Biology 2010 Content



YOUNGSTOWN CITY SCHOOLS

ACCELERATED MATH: GRADE 7

Unit 1: ADDING AND SUBTRACTING RATIONAL NUMBERS (3 WEEKS)

SYNOPSIS: In this unit, students will gain a greater understanding of how to add and subtract positive and negative rational numbers. Students learn that rational numbers include fractions, mixed numbers, and decimals. Students will solve real-life problems where addition and subtraction of rational numbers are used.

STANDARDS

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram

a. Describe situations in which opposite quantities combine to make 0. (e.g., a hydrogen atom has 0 charge because its two constituents are oppositely charged.) (7.NS.1a)

b. Understand p + q as the number located a distance | q | from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. (7.NS.1b)

c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. (7.NS.1c)

d. Apply properties of operations as strategies to add and subtract rational numbers. (7.NS.1d)

7.NS.3 Solve real-world and mathematical problems involving the four operations - - addition and subtraction only in this unit - - with rational numbers (note: computations with rational numbers extend the rules for manipulating fractions to complex fractions) [note: computations with rational numbers extend the rules for manipulating fractions to complex fractions. The standards define complex fractions as: a fraction A/B where A and/or B are fractions (B nonzero) e.g., 5/7 /1 + 3/5].

MATH PRACTICES:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning

LITERACY

L.1 Learn to read mathematical text - - problems and explanations

L.2 Communicate using correct mathematical terminology

L.4 Listen to and critique peer explanations of reasoning

L.5 Justify orally and in writing mathematical reasoning

|MOTIVATION |TEACHER NOTES |

|Review / determine students’ level of understanding about positive and negative numbers and zero - - |TEACHERS: USE CALCULATORS SPARINGLY AND |

|integers. Let students know that we are building on this to include rational numbers. Work with students |LIMIT TO 4-FUNCTION CALCULATORS. THE PARCC |

|to complete the visual organizer for the Real Number System: Counting/Natural Numbers, Whole Numbers, |ASSESSMENT WILL ONLY ALLOW THE 4-FUNCTION |

|Integers, and Rational Numbers - - see graphic attachment at end of Unit (page 8 ). Make a wall chart for|CALCULATORS AT GRADE 7. |

|student reference as they work through the unit. Use 4-part paper folding activity to show the components| |

|of the rational numbers in the Real Number System (MP-3, MP-7) |Stress that only whole numbers and their |

| |opposites and 0 are integers. |

|Let students know that there is another set of numbers, called irrational numbers that will be done in 8th| |

|grade. (page 9) | |

| | |

|Preview expectations for the Authentic Assessment at end of Unit. | |

| | |

|4. Have students set both personal and academic goals for this Unit. | |

|TEACHING-LEARNING |TEACHER NOTES |

|1. Teacher displays a horizontal number line with a range of -20 to +20. Identify zero as well as positive |Reference Materials for Teachers: |

|(to the right) and negative (to the left) integers. Teacher then turns the number line to a vertical position |Glencoe Pre-Algebra Teacher Manual: |

|(positive numbers are on the top and negative numbers are on the bottom). Relate the number line to real-world|Section 2.2 and 2.3, on adding |

|examples - - such as a submarine or iceberg with sea-level; a thermometer with plus and minus temperatures, |integers |

|etc. [7N.S.1a,b,c] For extra support and practice, use Distances on the Number Line, attached on page 10 and | |

|Distances Between Houses, attached on pages 11-13. |Scott Foresman Course 3: Chapter 2, |

| |sections 1, 2, and 3 |

|2. Teacher reviews VOCABULARY and concepts for the unit: absolute value, absolute value notation and symbol, | |

|opposites as additive inverse; positive and negative numbers, integers, rational numbers, real numbers. |Simplified Solutions: Grade 7: |

|[7N.S.1a,b,c] |Lesson 2 and 3 |

|a. have students work with a large number line on the floor and students hold a + or – number (e.g., +2, -7) | |

|and show how far each number is from zero. Note: you can also use a number line on the board or sets of stairs |BrainPop |

|with the landing being 0. Movement to the left for negative numbers and the right for positive. | |

|b. have students take +2 and -2 to show opposites equal zero. Use money example of “I have $2 and I owe $2 to | |

|someone; therefore, I have zero dollars to show additive inverse | |

|c. next move to +7 and -2; have students move along the number line to show that they are not the same distance| |

|from zero. (MP-1, MP-2) | |

| | |

|3. Teacher models how to represent fractions and their equivalent decimals that are positive and negative on | |

|the number line; teacher reminds students what makes a number an integer; if a number is a fraction or decimal,|Show number line and equation for 4a, |

|it is NOT an integer—it is not the sign that makes it an integer. |4b, 4c |

|a. Students offer other examples as the teacher places points on the number line | |

|b. Students identify the positive and negative fraction and decimal that names a point on the number line. | |

|c. Teacher relates fraction and decimal to the nearest whole number on the number line (e.g., -2 [pic] is | |

|closer to -3. Students give other examples to demonstrate understanding of fractions and decimals on the | |

|positive and negative side of the number line. [7N.S.1a,b,c,d] (L.2; L.5) (MP-5, MP-8) | |

| | |

|Website for integer football: | |

|games/integer_game/football.htr | |

|4. Teacher poses a problem for ADDITION OF RATIONAL NUMBERS: [7N.S.1a,b,c,d & 7N.S.3] | |

|a. ADDING A POSITIVE NUMBER AND A POSITIVE NUMBER (e.g., If you earn $4 on Monday and $2.50 on Tuesday, how | |

|much was earned?) Have students represent the problem on a number line and show answer using arrows as well as | |

|writing the equation to represent the situation. (L.1, L.2, L.4, L.5) | |

| | |

|Fraction Example: A bird watcher on a cliff saw an eagle 60 ¾ feet above him. The eagle ascended 23 [pic] | |

|feet. What is the eagle’s current altitude? (60 [pic] + 23 [pic] ) | |

| | |

|Decimal Example: At the beginning of 7th grade, Brandy was 146.2 cm tall. She grew 7.08 cm by the end of the | |

|school year. What is her height at the end of the year? (146.2 + 7.08) | |

| | |

|Integer Example: There are 18 players on the Panthers basketball team, 19 players on the Vikings basketball | |

|team, and 23 players on the Wildcats basketball team. Find the total number of players on the three teams. | |

| | |

|b. ADDING A POSITIVE NUMBER AND A NEGATIVE NUMBER (e.g., the temperature at noon was 8°Celsius; at midnight it | |

|had dropped 15°. What was the temperature at midnight?). Have students show on the thermometer and write the | |

|equation for the situation. Have students explain how to re-write the equation to have an addition equation; | |

|have them show on the number line how this would look and explain how this is different than the problem in | |

|4a. (L.2, L.4, L.5) (MP-2, MP-4) | |

| | |

|Decimal Example: You are starting a lawn mowing business. You borrow $255.75 from your parents for the | |

|equipment and gasoline. By the end of the summer you have earned $629.40. What is your profit? | |

|($-255.75 + $629.40) | |

| | |

|Fraction Example: A seagull dives down -3 [pic] feet below the water to catch a fish. It then soars up 15 | |

|[pic] feet to a rocky ledge. How far above sea level is the ledge? (3 [pic] + 15 [pic] ) | |

| | |

|Integer Example: At 7:00 a.m. the temperature in Youngstown, Ohio was -7°F. By noon the temperature went up | |

|10°F. What is the temperature at noon? | |

| | |

|c. ADDING TWO NEGATIVE NUMBERS (e.g., a whale is swimming at a depth of 50 feet below sea level, and then the | |

|whale dives another 30.5 feet. What is the depth of the whale now?) Students determine the depth and explain | |

|how they got to the answer. To help students see this, have a picture of water to show below sea level with | |

|scale of 10 on the number line. Students write the equation and model on the number line. | |

|Decimal Example: Carlos borrows $17.41 from his father and borrows $15.78 from his mother. How much money does| |

|he owe his parents? [$-17.41 + ($-15.78)] | |

| | |

|Fraction Example: A groundhog is in a hole [pic] yards deep. It burrows another [pic] yards. How far below | |

|the ground is the groundhog? [- [pic] + (-[pic])] | |

|Integer Example: The running back for the East Panthers lost 3 yards on the first play from scrimmage. On the | |

|second play he was dropped in the backfield for another loss of 9 yards. How many yards has he lost for the | |

|day? | |

| | |

|Have students use the concepts in a-c to show if the answers could be 0. For example, ask students - - “can | |

|you add 2 positive numbers and get 0? Can you add a positive and negative numbers to get 0? Can you add 2 | |

|negative numbers and get 0?” (L.1, L.2, L.5) (MP-1, MP-3) | |

| | |

|Have students play “Win A Row” game attached to unit plan on page 14 | |

|FORMATIVE ASSESSMENT: see Teacher Classroom Assessment #1. | |

| | |

|Teacher poses a problem for the SUBTRACTION OF RATIONAL NUMBERS: [7N.S.1.c,d & 7N.S.3] (MP-2, MP-4) | |

|As students are working through the problems below, develop a list of words that connote positive and negative | |

|for word problems. Some examples are: owed (-), earned (+), debt (-), below (-), above (+), deduct (-), | |

|increase (+), decrease (-), purchase/buy, ate, lose, sell, and stolen. | |

|SUBTRACTING A POSITIVE NUMBER FROM A POSITIVE NUMBER (e.g., you have $54 and you paid $37 for something; how | |

|much do you have?) | |

|Decimal Example: The temperature of the water was 76.5˚F at noon. The water temperature dropped 13.6˚F by 8 | |

|p.m. What is the temperature at 8 p.m.? (76.5-13.6) | |

| | |

|Fraction Example: There was 1 ¾ pizzas left over after the party. We ate [pic] of a pizza later. How much | |

|pizza remained? (1 ¾ - [pic]) | |

| | |

|Another Fraction Example: John is jumping into a pool from a 12 feet high diving board. He dives down 26 | |

|[pic] feet. How far is John from the water’s surface? (12 – 26 [pic]) | |

| | |

|Integer Example: You have $115. You go to the mall and buy a pair of shoes for $79. How much money do you have | |

|left to take your teacher out to lunch? | |

| | |

|SUBTRACTING A NEGATIVE NUMBER AND A POSITIVE NUMBER (e.g., you have $35 and owe $75…). Reinforce using | |

|subtraction to find distance and also finding the difference. The building elevation problem (e.g., basement | |

|floor elevation is -12 feet and the elevation of the roof is 32 feet. What is the total distance from roof to | |

|basement floor?) Have students speculate how they would figure this out and then try it, explaining each step | |

|as they go. Teacher should ask students what is wrong with adding to find the answer? Have students make a | |

|drawing to figure out the answer to the elevation problem and show on the vertical number line. Have students | |

|write a subtraction equation. NOTE: show students that 32 – (-12) is = to 32 +12. Discuss how one cannot | |

|have a negative distance and refer to absolute value as distance from zero or amount moved. | |

|Decimal Example: One day the Sahara Desert had a temperature of 136.8˚F. The same day the Gobi Desert had a | |

|temperature of -51.3˚F. What is the difference between these two temperatures? [136.8 - (- 51.3)] | |

| | |

|Fraction Example: The bucket of a well is hanging 2 [pic] yards above the ground. The bottom of a well is 10 ½| |

|yards below the ground. How far is the bucket from the bottom of the well? [2 [pic] - (-10 ½)]. | |

| | |

|Integer Example: You write a check to me for $499 for a new IPAD. You now have $879 in your bank account. I | |

|just hit the lottery and say “you don’t have to pay me.” If you remove the negative amount of the check, what | |

|is the balance in your checking account? | |

| | |

|Teacher poses other subtraction problems, using problems from Teacher Resources: Simplified Solutions, Grade 7| |

|page 21; lesson 5 and page 23, Lesson 5, question 5. | |

| | |

|SUBTRACTING TWO NEGATIVE NUMBERS (e.g., Juan owed Judy $6. She told him he could subtract $2 of what he owed | |

|if he would feed her dog. ) Students represent the problem on the number line and write the equation; students | |

|explain and discuss this problem; they should relate this problem to work they did in other problems. | |

| | |

|Decimal Example: Metal mercury at room temperature is a liquid. Its melting point is -39.1˚C. The freezing | |

|point of alcohol is -114.09˚C. How much warmer is the melting point of mercury than the freezing point of | |

|alcohol? [-39.1 – (-114.09)] | |

| | |

|Fraction Example: A shark is swimming 1[pic] miles below sea level. A sea turtle is swimming ¾ mile below sea| |

|level. What is the distance between them? [-[pic] - (- 1[pic])] or (-[pic] + 1[pic]) | |

| | |

|Integer Example: You have 7 negative checks on your behavior chart. Your teacher says if you behave for the | |

|rest of the week, she/he will take away 4 of those negative checks. How many negative checks will you have at | |

|the end of the week if you can control your behavior? | |

|Students then practice subtracting a variety of problems with the types in a-c above. Go to National Library | |

|of Virtual Manipulatives website to get color chip addition and subtraction activity – nlvm.usu.edu – Review | |

|the +1 -1 = 0 (zero / neutral pair concept; have students model using colored chips at their desks. (L.1, L.2)| |

|(MP-3, MP-7) | |

| | |

|FORMATIVE ASSESSMENT GAMES: see Teacher Classroom Assessment #2. | |

| | |

| | |

|6. Teacher asks students if the following statements are always, sometimes, or never true, to check for their | |

|level of understanding with strategies involved in the addition and subtraction of rational numbers: | |

|*Is this true always, sometimes, or never?* | |

|The sum of a positive number and a negative number is a negative number. (sometimes) | |

|The sum of a positive number and a positive number is a positive number. (always) | |

|The sum of a number and its opposite is zero. (always) | |

|The absolute value of a positive is a negative. (never) | |

|The sum of two negatives numbers is greater than both numbers. (never) | |

|The difference between a positive number and a positive number is a positive number. (sometimes) | |

|The difference between a negative number and a negative number is a negative number. (sometimes) | |

|If the answer is not “always,” students should provide an example of when the statement does not work. | |

| | |

|7. Teacher uses the lessons: ”Zeroing In” and “Irrational Numbers - - They’re Insane” in Teaching the Common | |

|Core Math Standards with Hands-on Activities pages 154 - 156. (8.NS.2; L.1, L.2, L.3, L.5, L.6 ,L.7, L.8; | |

|M.P.1, M.P.2, M.P.4, M.P.5, M.P.7, M.P.8) | |

|To review the idea of square roots and consecutive integers, have students identify the [pic] [pic] [pic] | |

|[pic] ; then ask them if you were to find the [pic] and show that it is between 2 and 3, etc.) Teachers | |

|follow the lesson in Teaching the Common Core Math Standards with hands-on Activities pages160-161. (8.EE .2) | |

| | |

|8. Have students practice a variety of problems. Resources: Foresman/Wesley Math 3 pages 369 – 373; Glencoe | |

|Pre-Algebra pages 436 – 439; Glencoe Algebra I page 107 #s 20 -31 (Approximate the square root problems only) | |

|(M.P.1) | |

| | |

|9. Students create a clock face to show the concepts illustrated throughout the unit. Sample is attached to | |

|Unit plan. Students should not have their clock face look like the numbers in the sample. They can use | |

|fractions, decimals, radicals, terminating and repeating decimals, sets with operations, etc. They identify | |

|the label for the type of number used. Students must show three examples of irrational numbers that could not | |

|be used for the situations in the project. Have students work independently to create their own clock faces. | |

|Have students evaluate each other’s work. Clock face attached on page 7 (8.NS.1; 8.NS.2; MP.2; L.2; L.4; L.5)| |

|TRADITIONAL ASSESSMENT |TEACHER NOTES |

|Paper-pencil test with M-C questions and 2-and 4-point questions | |

|Possible 2 pt. question: Alberto subtracts different negative integers from 13. Show three different examples of | |

|what Alberto does. Explain what happens when you subtract different negative integers from 13. | |

|TEACHER CLASSROOM ASSESSMENT |TEACHER NOTES |

|1. FORMATIVE ASSESSMENT that follows Teaching –Learning Activity #4: students solve 3 types of word problems for | |

|adding integers where students show the equation and represent each problem on the number line. | |

| | |

|FORMATIVE ASSESSMENT GAMES follows Teaching-Learning Activity #5: | |

|Positive & Negative Playing Card Games: Students use the numbers 1 (ace) through 10 in a regular deck of playing | |

|cards. The red cards represent negative numbers and the black cards represent positive numbers. Students can play | |

|war with a partner by comparing the value of the cards. Also, teacher can assign equations for students to complete| |

|with their partner. For example, x + y = ? or x – y = ?, where the first card flipped represents “x” and the second| |

|card flipped represents “y”. Students can work together to solve the problem using the strategies learned for | |

|positive and negative numbers. | |

|Tic-Tac-Integers Game: Students work with a partner by placing either their positive or negative numbers on a grid | |

|sheet. Together with their partner, students find the sum of their rows and columns. If more sums are positive, | |

|the student who played the positive numbers wins. If more sums are negative, the student who played the negative | |

|numbers wins. Tic-Tac-Integers Game instructions are included in the Unit Plan on page 15 | |

|AUTHENTIC ASSESSMENT |TEACHER NOTES |

| Students evaluate goals they set at beginning of unit. | |

| | |

|Alphabet Integer Activity- attached on pages 16-17 of Unit Plan | |

| | |

|Students write real-life word problems that require addition or subtraction of rational numbers for the solution. | |

|Each student should present the solution for the problems written. Problems will be distributed to other students | |

|to solve. | |

|RATIONAL NUMBERS |IRRATIONAL NUMBERS |

|Integers | |

|Whole numbers | |

|Natural/Counting Numbers | |

REAL NUMBERS

[pic]

DISTANCES ON THE NUMBER LINE

[pic] [pic]

DISTANCES BETWEEN HOUSES [pic] [pic] [pic]

WIN A ROW

OBJECTIVE: To win the largest number of rows and columns on the game board.

MATERIALS: pencil and game board

PROCEDURE:

❖ Determine who is Player #1 and who is Player #2

❖ Player #1 places one of the numbers 1, 2, 3, 4, 5, 6, 7, or 8 in the square of his/her choice. Player #2 does the same but with one of the number -1, -2, -3, -4, -5, -6, -7, or -8. As the numbers are placed, cross them off below.

❖ Alternate play until the squares are filled and all of the numbers are used.

❖ Add the numbers in each row, and place in the blanks to the right under the word, “SUM.”

❖ Add the number in each column, and place in the blanks below each column.

❖ Player #1 gets a point for each positive sum, and Player #2 gets a point for each negative sum.

❖ If there is a tie, find the sum of the downward (from left to right) diagonal to decide the final winner.

CHALLENGE: Play again and use larger numbers!

| | |SUM |

| | | | | | |

| | | | | | |

| | | | | | |

| | | | | | |

| | | | | | |

| | | | | | |

| | | | | | |

| | | | | | |

______ _____ _____ _____ _ _ _ _ _ _ _

1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 -7 -8

Tic-Tac-Integers (A Game involving the Addition of Integers)

[pic]

Materials

[pic]Grid box that is 4 boxes by 3 boxes

[pic]

Players

2

[pic]

Skill

Addition of positive and negative numbers

[pic]

Object of the game To score more points.

[pic]

Directions

[pic]

1.

Player 1 uses the positive numbers 1, 2, 3, 4, 5, and 6. Player 2 uses the negative numbers -1, -2, -3, -4, -5, and -6.

[pic]

2.

Player 1 begins the game. Players take turns writing one of their numbers in a cell within the 3–by–4 rectangle outlined on the spreadsheet. Once a player has written a number, it cannot be used again.

[pic]

3.

After all 12 numbers have been used, fill in Total cells F2, F3, and F4 by adding each row across. For example, F2 = B2 + C2 + D2 + E2. Fill in Total cells B5, C5, D5, and E5 by adding each column down. For example, C5 = C2 + C3 + C4.

[pic]

4.

Seven cells show row and column totals: F2, F3, F4, B5, C5, D5, and E5. Player 1 gets one point for each cell that contains a positive number. Player 2 gets one point for each cell that contains a negative number. Neither player gets a point for a cell that contains 0. The player with more points wins.

[pic]

[pic]

AUTHENTIC ASSESSMENT: ALPHABET INTEGER ACTIVITY

Name: _________________________

Using your Alphabet Integer Card (on the next page), complete the following activities:

1. Find the value of your first name and compare it to a classmate’s. Is your first name greater than, less than, or equal to your classmate’s name?

2. Find the value of your last name and compare it to a classmate’s. Is your last name greater than, less than, or equal to your classmate’s name?

3. Find a five-letter word with the least possible value.

4. Find a five-letter word with the greatest possible value.

5. Find the value of the month in which you were born. Is it a “positive” month or a “negative month?

6. Add the value of your first name to the value of the first name of one of your friends. If the value is positive, maybe you have found your best friend. If you do not want to do a friend, add the value of the first name of your teacher.

7. Predict which of the following State names will have the highest value: MISSISSIPPI, WYOMING, VERMONT, WASHINGTON, NEW YORK, MINNESOTA, PENNSYLVANIA, and MISSOURI. Check your prediction by computing the value of each one.

8. Find the integer value of both Martin Luther King, Jr. and another famous person (your choice) . Compare the values of the names.

ALPHABET INTEGER CARD

Use the Alphabet Integer Card to find the value for given words by finding the sum of the integer values.

Example: MATH = M (-1), A (-13), T (7), H (-6) = (-1 + -13 + 7 + -6) = -13

| |A |B |C |D | |

| |-13 |-12 |-11 |-10 | |

|E |F |G |H |I |J |

|-9 |-8 |-7 |-6 |-5 |-4 |

|K |L |M |N |O |P |

|-3 |-2 |-1 |+1 |+2 |+3 |

|Q |R |S |T |U |V |

|+4 |+5 |+6 |+7 |+8 |+9 |

| |W |X |Y |Z | |

| |+10 |+11 |+12 |+13 | |

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