Tier 2 vocabulary with the following activities:
Engagement Activity:SW play the game: Describe and Draw Students will draw an organelle and give directions on how to draw to a partner. The partner tries to follow the directions.SW see if the organelles match.
TW show the video clip: Plant Cells vs. Animal Cells (6:05)http://player.discoveryeducation.com/index.cfm?guidAssetId=4df7766c-b8ec-4d27-8b4e-e4f67760b592 TW show image of a cell and have student identify organelles.
Special Project: Students can use recycled materials or technology to make a model of a plant cell or animal cell. May use resources to assist in labeling the model. This project is designed to encourage student engagement and can be done by pairs or a small group of students.
SW play concentration game or Pictionary Game to review organelles.
Image of Cell with Organellehttp://player.discoveryeducation.com/index.cfm?guidAssetId=8f1c8464-e73e-45d4-bcd1-af04a7d82707
SW complete and present their Special Projects to the class.
Special Project: Students can use recycled materials or technology to make a model of a plant cell or animal cell. May use resources to assist in labeling the model. This project is designed to encourage student engagement and can be done by pairs or a small group of students.
Essential Question:What are some single-celled organisms?TW show the video: One-Cell Organisms (3:21)http://player.discoveryeducation.com/?guidAssetId=ce0b6b4c-945e-45ae-83d9-7256d10443cf
TW introduce key vocabulary: Tier 1: Earth, shapes, sizes Tier 2: single-cell organisms, bodyTier 3: bacteria, protists, euglena, amoebaTW read article: Living Things You Cannot See and model summarizing and clarifying key words in the first paragraph.http://player.discoveryeducation.com/?guidAssetId=2bf778fe-b387-4c2d-b129-8dbf3b01b5de
SW partner read next three paragraphs and sum up at the end of each paragraph. SW highlight key vocabulary.Engagement Activity:SW create a poster to share their summary.
Optional Activities:DE Video clips:Bacteria (1:34)http://player.discoveryeducation.com/?
21
Exit Ticket: SW write a sentence or paragraph to compare/and or contrast plant and animal cells.
guidAssetId=90875520-a950-4b15-b786-12a1c78d4c0aOne-Celled Animals: Kingdom of Protists
Organisms Found in Pond Water: Bacteria and Algae (3:37)http://player.discoveryeducation.com/?guidAssetId=b1617d52-5124-4554-affa-64caa57e964a Article:All About Bacteriahttp://player.discoveryeducation.com/index.cfm?guidAssetID=6eceeb09-b7cd-4301-baef-3e2013df7217&productCode=DSC
Biology
Goal: Provide a foundation in key vocabulary and concepts of living organism structure and functions.
Week 3: SWBAT identify, name, and discuss some single-celled organisms in the body. SWBAT discuss the pros and cons of single-celled organisms’ effect on the human body or the environment. Students will debate these pro and cons of organisms in the body or environment. SWBAT take on the perspective of an organism an present their argument of why they should live in an environment or the body.
July 7 July 8 July 9 July 10Essential Question:What are protist and how do they effect our environment and our body? Engagement Activity: TW do a “Word Splash” to review vocabulary from June 27. Word Splash is an activity in which the key vocabulary word is placed on the chart paper and students add words/phrases associated with the topic.
TW show video clip: Protists (2:31)http://player.discoveryeducation.com/?guidAssetId=1364c7c6-5bc4-4031-b18f-e87733ae79a4After viewing the video, TW/SW describe protist based on the video. Create a web of
Essential Question: What are the positive and negative effects of bacteria on the body?
TW introduce key vocabulary: Tier 1:hundred, thousands millions, trillions, microscope, Tier 2: waste, unlike, harmfulTier 3: bacteria, bacterium
TW introduce the article: Bacteria and Your Body.http://player.discoveryeducation.com/?guidAssetId=f427abf5-2d59-4449-b756-daca6c12ebe9
TW do a think aloud and read the first paragraph to model summarizing key points.
SW do a jigsaw reading of the rest of the article: Bacteria and Your Body.
Essential Question:Which organism would you like to be and how can you support the need of living in the body or environment?
TW review single-celled organisms that help and harm our environment: protist, and bacteria.
SW decide which organism they would like to be and make a poster of that organism.TW briefly outline how to write an essay and what is an argument.
SW write a paragraph or essay that takes the perspective of that organism. They will write an argument of why they should live in the environment or the body.Students may refer to the T-charts from previous lesson to
Teacher Workday
22
characteristics.
TW/SW make a T-Chart of ways protists affect the environment and our bodies. TW introduce the vocabulary words: pro, con
Pros of protist
Cons of protist
SW discuss the pros and cons of protist on the environment and our body.
Exit Ticket: SW illustrate or write a sentence about the pros and cons of protist on the environment or the body.
SW share their summary of the article with the group. SW use a chart to display their summary.
TW create a T-Chart of pros and cons of bacteria in the body and environment.
TW show the DE video clip: Bacteria (1:34)http://player.discoveryeducation.com/?guidAssetId=90875520-a950-4b15-b786-12a1c78d4c0a
SW discuss the video and add more pros and cons to the T-Chart from the video
Exit ticket: SW illustrate or write a sentence about the pros or cons of bacteria on the environment or the body.
create their argument.
SW present their poster and argument to the class.
Related Articles:This Means War!http://player.discoveryeducation.com/index.cfm?guidAssetID=40dfe743-0b4f-49af-b039-66808214a1cd&productCode=DSC
Life Cycle of a Killer Protisthttp://app.discoveryeducation.com/player/view/assetGuid/A8283118-C53A-4ADC-9034-08F458DD5400
Biology
Goal: Provide a foundation in the stages of cell division, tissue, organs, and body systems.
Week: 4 SWBAT identify, name, and discuss the different phases of cell division. SWBAT create a digital gallery of the different phases of cell division. SWBAT write an informative paragraph about cell division or human cells and tissue.
July 14 July 15 July 16 July 17Essential question: How do cells divide?
TW introduce key vocabulary words:Tier 2 Tier 3 Words:duplicatecopyprophasemetaphaseanaphasetelophasecentromeresspindle fiberschromosomes
SW view the DE video segment: Cell Division (1:19)
Essential question: What are the steps of Mitosis?
Tier 2 & Tier 3 words:zygoteeggdissolveidenticalsplitblastocystembryooxygen
TW make cards of the phases of mitosis. SW put the cards in order. SW use key vocabulary to discuss what is happening on the cards.
Essential question: What is Mitosis?
Tier 2 & Tier 3 words:zygoteeggdissolveidenticalsplitblastocystembryooxygen
TW review cell division and the steps to mitosis by playing a sequence game.
Special Project: SW make a digital representation of
Essential Question: What is the difference between cell, tissues, and organs?
Tier 2 & 3 words: tissue, multicellular, reproduce, neurons, contract, expand, nerve cells, bone cells, blood cells, muscle cells, dendrites, axon , organ
TW introduce the vocabulary words and model a reading strategy for the article: What is Tissue?
http://player.discoveryeducation
23
http://player.discoveryeducation.com/?guidAssetId=85e15175-48b3-456a-a111-160fe5c7ccfd
SW view an DE exploration activity of cell division: http://player.discoveryeducation.com/player.cfm?guidAssetID=1cfccb34-38e6-43bc-8d66-70941bafcc2b&productCode=DSC
Exit Ticket: In your journal, Illustrate or write a paragraph about how a cell divides. Try to use new vocabulary words.
TW introduce the DE article: Getting to Know: Cell Cycle and Mitosishttp://app.discoveryeducation.com/player/view/assetGuid/B19DC4D7-DC32-4A94-B0DF-C6137C4D10D5TW read the introduction and model summarizing.
SW read with a partner and summarize after each paragraph. SW do an illustration of their summary. TW show Brainpop Video: Mitosishttp://glencoe.mcgraw-hill.com/sites/dl/free/0078802849/164155/00053413.html
Exit Ticket: In your journal, compare the article with the information you saw in the video
the stages of mitosis using technology.
.com/?guidAssetId=6b225f36-a3bc-498a-aae6-44b98a847673SW partner read the rest of the article and summarize in their journals.
TW show DE video clip: Specialized Cells and Tissues (4:26)http://player.discoveryeducation.com/?guidAssetId=06b81218-cd77-4214-88d7-1506a9c566fe
TW show DE video clip: What is an Organ? (1:26)http://player.discoveryeducation.com/?guidAssetId=506607e0-0bc2-438a-aa18-a6f4a323c180
SW compare and contrast cells, tissues, and organs in a discussion with classmates.
Exit Ticket:SW create an illustration or write a paragraph in journal to about how cells form tissues, and tissues form organs.
Biology
Goal: Provide a foundation in the stages of cell division, tissues, organs, and body systems.
Week: 5: SWBAT identify, name, and discuss a system in the body. SWBAT recreate a system using technology or illustrations. SWBAT discuss the functions of some of the organs within the systems
July 21 July 22 July 23 July 24
Essential Question: What is the difference between cell, tissues, organs, and systems?
TW review vocabulary from previous day.
Essential Question: What are some of the systems in the body?
TW review definition of a system and the organs in the digestive system.
TW show the DE video clip:
Essential Question: What are some of the systems in the body?
TW meet with students to assess their progress on their projects.
SW complete special
Students will work on final projects for presentation.
24
TW can have students use Oxford Picture Dictionaries to discuss various organs in the body.
TW introduce new vocabulary and concept: systems using the DE video clip: Systems (2:35)http://player.discoveryeducation.com/?guidAssetId=56e6f468-db65-4e0d-bef0-16721d51453c
TW do the DE Exploration activity with the class:Building a Bodyhttp://player.discoveryeducation.com/?guidAssetId=f5cd2857-609c-4d4f-8af4-62ee4a89a882
SW explore a system in the body by doing an interactive DE activity: Follow Your Food:http://player.discoveryeducation.com/player.cfm?guidAssetID=2e55cdfb-b30d-476e-a201-959d31d3c498&productCode=DSC
Optional Activity:
SW explore a system in the body by reading the DE article: A Day in Your Digestive Systemhttp://player.discoveryeducation.com/?guidAssetId=6d881966-a64f-4e80-9cc6-9ca403718599
Exit Ticket:SW illustrate or write a paragraph in their journals explaining how food travels through the body.
Organs and Their Systems
http://player.discoveryeducation.com/player.cfm?guidAssetID=dc3d3c94-d37d-49a0-b228-e0fcef5ab1f1&productCode=DSC
TW/SW create a list of body systems. SW name some of the organs in these systems.
SW select a system to explore for a project. DE has an entire section on the body for each system that students can explore: Human Systems. Great visuals for students.http://science.discoveryeducation.com/index.cfm?UID=da85edb7-1eef-442c-ad26-f68e69b48f36
Special Project: SW explore a body system. Students may work with a partner. They will create a visual representation of the system and label the organs. SW write an informational paragraph about the system. Students may use technology to complete the project.
project and present to the class.
Special Project: SW explore a body system. Students may work with a partner. They will create a visual representation of the system and label the organs. SW write an informational paragraph about the system. Students may use to complete the project.
Biology
Goal: Provide a foundation in living organism structure and function.
Objective: SWBAT select a final project and present the information to an audience to reflect what they have learned during summer school.
25
July 28 July 29 July 30 July 31Students will work on final projects for presentation.
Students will work on final projects for presentation.
Students will present their final projects.
Possible projects
Students will select a project to work on with a partner or individually.
Pretend you are an organ in the body. Write a letter to another organ in your system. Incorporate information about what you do in the body and what the organ you are writing to does in the body.
Create a commercial to explain what teenagers can do to be healthy. Use information you learned about the body.
Should we eat foods that have been genetically changed? Write an argument for or against genetically changing foods. You must do research to support your argument.
Create a commercial to sell cigarettes or a commercial that is against smoking.
Cancer effects the body. Research one type of cancer and tell about the effects on the body. Write or illustrate how to prevent this cancer.
Create a pamphlet to explain the differences between plant cells and animal cells. You must include the parts of both types of cells.
What is photosynthesis? Create a digital presentation that explains the process. Your presentation should include an illustration of the cell and a sentence about the function of each part. You should also demonstrate how the parts work together during photosynthesis.
Create a picture book for small children on major organs in the body and how they work.
Create a game about the body. This game must include key vocabulary from summer school. You should also write directions on how to play the game.
What is stem cell research? How can it be helpful for the body? Write an essay to inform your classmates about stem cell research.
Write a song about the body. Include some facts and key vocabulary.
Create a survey about how much teenagers exercise each week. Interview the summer school students. Create a chart or poster to display your results.
26
2014 Language Discovery Camp
Math Curriculum
27
Introduction
Welcome to the math curriculum for the 2014 Language Discovery Camp. The math portion of our program is intended to address three goals:
Language – as this is for newcomer ELLs, the main focus is to provide students with exposure to and skills in parsing the language of math. To that end, we have daily vocabulary, mini-lessons focused on specific syntaxes and structures found in math, and multiple reading opportunities. Additionally, HELP Math is an excellent tool for teaching fundamental math-specific vocabulary in context.
Higher-level thinking skills – we believe that one aspect of ELL difficulty with high-school level math (and there is a significant incidence of difficulty) stems not simply from lack of language proficiency, but from the barriers that low proficiency creates to students using their higher-level thinking skills. In other words, elementary math is very concrete and not necessarily language-bound, while secondary math is very abstract, involving rule application, deduction, pattern recognition and other forms of cognition high up on Bloom’s taxonomy, and the hard truth is that all of these skills, as they are traditionally taught, are extremely language-bound. This curriculum attempts to present students with abstract thinking tasks that are not so dependent on language for success.
Fundamental math skills – the HELP Math online tutorial program has proven itself to be an excellent way to solidify the basic math skills necessary for students to succeed in high school level math.
This summer, we’ve attempted to provide you, the teacher, with flexibility in how you plan each day, while having ready-made mini-lessons and activities available to minimize your planning time. We hope you keep the three goals of the math program in mind to keep your week balanced.
28
Table of Contents
Note: While this year we’re encouraging teachers to select whichever activities they feel would fit best with the needs/proficiency of the class, do keep in mind that each section below presents the items in the order which they should probably be taught, as the progression is from easier to more difficult, and some lessons, especially in the Reading Skills and Logic sections, build on previous lessons.
1. Reading Skills – Items in this section address language and literacy skills, especially as they relate to reading math texts and math word problems.
Daily 7-Step Vocabulary Describing Relationships in Math Whole Number Computations The Parts of a Word Problem How Much – How Many Question Stem Phrases Metaphorically Idiomatic Aphorisms
2. Logic – Items in this section are meant to guide students through the process of solving logic puzzles and provide practice in employing deductive reasoning skills.
Daily Deductive Thinking Skills Warm-Ups Logic Puzzlers Falsehood Follies Peculiar Patterns
3. Patterns – Items in this section are largely visual activities intended to allow students to explore patterns in various creative ways.
Tangrams Mandalas Celtic Knots Fibonacci Series
4. Games – This section presents two different math-based games.
Magic Squares King Shamba’s Game
5. Rules – The items in this section may appeal more to students with higher language proficiency. They specifically address the higher-order thinking skill of divining rules or rule-based patterns.
Secret Codes Psychiatrist Analogies
29
Section One:Reading Skills
30
Daily 7-Step Vocabulary
ExC-ELL Vocabulary Instruction Framework
Every day, some math-related vocabulary has been assigned. You can see it on your lesson planning matrix/calendar and the full list is below.
After the terms, the numbers in parentheses indicate sample EOG problems (available in the next section of your binder) that use these terms in context.
Use the framework below to teach each vocabulary word assigned for the day. Each word should take 3-5 minutes. Less is fine, as long as the full framework is followed.
Example of Seven Steps
STEPS EXAMPLE1. Teacher states the word in context from a text. 1. “A surveyor determined that the distance across a
pond is √2255 feet.”2. Teacher asks students to repeat the word three times.
2. Say distance three times.
3. Teacher provides the dictionary definition(s). 3. The distance between two places is the amount of space between them.
4. Teacher explains the meaning with student-friendly definitions.
4. Geraldo is about five feet away from me. The distance between me and Geraldo is five feet. The distance between Raleigh and Charlotte is 166 miles. You have to drive 166 miles to get to Raleigh from here.
5. Teacher highlights features of the word: polysemous, cognate, tense, prefixes, etc.
5. Notice how we spell distance. Spell it with me. What is the cognate in Spanish?
6. Teacher engages students in activities to develop word/concept knowledge.
6. Pick a spot that is not close to you. Count the floor tiles between you and that spot. When I call on you, tell me, “The distance between ___ and me is ___ floor tiles.”
7. Teacher reminds students how this will be used during class.
7. You will see distance in word problems, and in problems about measuring. The number that follows the word distance is usually the measure of how far apart two objects are.
-- Adapted from Preventing Long-Term ELs: Transforming Schools to Meet Core Standards by Margarita Espino Calderon and Liliana Minaya-Rowe; 2011; p. 57.
31
Complete Vocabulary List
is represented by (S2)shaded (S3)approximately (1) plotted pointslie on the line (2)graphed (3)comparing (6) what is the value of… (7)let point P represent… (9)doubling (11)fixed (13)when x =… (14) increasedconstantexpress the answer as… (15)suppose thatestimates (16)satisfies the equation… (18)charges (19)additionalmodelsaccurately (21)for awhile (23)to the nearest… (27)displays (29)set of data (31)collected datatrend lineabout (32)connect (34)what is the x-value… (36)passes through (38)a rapid pace (39)creating (41)cut by (42)follow the diagram (43)the measure(s) of… (46)surveyed (49) concluded (49)
Vocabulary Context: Released Form North Carolina READY End-of-Grade Mathematics Grade 8
32
Vocabulary Pre-Assessment
Before beginning daily vocabulary instruction, please use the following vocabulary pre-assessment. In hopes of keeping things light and fun, the assessment is presented in the form of a game – match the term to the picture. Make copies of the following pages, cut out and separate the pictures and terms, then give them to the students to see how quickly and accurately the students can match them up. Use the following data table to record performance:
Student Name Order of completion
Approximate time to complete
x/15 correct
33
It weighs approximately four
kilograms.
It weighs about four kilograms.
comparing
34
connect
The shape is constant.
Lines AB and CD are cut by line EF.
doubling
35
estimates
A line has been graphed.
increased
Line EF passes through line AB and
line CD.
36
A and B are plotted points.
This answer satisfies the equation.
37
shaded
Suppose that pigs could fly.
38
Vocabulary Review 1
Fill in the blank in each sentence with the best word or phrase from the word bank below.
x y If Ben buys erasers in packs of three. If x is the number of packs of erasers Ben buys,
1 3 then ____________________________________ y .
2 6
3 9
4 12
Jenny is measuring two lines to see which is longer. Jenny is ___________________________ the length of the two lines.
34 of this square are ______________________ .
It is exactly 627 miles from Charlotte to New York City. New York City is ________________________ 600 miles away.
A B C D
Points A, B, C and D ___________________________________.
39
After he connected the ________________________, Ryan saw that he had ___________________ the face of a wolf.
40
approximately comparing graphed
lie on the line is represented by
plotted points shaded
Describing Relationships in Math
Use chart paper or poster board to recreate the eight images that follow. Each image illustrates a common relationship between numbers and/or figures used in math. These relationships can be described by multiple terms.
For each image, you will have a list of terms. Write these out on index cards, sticky notes or segments of sentence strips. If you think of more terms than the ones provided, fantastic! Use those as well. The final product is going to be a word wall that the students can use as a tool, so make the lettering large and neat.
Have the students affix the cards with the terms on them to the appropriate posters. If the students think of more terms, that’s also fantastic and they should be added.
A. within, inside of, in, inside
B. beside, next to, on the side, to the side, to the left of (you could also make a poster illustrating “to the right of”)
C. above, on top of, over, on
D. under, below, beneath, on the bottom of, underneath
E. together, grouped together, with, separate from
F. equals, equal to, equivalent to, the same as, as much as, as big as
G. less than, smaller than, not as much as
H. greater than, more than, larger than
Expansion activities:
Students could write complete sentences, using the terms you just sorted (“The small square is above the large square.”) Or, to make it more amusing, they could draw their own figures, using cartoon images or goofy symbols (or stickers, whatever) and write sentences about those (“The cat is next to the unicorn.”) As long as they’re using the phrases or terms describing the relationships.
Students could draw a figure (say a red triangle on top of a blue circle) then cover it, describe it to a partner, have the partner draw it, then see if they match.
Find different objects or ideas around the room that can be compared (books that are bigger, smaller, and the same size; students who are older, younger and the same age) and orally or using cards with <,>, and = signs line things up and compare them.
41
Model Wall Charts for Describing Relationships
42
A
B
43
C
D
44
( )
E
F
45
G
H
Whole Number Computations
This activity is intended to help students review the terms strictly associated with mathematical operations. You can see in the activity that the numbers (0-100, 1000) are written out (review, if necessary) and the operations, which are the following terms and should be reviewed:
Plus Times Minus Divided by The remainder of The largest Prime number Less than The smallest Factor Other than itself Quotient Doubled Prime factor Difference Product Sum Negative Square root Cube root To the third power To the second power
46
Model problems 1, 5, and 17. The process should be to first write out the problem in numbers and symbols, then to solve the problem. The directions on the sheet specify “do all the operations in the order in which they are given” so do not worry about following the Order of Operations here, just do ‘em as they come*. So, problem 1 would look like this:
Four plus seven times three minus six divided by three
4 + 7 x 3 – 6 ÷ 3
Which, if we’re going in order, would go:
11 x 3 – 6 ÷ 3
33 – 6 ÷ 3
27 ÷ 3
9
Always, when going over the answers on activities such as this, give the students the opportunity to come to the front of the room and use the board to demonstrate how they solved the problem. Students typically enjoy working on the board, and need to be given lots of opportunities to talk about their work.
*If your students are good little arithmeticians, not following the Order of Operations is going to bug the heck out of them. Discussing how the answer might come out different for certain problems, given the order in which the problem is solved, could be a good teachable moment, if the question comes up. Remember, the Order of Operations is: parentheses, exponents, multiplication/division, addition/subtraction. The problems below don’t have parentheses, but all the other elements do come into play.
47
48
The Parts of a Word Problem
This activity is intended to help ELLs understand better how word problems work by looking at their structure. Students need to understand that the mathematical information they need to select and generate the operations that will provide the solution is found in the middle and final section of the problem (referred to here as the “conditions” and “question”).
Objectives: Students will understand that word problems provide three separate stages of information: the setup, the conditions, and the question. Students will be able to identify each of these stages in examples of word problems.
Procedure: Use the first two pages of the activity to explain the three stages of information in a word problem and to model separating a word problem into these stages. The latter two pages (the list of word problems and the graphic organizer) are the activity the students will do, in which they cut apart the problems and paste the appropriate sections into the organizer. This would be a good activity for completing in groups. The students are not expected to solve the word problems in this activity (unless they want to). The main purpose is the reading of the problems.
49
The Parts of a Word Problem
Word problems follow a general pattern:
50
SET UP , OR ENVIRONMENT IN WHICH THE PROBLEM TAKES PLACE -- This is the first part of the word problem. It will tell you about the people and things in the problem. This part helps you understand what is going on in the problem.
CONDITIONS SPECIFIC TO THE PROBLEM -- This is the middle part of the word problem. It will tell you about changes being made to things. There are generally numbers and words that tell you what happens to those numbers. The information in this section will become an important part of the number sentence you write to solve the problem.
THE QUESTION YOU NEED TO ANSWER – The question is the last part of the word problem. It works with the conditions section to tell you exactly what kind of math problem you are going to write. The question will almost always include one of the following words: find, what, which or how. Often there is other important information in the question, such as units of measure, or words like approximately, most likely, or best, that tell you more about what your answer should look like.
Take a look at this word problem:
The regular price of a refrigerator is $1100. It is going to be discounted by 20%.What is the discounted (sale) price?
Now, work in groups to cut up the following word problems and glue their segments in the appropriate part of the graphic organizer.
51
SET UP , OR ENVIRONMENT IN WHICH THE PROBLEM TAKES PLACE
The regular price of a refrigerator is $1100.
CONDITIONS SPECIFIC TO THE PROBLEM
It is going to be discounted by 20%.
THE QUESTION YOU NEED TO ANSWER
What is the discounted (sale) price?
A baseball league has 192 players and 12 teams, with an equal number of players on each team. The number of teams was reduced by four but the total number of players remained the same. How many players are on the new teams?
Julie bought a card good for 35 visits to a health club and began a workout routine. After y visits, she had y fewer than 35 visits remaining on her card. After 18 visits, how many visits did she have left?
Ron bought two comic books on sale. Each comic book was discounted $1 off the regular price r. If each comic book was regularly $2.50, what was the total cost?
In basketball, players score 2 points for each field goal, 3 points for each three-point shot, and 1 point for each free throw made. The Bobcats scored 23 field goals, 6 three-point shots, and 11 free throws. What was the total score for the Bobcats?
Gary needs to buy a suit to go to a formal dance. Using a coupon, he can save $60, which is only one-fourth of the cost of the suit. What is the original cost of the suit?
Einar has $18 to spend on his friend’s birthday presents. He buys one present that costs $12.35. How much does he have left to spend?
A leak in a commercial water tank changes the amount of water in the tank each day by -6 gallons. When the total change is -192 gallons, the pump will stop working. How many days will it take from the time the tank is full until the pump fails?
Julie is balancing her checkbook. Her beginning balance is $325.46, her deposits add up to $285.38, and her withdrawals add up to $683.27. What is her ending balance?
There were 7 legs of the BT Global Challenge 2000 yacht race. The crew of the winning boat, the LG Flatron, sailed at a rate of at least 6 knots (6 nautical miles per hour) continually on the leg between Cape Town, South Africa and La Rochelle, France, a distance of 5820 nautical miles. How many hours did this leg take?
Elaine runs the same distance every day. On Mondays, Fridays and Saturdays, she runs 3 laps on the track and then runs 5 more miles. On Tuesdays and Thursdays, she runs 4 laps on the track, and then runs 2.5 more miles. On Wednesdays, she just runs laps. How many laps does she run on Wednesdays?
52
o
53
SET UP , OR ENVIRONMENT IN WHICH THE PROBLEM TAKES PLACE
CONDITIONS SPECIFIC TO THE PROBLEM
THE QUESTION YOU NEED TO ANSWER
How Much – How Many
The question section of word problems frequently center on either the term “how much” or “how many”. Which phrase is used depends on the count/non-count nature of the nouns in question. Count and non-count nouns are a common source of confusion for ELLs, so this activity is meant to approach the problem from the math angle and help elucidate what is being asked for when “how much” or “how many” appears in a mathematical task.
Objectives: Students will be able to categorize nouns as “count” or “non-count”. Students will recognize that “how much” is used in questions about non-count nouns and “how many” is used in questions about count nouns.
Procedure: Use the first page of the activity as your mini-lesson guide and talk through the distinctions between and examples of count and non-count nouns.
Model the first two items, found at the bottom of the first page. Have the students complete the remaining items.
54
How Much – How Many
Some things can be COUNTED. Some things can be MEASURED.
Examples of things that can be COUNTED:
students pennies rocks M&Ms pencils toes cars books points birds
But, you can’t count some things, like water. Water, like any liquid, is only limited in size or shape by its container, so we often describe water as a glass of water, a bucket of water, a tub of water. When we talk about water or other liquids in a math problem, we usually describe them through measurement: a gallon of water, a pint of milk, a liter of liquid nitrogen.
Likewise, you can’t count time. Time is infinite, so we generally refer, when we talk, to a segment of time: some time, a long time, lots of time. In math problems we again usually describe time in terms of measurements: a second, a minute, an hour, a day.
Things that you can count are called count nouns. Things like water and time that you can’t count are called non-count nouns. We treat them differently when we use them in sentences.
In math, the main difference you will see is the way we ask about them. You can count pencils, so a math problem will ask, “How many pencils?” You can’t count juice, so a math problem will ask “How much juice?”
On the following page, read each sentence, and then decide if the question should be “how MUCH” or “how MANY,” depending on the type of object that is being counted.
55
1. Jack had seventeen jelly beans. He ate six of them. How ___________ jelly beans did Jack have left? (much/many)
2. The recipe called for two cups of apple juice and one cup of pineapple juice. How ______________ (much/many)
juice did the recipe need?
3. Judy spent one hour studying math, two hours studying science, and a half hour finishing her art project. How _______________ time did Judy spend working on her homework altogether? (much/many)
4. Shari’s bucket can hold a pint of sand. She used four buckets of sand to build her sandcastle. How ____________ sand did Shari put in her sandcastle? (much/many)
5. Byron’s yard has two hummingbirds, four bluebirds, and one mockingbird. How ______________ birds live in Byron’s yard altogether? (much/many)
6. Larry’s tub holds ten gallons of water. Larry filled the tub completely, then drained 25% of the water. How ____________ water was left in the tub? (much/many)
7. Mrs. West requires that students leave their cell phones in a box on her desk during class. Mrs. West has 30 students, two-thirds of whom have cell phones. How ____________ cell phones are in Mrs. West’s box? (much/many)
8. Leanne wants to put down carpet in her bedroom. Leanne’s bedroom is 8 feet long and 10 feet wide. How _______________ carpet, in square feet, does Leanne need to buy to cover her whole floor? (much/many)
Note: Money is a little bit odd with the how much/how many rules. Although it is possible to count dollars and cents, generally the typical phrasing when asked about a total amount of money, such as a price, is phrased “How much money?” So use your brain and try to figure out these last two!
9. Nigel had $2.40 in his pocket, earned $5 from Mrs. Hart for mowing her lawn, then spent $1.70 on a soda. How ___________ money does Nigel have now?
(much/many)
10. Bethany saves all the pennies she gets in a jar. When the jar gets full, she goes to the bank and deposits the pennies into her account. The last time she took the jar to the bank, she deposited $27.83 into her account. If that total amount came out of her penny jar, how _____________ pennies did Bethany have in the jar? (much/many)
56
Question Stem Phrases
Secondary math state testing questions are often characterized by not having concrete, absolute answers, but rather by asking students to select the best of a set of flawed options. This activity is meant to help students recognize when a question is calling for an exact, incontrovertible answer, and when it is asking them to use the information in the question to compare and judge the options based on the information given.
Objective: Students will be able to recognize when a test question requires an exact answer, and when the question is asking them to use information given to select the best option available.
Procedure: The following lecture notes are also available as the PowerPoint presentation titled “Question Stem Phrases.” If possible, use the PowerPoint. The work done by the students here is embedded in the presentation.
57
Question Stem Phrases
How are these two test questions DIFFERENT?
1. What is 2+2?
A. 2 B. 4 C. 6 D. 8
2. What is Mary’s favorite color?
A. pink B. blue C. red D. purple
Question 1 has a clear answer. Question 2 does not. Let’s improve Question 2:
Mary always wears red shoes and a red hat. Her house is red brick, and she rides a red motorcycle. What is Mary’s favorite color?
A. pink B. blue C. red D. purple
You are probably guessing “red,” because there are clues that suggest that Mary likes red. But you don’t KNOW that. Maybe red stuff was on sale. Maybe the four things listed above are red, but everything else Mary owns is blue.
So actually, the “fixed” Mary question is still written incorrectly. On a test, the question should look like this:
Mary always wears red shoes and a red hat. Her house is red brick, and she rides a red motorcycle. What is most likely to be Mary’s favorite color?
A. pink B. blue C. red D. purple
The phrase “most likely” recognizes that you do not have all the facts, but asks that you use the facts you have been given to make your best guess.
When you see the words LIKELY, MOST, MORE or BEST in the question part of a math test stem, it usually means:
there is not one single correct answer, but many answers that may be correct clues that will help you make a good guess are in the conditions set in the stem, before the part
where the question is asked the choice that matches best with the clues given in the conditions set in the stem is the right
choice
58
Which question is written correctly?
Mark asked for pizza for his birthday. Mark has a pizza oven in his kitchen and has learned how to make his own pizza. Mark has Dominos, Pizza Hut and Papa John’s on speed dial.
What is Mark’s favorite food?
Mark asked for pizza for his birthday. Mark has a pizza oven in his kitchen and has learned how to make his own pizza. Mark has Dominos, Pizza Hut and Papa John’s on speed dial.
What is most likely to be Mark’s favorite food?
Robert builds a path out of bricks. Each brick is a square, six inches long on all sides. He lays twenty-four bricks end-to-end.
How long is Robert’s path?
Robert builds a path out of bricks. Each brick is a square, six inches long on all sides. He lays twenty-four bricks end-to-end.
How long is Robert’s path most likely to be?
In the first example, “What is most likely to be Mark’s favorite food?” is correct, because we don’t have enough facts to prove definitively that any one single food is Mark’s favorite… although we do have a good guess.
In the second example, “How long is Robert’s path?” is the correct way to phrase the question. There is only one right answer and no need for guessing, so there’s no need to point to a “best” or “more likely” answer, there is only the right answer.
More practice – which is the right way to phrase the question?
1. Jenny runs twice a week. On Tuesdays she runs two miles. On Thursdays she runs four miles.
A. How many miles does Jenny most likely run in a week?
B. How many miles does Jenny run in a week?
2. Tom went to Johnson’s Store and bought two pairs of pants, five pairs of socks, and three shirts.
A. What type of store is Johnson’s Store most likely to be?
B. What type of store is Johnson’s Store?
3. Tom went to Johnson’s Store and bought two pairs of pants, five pairs of socks, and three shirts.
A. How many items did Tom most likely buy?
B. How many items did Tom buy?
59
“Most likely” is common, but there are other phrases that let you know the answer is a best guess, and not an absolute right answer:
Which graph best describes how well Diggity Dog Brand Dog Food has sold over the past year? What scatterplot best fits the data set? Which poster best represents why Harry should be class president? Which route is Laura more likely to take? Which is the best name for Paula’s restaurant? Which argument best supports Richard’s answer?
60
Metaphorically Idiomatic Aphorisms
Sometimes people say, “a bird in the hand is worth more than two in the bush.” This means, “What you have is better than what you think you can get. Because you have it.”
How can we guide students from the aphorism to the plain English translation?
The aphorism is a metaphor that paints a picture. Literally, you can imagine a person holding one bird, and covetously eyeing two other birds sitting in a bush some ways off.
There’s a story in this picture. Get the students to tell it to you, and explain why the bird in the hand is worth more than the two in the bush.
Now, point out that “A bird in the hand is worth more than two in the bush” is something we say all the time. However, do people walk around valuing actual birds in their actual hands on a regular basis? No, because pecking, and hysterical elimination, and also, probably, mites. “A bird in the hand…” is meant to be useful advice. Discuss with your students how this concept can actually be helpful advice. This should guide them to a good approximation of the definition already given above.
Two key points fall out here: 1) it’s not about birds, even though it says “birds” and 2) it’s supposed to be helpful advice. Show the students “Don’t judge a book by its cover” and “The squeaky wheel gets the grease.” If the first aphorism isn’t about birds, then what should each of these NOT be about? Books. Wheels. Grease. The point is not wheel maintenance and book selection, the point is helping people understand something about themselves or other people.
In this activity, cut out the aphorisms and separate them from their definitions. Post the definitions around the room, give the students the aphorisms, and ask them to find the correct definition and match them up.
61
Take it further: After students find their definition, have them draw a cartoon that literally represents the aphorism, then another that represents the advice or wisdom meant to be conveyed.
Challenge: Which one of the following aphorisms isn’t real, but rather is actually something I made up five seconds ago?
Don’t go punching hippos if the mud is not sticky enough. If you can’t stand the heat, get out of the kitchen. Least said, soonest mended.
Can the students write their own definitions of these aphorisms?
A stitch in time saves nine.
Doing the job well now saves doing a bigger job to fix things later.
Hint 1: “in time” here means “at the right time”
Hint 2: “Nine” what? Nine stitches, later on.
A dictionary could help with: stitch
People in glass houses should not throw stones.
People who aren’t perfect shouldn’t talk about what others are doing wrong.
Six of one, half a Both choices are the
62
dozen of the other. same.A dictionary could help with: half a dozen
Birds of a feather flock together.
People who are the same stay together.
Hint 1: “of a feather” means “that are the same”
A dictionary could help with: flock (v.)
Great minds think alike.
We had the same idea, therefore we are both very smart.
The early bird gets the worm.
You can get what you want if you get there earlier than everyone else.
Don’t judge a book by its cover.
You can’t decide who a person is just by looking at them.
63
The squeaky wheel gets the grease.
People who say what they want are more likely to get what they want than people who stay quiet.
A dictionary could help with: squeaky, grease
In for a penny, in for a pound.
If I am going to do this (probably bad) thing, I’m not going to do it a little bit, I’m going to do it all the way.
Hint 1: this saying comes from England, where a “pound” is similar to a dollar.
Hint 2: “In for” here is like with poker: you have put in a penny so that you can play the game – you’re “in for” a penny.
Idle hands are the Devil’s workshop.
People with nothing to do are likely to get in trouble.
Hint 1: if necessary, elucidate who the Devil is
A dictionary might help with: idle, workshop
64
Too many cooks spoil the broth.
If many people try to control a project, that project will probably turn out badly.
A dictionary might help with: spoil, broth
65
Section Two:Logic
66
Deductive Thinking Skills Warm-Ups
Explanation – As mentioned in the introduction to the curriculum, we believe that ELLs suffer from lack of exposure to abstract thinking and higher-level thinking skills, because the traditional instruction of these skills is so language-based. These daily warm-ups are just one way to provide students with a chance to exercise their deductive reasoning skills, and tasks to follow in the curriculum will address other aspects of high-level thinking. These warm-up were taken from a text designed for
Model Lesson
6/24:
Mary and James each work. One is a bricklayer. One is a skycap. The man is not a bricklayer. Who does what?
Support tips:
Because this is the first warm-up, you should model the thinking that goes into solving it. Consider modeling through the first week, depending on how quickly students pick up on it.
“Bricklayer” and “skycap”, while probably unfamiliar terms, are not particularly important to the exercise. Define them briefly and emphasize that the important fact is that they are the names of two completely different jobs, and our goal is to figure out which job belongs to whom.
For these warm-ups, always make sure that students know the commonly expected gender attached to names.
Solution: If the man (James) is not a bricklayer, then Mary is the bricklayer, which leaves James to be the skycap.
6/25:
Malinda’s report card showed a C in math. Malinda’s mother was angry. She said that if Malinda’s next report card didn’t show a better grade in math, Malinda would be grounded. Malinda’s mother never lies. Malinda’s mother saw Malinda’s next report card but Malinda did not get grounded. What must have happened?
Support tips:
Review the American A, B, C, D, F grading scale. Explain “grounding”.
67
Solution: Malinda’s mother requires a grade better than C on the new report card or she will punish Malinda. If Malinda is not to be punished – and she isn’t punished -- her new report card must show a grade higher than C (I guess, C+ through A+).
6/26:
Mrs. Raynor and Mr. Sartin each went to the store. One was supposed to buy cheese. The other was supposed to buy eggs. Mr. Sartin was not supposed to buy cheese. What was each person supposed to buy?
Support tips:
Define “supposed to.” Define “The other” as it is used in the third sentence.
Solution: If Mr. Sartin was not supposed to buy cheese, then he was supposed to buy the other item, which was eggs. So, Mr. Sartin is buying eggs, and Mrs. Raynor is buying cheese.
6/30:
Mandy believes that everyone should go to a dentist at least twice a year. Mandy knows her brother has been to a dentist only once in the last two years. What must Mandy believe about her brother?
Support tips:
Clarify, perhaps by drawing a timeline on the board or using a calendar, the difference between “twice a year” and “once in the last two years.”
Students might need help with the phrase “What must Mandy believe…”
Solution: Mandy probably believes that her brother doesn’t go to the dentist enough.
7/1:
I am thinking of three colors. I like the first better than the second. I like the third better than the first. Of these three colors,
a. Which one do I like the best?b. Which one do I like the least?
Support tips:
Review ordinals (first, second, third, fourth, etc. …) if necessary.
68
Review the comparative “I like… better than…” if necessary. If students are struggling, ask them to pick three colors, then label them “first”, “second” and
“third”, and then try to order them by which one is liked more.
Solution: a. The “third” is the color liked best.
b. The “second” is the color liked least.
7/2:
Amy’s hair is longer than Marlene’s. Tanya’s hair is shorter than Marlene’s.
a. Who has the shortest hair?b. Who has the longest hair?
Support tips:
If needed, define “shorter than”, “longer than”, “shortest” and “longest” (comparatives and superlatives).
Solution: a. Tanya has the shortest hair.
b. Amy has the longest hair.
7/3:
Rocky and Terrible are a bird and an elephant. Rocky weighs more than Terrible. Who is what?
Support tips:
Does everybody know what a bird and an elephant are? The names are not important. Define “weighs more than”. Make sure the students understand what the question “Who is what?” is asking.
Solution: Elephants generally weigh more than birds. Rocky weighs more than Terrible, therefore Rocky is probably the elephant.
7/7:
If Randy were 5cm taller, his height would be 89cm. How tall is he?
Support tips:
69
Explain how “If… were…” presents a conditional situation, or a situation that is not currently true but where the solution will be found by pretending that it is true. In other words, Randy is not 5cm taller. However, in order to find the solution to the problem, it is necessary to imagine that he is, and then compare that height to how tall Randy really is.
If necessary, explain that “cm”=centimeters and define or illustrate centimeters. “Taller” in this sentence is defined as “taller than Randy is now” (see convoluted explanation of
conditional, above). If necessary, define “taller” (in and of itself) and “height” and point out their relationship to one
another.
Solution: 89cm is Randy’s new pretend height that he attains with the addition of 5 imaginary cm. To find out how tall Randy really is, subtract 5 from 89, which leaves 84cm.
7/8:
If Rod were 10cm shorter, he would be the same height as Stacy. Stacy is 67cm tall. How tall is he?
Support tips:
Remind students of the 7/7 warm up about how tall Randy is, because the principle, especially of the conditional (if… then…) element is essentially the same.
If necessary, define “shorter.” Make sure that students realize that “How tall is he?” refers to Rod, not Stacy. It’s actually a
pretty common confusion.
Solution: Rod’s real height minus 10cm is 67cm, so to find Rod’s actual height, add 10cm back to 67cm, finding that Rod is 77cm tall.
7/9:
An airplane was flying at an altitude of 1500 meters. A second airplane was flying at an altitude of 500 meters higher than the first. What conclusion can you draw from this?
Support tips:
Define “altitude.” This one may require you to model finding the solution.
Solution: The second airplane was flying at an altitude of 2000 meters.
7/14:
70
We all know that no 2-year-old can ride a bicycle. Danielle is 2 years old. So, what must be true?
Support tips:
Students may not be familiar with the construction “no 2-year-old can ride a bicycle” as opposed to “2-year-olds can’t ride bikes”.
If students seem a little stuck, amend the second sentence to “What must be true about Danielle?”
Solution: Danielle can’t ride a bike.
7/15:
Anyone who is completely happy has no worries. Ms. Neuman has a few small worries. What must be true?
Support tips:
Discuss how “completely happy” and “no worries” suggest absolute states (as would using words like “all”, “always” or “every”) and that for those states to be “true” there can’t be any flaws or little tiny deviations.
If necessary, define “a few.”
Solution: “A few small worries” is a flaw, however tiny, in the state of “no worries.” So, “no worries” = FALSE, therefore the dependent state, “completely happy” must also = FALSE, therefore, Ms. Neuman can’t be completely happy.
7/16:
Barry spends all of his spare time reading books. Mr. Darton is a grade school teacher. He belongs to a teacher’s bowling league. What must be true?
Support tips:
If necessary, define “spends… time”, “spare time”, “grade school”, “belongs to” and “bowling league.”
Understanding the difference between first names (“Barry”) and last names (“Mr. Darton”) is necessary to finding the solution.
You may need to model thinking on this one (see below).
Solution: This one is moving into slightly new territory, in which the authors are expecting the kids to be hip to their devious, devious ways. The solution to this question depends entirely on the students making an assumptive leap which winds up being definitively not true, but has to be made anyway.
71
In order to figure out what the question is asking, the students have to understand that it is possible for “Barry” and “Mr. Darton” to be the same person. Once they understand that possibility, then they realize the question “What must be true?” is really asking “Are Barry and Mr. Darton the same person?” That’s the hard part. The final answer is actually pretty easy: no, Barry can’t be Mr. Darton, because Mr. Darton spends some of his spare time bowling, and Barry spends all of his spare time reading. Another one of those “absolute state” questions, like the one about Ms. Neuman.
7/17:
Ezra likes milk better than lemonade. But he likes lemonade better than soda. Of these three drinks:
a. Which does he like best?
b. Which does he like least?
Support tips:
If necessary, define “likes… better than…”, “like best” and “like least”.
Solution: Ezra likes milk best and he likes soda least.
7/21:
Marsha’s mother sent Marsha to the store three times today. One time Marsha bought bread. Another time she bought hamburger. The other time she bought mustard. She bought the mustard before she bought the bread. She didn’t buy the hamburger last, but she didn’t buy it first, either.
What did Marsha buy on each of her three trips to the store?
Support tips:
Have the kids make a little time-line and label three points on it “first”, “next” and “last”, then try to use the clues from the question to sort out which .
Solution: Marsha bought the mustard first, the hamburger second, and the bread last. Marsha’s mother clearly needs to get organized.
7/22:
A SUPER-8 is more expensive than a TIGER. A LEOPARD is cheaper than a FASTCAR. A TIGER costs more than a FASTCAR. List these four products in order, starting with the one which costs the least.
72
Support tips:
The names (SUPER-8, TIGER, LEOPARD, FASTCAR) mean nothing and should not have time wasted on being defined. They seem to be four different brands of cars, but it totally doesn’t matter to solving the problem.
Define, if necessary, “more expensive”, “costs more” and “costs the least”. This is the first warm-up where four, rather than three items are to be put in a specific order. If
three items is still challenging some students, you should model solving this item. (I had to use sticky notes, so I could move them around.)
Solution: From least expensive to most: LEOPARD, FASTCAR, TIGER, SUPER 8.
7/23:
Celeste had an apple, a pear, and a banana. She put them in a row. She put the apple to the right of the pear. She put the banana to the right of the apple. Name the way she set the fruits from left to right.
Support tips:
If your students are struggling with right, left, “to the right” and “from left to right”, try modeling the following practice item with sticky notes: “Cedric had a carrot, a tomato and an onion. He put them in a row. He put the onion to the left of the tomato. He put the carrot to the left of the onion. Name the way he sets the vegetables from left to right.” (Solution for practice item: carrot, onion, tomato.) Then have the students do the actual item on their own.
Solution: Pear, apple, banana.
7/24:
Amos had a grape, a lemon, and a watermelon. He put them in a row. He put the largest one in the middle. He put the smallest one to the right of the largest one. Name the way he set the fruits from left to right.
Support tips:
Make sure everyone knows that the grape is the smallest and the watermelon is the largest. In addition to “to the right” like we saw yesterday, we also have “in the middle” today, so define
that if necessary.
Solution: Lemon, watermelon, grape.
73
7/28:
The sum of the ages of Darlene and her mother is 29. Darlene’s age is 4. How old is Darlene’s mother?
Support tips:
If necessary, define “sum.”
Solution: Darlene’s mother’s age is 29 minus Darlene’s age (4), so Darlene’s mother is 25.
7/29:
Two people share a ride to work each morning. Their first names are Sue and Terry. Their last names are Rawls and Peters. Sue is almost never ready on time. Terry drives a blue car. Rawls likes to watch TV. Peters is almost always ready on time. What is each person’s full name?
Support tips:
If necessary, define “share a ride”, “ready on time” and “full name”. This is a fun one, in that the key to solving it lies in eliminating a lot of useless information. The
question at the end indicates that the solution involves correctly connecting “Sue” and “Terry” to “Rawls” and “Peters”, which is accomplished through finding something that a specific first and last name must have in common OR a reason why they can’t possibly be together. The only facts that help in this way are that Sue is almost never ready on time and Peters is almost always ready on time, which means that Sue can’t be Peters. That they share a ride, that Terry drives a blue car, and that Rawls like to watch TV are all useless bits of information. Help the students see how they can put the distractions aside to find the hints that actually help (literally crossing things out, for instance).
Solution: If Sue can’t be Peters, then it’s Sue Rawls and Terry Peters.
7/30:
Three years ago, Jefferson was a year older than his brother. Jefferson’s brother is now 6 years old. How old is Jefferson now?
Support tips:
Don’t think we need any tips here, although I know some kids are surprised by the fact that, if their brother is a year older than them now, he will always be a year older.
Solution: Jefferson is still a year older than his now-6-year-old brother, so Jefferson is 7.
74
Logic Puzzlers
This activity is intended to extend on the technique of breaking down word problems into three separate stages of information. The problems here are not actually math word problems, but rather logic problems, but they follow the exact same format as math word problems. This will hopefully a) keep the focus on the reading aspect of working with the problems while reinforcing the technique from the previous lesson, helping students improve the skills they’ll be using in the warm-ups, and encouraging abstract thinking skills.
Procedure: Ask students to identify the set-up, conditions and question of each problem, either by highlighting them in three different colors or by circling the conditions, underlining the question, and leaving the set-up blank.
Model solving the first problem. You could say something like:
The question is which person is wearing yellow, so I have to figure out from the clues given in the problem which person is wearing yellow. The set-up tells me there are three people, so I’m going to put three circles on the board, one for each person. I see a bunch of colors mentioned in the conditions section, so I bet that’s where I will find the clues that help me solve this problem. Here it says: “’I’m not wearing red or blue,’ says the first.” So my first circle is the first person, and I’m going to write “red” and “blue “ under that circle, then cross them out to show that they are not wearing red or blue. Here it says: “’But one of us is wearing yellow,’ says the second.” All that tells me is that one person is wearing yellow, but it doesn’t tell me anything about which person, so I’m not going to write anything under the second circle, which is my second person, just yet. Now the problem has the third person saying “I don’t see any yellow or red on either of you.” This doesn’t tell us anything exactly for the third person, but it does tell us that both the first and second person aren’t wearing yellow and they aren’t wearing red. I already have “red” written under the first person and crossed out, but I don’t have it written and crossed out for the second person, so I’m going to do that now. Also he said that neither the first nor second person were wearing yellow, so I’m going to write “yellow” under each and then cross it out.
So I can see that both the first and second person can’t be wearing yellow, but somebody is wearing yellow, because the second person said so. Look at the circles: who’s left? That’s right, the third person must be the one wearing yellow, because we’ve already figured out the other two can’t be.
Have students work in pairs to complete the other problems. Ask them to volunteer to explain how they worked out the solution. Getting them to talk about this may take some coaching/modeling.
75
1 2 3
RedBlue
Yellow
Yellow
76
77
Section Three:Patterns
78
Tangrams
A tangram is a geometric puzzle of sorts, consisting of a set group of polygons that can be rearranged to make an infinite number of shapes and patterns. Work with tangrams helps familiarize students with a host of geometry concepts, especially about polygons and angles.
First, print out the tangram template below, and cut along the lines to create the tangram pieces (gluing to a pasteboard or construction paper backing will make the pieces sturdier).
79
In addition to doing the standard tangram picture-puzzles on the following pages, students can also exercise their critical thinking skills by doing the following activities:
1. Sort the tangram pieces using your own classification or rules. 2. Put two or more of the tangram pieces together to make other shapes.3. Put two or more of the tangram pieces together to form shapes that are congruent (identical in shape and size).4. Use all of the tangram pieces to make a square. DO NOT look at the existing pattern.5. Use the seven tangram pieces to form a parallelogram.6. Make a trapezoid with the seven tangram pieces.7. Use two tangram pieces to make a triangle.8. Use three tangram pieces to make a triangle. 9. Use four tangram pieces to make a triangle. 10. Use five tangram pieces to make a triangle. 11. Use six tangram pieces to make a triangle.12. Take the five smallest tangram pieces and make a square. 13. Work with a partner to come up with as many mathematical terms or words related to tangrams as you can.14. Make a rhombus with the smallest three triangles, make a rhombus with the five smallest pieces and make a rhombus with all seven pieces.
80
Below are some patterns you can challenge students to reproduce – using all of the tangram pieces with none left over. After that, what new pictures can they design themselves?
81
Mandalas
A mandala, common to Indian meditation traditions, is a repetitive design within a circle. Encourage students to develop color patterns when coloring the following designs. The final mandala page is actually a blank mandala, where students can create their own mandala.
82
83
84
85
86
Celtic Knots
Maybe it’s because, if you trace all the lines of my heritage (except the apocryphal Cherokee one) back far enough, you hit a Celt tribe somewhere, but I think Celtic knots are nifty as all get-out. I’m including some fun with them here because a) they’re beautiful and b) they are patterns with allowances for on-the-fly rule-making, which fits in nicely with some of our work on abstract thinking.
We’ve got some knot work from the Book of Kells to study and color, directions on how to build knots using the traditional method, and directions on how to build easier knots that I made up myself during Finite Math back during my freshman year in college (D+!).
87
88
89
90
91
92
Making Celtic Knots (dots method)This is a method of drawing Celtic knots that I found in a book of Celtic and Anglo-Saxon painting. It called the knots 'interlace', and said "Interlace is not a motif that can be learned by simply looking at a model. One must know the 'trick', and from unfinished interlace borders we can tell how it was usually made up." This suggests that there was only one method, but looking at examples of Celtic knots, I suspect that several methods was used. This method would only work for close-weave knots in a simple border.
Start by drawing dots in a diamond lattice pattern like this. You would normally draw this in black, but I'm making the dots red to contrast with the later lines.
The dots should be diamond-shaped themselves. When you start drawing lines, draw them alongside the dots rather than through the centre, otherwise this technique doesn't work.
The patterns below are from the Durham Gospel.
Simple plait with four strands
Draw the top left diamond. Draw the top left and bottom right sides only. Keep inside the dots. This is the first strand.
Draw a curved line at the top. This represents the strand bending round to go downwards.
Draw the lower diamond the same, still keeping inside the dots. This will make the long line look wonky. This is the second strand.
Draw the middle diamond. This time you draw the bottom left and top right sides. Keep within the dots! This is the third strand.
Draw the top diamond and the top curve, as before. This continues the second strand.
Draw a bottom curve and bottom diamond, to start the fourth curve.
The middle diamond continues the first strand.
93
The top diamond and the top curve diamond continues the fourth strand.
Continue to complete the knot. I have changed the red dots to black so you can see the finished effect. There is a suggestion of a black background as well, to heighten the effect.
Twists with four strands
This design starts the same as the last one.
Continue the top curved line twice as far as last time. It's better to rub out the surplus dot altogether.
Continue with the next two diamonds, the same as last time.
Make a second shorter curve, below the top one.
Make a long curve at the bottom, remembering to remove the surplus dot.
Make a short curve above the bottom curve.
Draw the second middle diamond.
Draw the second middle diamond.
Draw the two outer curves...
... then the middle two diamonds.
94
Here is the final result.
Entangled loops
Draw a line straight down in the centre. This is the start of a new loop.
Draw in a normal under and over from bottom left heading up and right, and curve it round.
Make a short curve, bending round the top of the loop.
Draw in another under and over next to the previous one, but this time bend it round with a long curve. removing the middle dot.
Make a long curve at the bottom in the same way.
Draw a line straight down in the centre. This is the end of the old loop.
Repeat.
The final pattern.
I don't think this can have been a design tool for Celtic knots, since it's quite easy to get lost (which is why I've broken it down into small steps). But if you designed a rough draft using a looser design technique (see below), then this method could be useful for transferring your pattern to the final copy. It would also be useful for bending patterns round curves, to fit inside letters, for example. It can be hard to predict the angles of the lines, but you could mark a pleasing regular pattern of staggered dots, then fit the pattern round it.
95
Making Celtic Knots – Square Matrix Method
1. First, draw small squares around the perimeter of a square or rectangle:
There must be a minimum of 4 squares on a side – but anything more than 4 is fine. This is a square with 5 small squares on each side.
2. The small squares are the holes in the knots. Now you need to draw the knots around the squares:
The knots are formed by sets of parallel lines on the sides of the small squares that cross over and under each other.
3. The finished basic weaving:
96
4. Now the ends of the strings are hanging loose, and they need to be connected. This is the fun part. Use loops and arcs to connect one loose end to another:
5. When the ends are all connected, the final product will look like a very simple Celtic knot:
97
Fibonacci Series
More fun with math and reading! Start this one off by putting some of the Fibonacci sequence on the board (1, 1, 2, 3, 5, 8, 13, 21, 34, 55…) and challenging the students to discover the rule and/or find the next number in the pattern.
The explanation is in the reading that follows (from the same source as “Magic Squares” and “King Shamba’s Game”).
You can challenge the students with some other Fibonacci-related puzzles, such as:
List the five 3-digit Fibonacci numbers. (144, 233, 377, 600, 977)
Which of the following is a Fibonacci number: 4666, 1077, 6685, 3114 (6685)
Which Fibonacci numbers under 100 are prime numbers? (1, 2, 3, 5, 13, and 89)
98
99
100
Fibonacci Project
An interesting thing about the Fibonacci series is that it is found everywhere in nature. The text shows three different flowers that present three, five and thirteen petals. Have students work in groups to find images online -- or, even better, samples from outdoors -- of plants and even animals that have parts in multiples from the series. If working online, students can put together a slide show. If working with actual bits of nature, have students mount the items on a poster or otherwise display it.
Product: Create a display or slideshow presenting examples of Fibonacci series numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55…) in natural items (five fingers on humans, thirteen petals on ragworts, eight legs on spiders).
Content objective: Students will be able to identify and explain the pattern that generates the Fibonacci series. Students will recognize an example of how mathematical rules operate in nature (other examples of mathematical rules operating in nature involve symmetry and fractals).
Language objective: Students will be able to explain orally and/or in writing the pattern that generates the Fibonacci series. Students will be able to present their displays and explain the relationship between Fibonacci numbers and the nature examples they have placed on their displays.
Rubric: [Teachers, please feel free to adapt the elements of this rubric in whatever way you think appropriate to how your particular students will best execute the project.]
Project Element Didn’t Do It Completed Completed
CorrectlyExcellent Example
Product has at least five different images or samples, each showing the presence of a different Fibonacci number. 0 1 2 3Group/student took on the challenge of finding two or more examples of two-digit or larger Fibonacci numbers. 0 1 2 3Display/slide show is neat and attractively presented. 0 1 2 3Group/student gives an oral presentation explaining each sample and its evidence of a Fibonacci number. 0 1 2 3
TOTAL POINTS(If you want to assign grades, 0-3 is an F, 4-5 is a D, 6-7 is a C, 8-10 is a B and 11-12 is an A.)
101
Section Four:Games
102
Magic Squares
This is a fun-with-math activity with some reading thrown in. Make student copies of the following four pages. Have students read the first two pages either through round-robin reading or having partners read to each other. Go over the key facts: magic squares are math crossword puzzles, they’ve been around for thousands of years, and the goal is to use all of the single-digit numbers (1-9) and have the horizontal, diagonal and vertical rows add up to 15. On the second page are some example puzzles. Have the students present on the board how to solve them or model solving them yourself, whichever is necessary.
8 3 41 5 96 7 2
Item C on this page is taking things a step further. Try to get the students to note that, if there are 16 squares, you have to use each number, 1 through 16, one time. Also, the third row is completed, so the target sum for all rows, columns and diagonals should be 34.
The final two pages provide instructions on how to construct and play a game around the concept of the Magic Squares, which students can work in partners or in groups to complete and play.
103
2 7 69 5 14 3 8
7 12 1 142 13 8 1116 3 10 59 6 15 4
104
105
106
107
King Shamba’s Game
Like the “Magic Squares”, King Shamba’s Game is another delightful mix of reading practice and mathy fun. Again, have students partner up to read (the first page and the top of the second page), go over the key facts in the history of the game, then have them work together to follow the directions to build and play the game. The game can be constructed with egg cartons and jellybeans (or similar).
108
109
110
111
112
113
114
Section Five:Rules
115
Psychiatrist
Objectives: Students will practice identifying patterns and rules. Students will describe these patterns or rules orally.
In the game of Psychiatrist, “It”, or the Psychiatrist, leaves the room for a minute, while the rest of the group decides on a weird behavior for the Psychiatrist to diagnose. The Psychiatrist then returns to the room, interacts with the group, and attempts to determine what the rule of the selected weird behavior is.
The group needs to agree upon a simple rule that will guide their behavior when the Psychiatrist returns. For example, everyone could decide to lie whenever the Psychiatrist asks them a question. Or they have to say a color every time they answer. Or they could choose to pat their head every time the Psychiatrist looks at them.
Probably it would be good to model generating the rule for the students, until they get the idea and take over. Encourage goofiness – this game can be hilarious. When the Psychiatrist correctly guesses the rule, let the Psychiatrist pick his or her successor, or draw a name from a hat.
The challenge for newcomer ELL students – and what they have to do in order to succeed at the game – will be communicating the diagnosed rule accurately and effectively. In the case of this game, the rule will be determined by WHO is doing WHAT and WHEN.
WHO will probably be “everybody,” so a good sentence starter for the solution would be “Everybody is…” If it’s not everybody, it will be an identifiable group, such as “all of the boys,” so then the sentence starter would be “All of the ________ are…”
WHAT is the action, be it lying, head-patting, color-mentioning, or whatever. Given the way we’ve started the solution sentence, this should be expressed as a present participle: “Everybody is lying…”, “Everybody is patting their head…” Now a scaffolded framework for the solution sentence would read: “Everybody is ______ing…” or “All of the _______ are _______ing…”
WHEN is the conditions under which the students perform the action of the rule. Everybody is lying when the Psychiatrist asks them a question. Everybody is patting their head when the Psychiatrist looks at them. Now the end of the solution sentence is, for the Psychiatrist: “… when I (do something).” So…
Everyone is ________ing when I __________.or
All of the _________ are ___________ing when I _________.I would have these frameworks up on the board for the Psychiatrist to reference (and for the rest of the students to reference while developing a new rule), and I would demarcate the different elements of the rule within the sentence:
All of the _________ are ___________ing when I _________.
116
WHO
WHAT
WHEN
117
118
119
120
Analogies
121
122
Find more worksheets at http://englishforeveryone.org/Topics/Analogies.htm
123
124
Analogies
Objective: Students will be able to identify then explain the rules that support analogies.
A B C Ddog puppy cat
A B C Ddog puppy cat kitten
Explanation: B is ________ to A, so D must be ________ to C. rule rule
B is the baby to A, so D must be the baby to C.
A puppy is the baby to a dog, so a kitten must be the baby to a cat. A B C D
yes no up
A B C Dyes no up down
Explanation: B is opposite to A, so D must be opposite to C.
No is opposite to yes, so down must be opposite to up.
A B C Dday night light
Explanation: B is ________ to A, so D must be ________ to C. rule rule_____________________________________________________________________________________
A B C Dpine tree rose
Explanation: A is ________ to B, so C must be ________ to D. rule rule_____________________________________________________________________________________
A B C DWashington, D.C. United States Paris
Explanation: A is ________ to B, so C must be ________ to D.
125
rule rule_____________________________________________________________________________________
A B C Dmorning breakfast noon
Explanation: B is ________ to A, so D must be ________ to C. rule rule_____________________________________________________________________________________
A B C Dhead hat feet
Explanation: B is ________ to A, so D must be ________ to C. rule rule_____________________________________________________________________________________
A B C Dpen write scissors
Explanation: B is ________ to A, so D must be ________ to C. rule rule__________________________________________________________________________________________________
A B C Dsummer hot winter
Explanation: B is ________ to A, so D must be ________ to C. rule rule
__________________________________________________________________________________________________
Answer Keys
126
127
How Much – How Many
1. Many2. Much3. Much4. Much5. Many6. Much7. Many8. Much9. Much10. Many
128
Analogies
Sentence Analogies 1:
1. C 2. B 3. C 4. A 5. A 6. A 7. A 8. C 9. B 10. C
Sentence Analogies 2:
1. A 2. A 3. B 4. B 5. A 6. A 7. A 8. B 9. C 10. B
Analogies
Dark: Night is the opposite of day, so dark must be the opposite of light.Flower: A pine is a type of tree, so a rose must be a type of flower.France: Washington, D.C. is the capitol of the United States, so Paris must be the capitol of France.Lunch: Breakfast is the meal you eat in the morning, so lunch must be the meal you eat at noon.Shoes/Socks/Etc.: A hat is worn on the head, so shoes must be worn on the feet.Cut: You write with a pen, so you must cut with scissors.Cold: It is hot during the summer, so it must be cold during the winter.
129
130
