Free Essay

Power to Maths

In:

Submitted By thamim
Words 1102
Pages 5
|Question |Working |Answer |Mark |Notes |
|1(a) | |(400 – 308)/2 + 1 |47 |2 |M1 for (400 – 308)/2 or 46 seen |
| | | | | |A1 cao |
| | | | | | |
|1(c) | | |2n – 1 |2 |B2 cao |
| | | | | |[B1 for 2n ± k where k ≠ -1] |
|2(a) | | |4 5 6 7 8 |2 |B2 for a fully correct table |
| | | |5 6 7 8 9 | |[B1 at least 5 correct entries] |
| | | |6 7 8 9 10 | | |
| | | | | | |
|2(b) | |P(7 or 8) = 7/24 |A loss of £15 |5 |M1 for P(7 or 8) {= 7/24}or P(9 or 10) {= 3/24} oe |
| | |P(9 or 10) = 3/24 | | |M1 for ‘7/24’ x 360 x 1( = 105) or’3/24’ x 360 x 2 (= 90) |
| | |7/24 x 360 x 1 = 105 | | |M1 for 360 x 0.5 (= 180) |
| | |3/24 x 360 x 2 = 90 | | |A1 for 180 and 195 seen |
| | |Takings = 360 x 0.5 = 180 | | |C1 for ‘a loss of £15’ oe |
|3(a) | |√(48/3) |±4 |2 |M1 for √(48/3) |
| | | | | |A1 for 4 or -4 or ±4 |
|3(b) | |2x + 4 = 6(x – 1) |2.5 | | |
| | |2x + 4 = 6x – 6 | |3 |M1 for 2x + 4 = 6(x – 1) |
| | |10 = 4x | | |M1 for 4 + 6 = 6x – 2x |
| | | | | |A1 cao |
|4 | |9 x 8 + ½ x 5 x 12 |102 |4 |M1 for splitting |
| | | | | |M1 for either 9 x 8 or ½ x 5 x 12 oe |
| | | | | |M1 for 9 x 8 + ½ x 5 x 12 |
| | | | | |A1 cao |
|5(a) | | |Vague response boxes |2 |B1 for a correct criticism of the question |
| | | |Question does not include a time period| |B1 for a correct criticism of the response boxes |
| | | | | | |
| | | |How many times a month do you go to a | | |
|5(b) | | |restaurant? |2 |B1 for a relevant question inc. time period |
| | | |0 1 – 3 4 – 5 6+ | |B1 for at least 3 non-overlapping response boxes |
| | | | | | |
| | | | | | |
|5(c) | | |A leading question |2 |B1 for a ‘leading/biased’ question oe |
| | | |Restricted/biased sample | |B1 for ‘small/biased’sample oe |
| | | | | | |
|6(a) | |19.5 + 19.5/5 |23.40 |3 |M1 for 19.5/5 |
| | | | | |M1 for 19.5 + 19.5/5 oe |
| | | | | |A1 cao |
| | | | | | |
|6(b) | |72 ÷ 6 = 12 |24 |3 |M1 for 72 ÷ 6 |
| | |12 x 2 | | |M1 for ‘12’ x 2 |
| | | | | |A1 cao |
| | | | | | |
|7 | |(1 – 0.3 – 0.2)/2 x 200 |50 |4 |M1 for 1 – 0.3 – 0.2 |
| | | | | |M1 for (1 – 0.3 – 0.2)/2 or 0.25 seen |
| | | | | |M1 for ‘0.25’ x 200 |
| | | | | |A1 cao |
|8 | |½ x 6 x 8 x 2 + (8+6+10) x 9 |264 cm2 |4 |M1 for ½ x 6 x 8 or 8x9 or 6x9 or 10x9 |
| | | | | |M1 for ½ x 6 x 8 x 2 + (8+6+10) x 9 oe |
| | | | | |A1 for 264 |
| | | | | |B1 ft for cm2 |
|9(a) | | |9, 3, -1, -3, -3, -1, 4 |2 |B2 for fully correct table |
| | | | | |[B1 for 1 or 2 correct entries] |
| | | | | | |
|9(b) | | |Graph |2 |B2 ft for a fully ‘correct’ graph through their points |
| | | | | |[B1 at least 6 of their correctly plotted points] |
| | | | | | |
|9(c) | | |-3.25 |1 |B1 for an answer in the range –3.1 to -3.5 |
|10(a) | |6/12 |½ |2 |M1 for 6/12 oe |
| | | | | |A1 cao |
| | |[pic] |[pic] | | |
|10(b) | | | |3 |M1 for [pic] |
| | | | | |M1 for [pic] |
| | | | | |A1 cao |
| | | | | | |
|11(a) | |44800 ÷ 5 |8960 |2 |M1 for 44800 ÷ 5 |
| | | | | |A1 cao |
| | | | | | |
|11(b) | |7130 x 5 |35650 |2 |M1 for 7130 x 5 |
| | | | | |A1 cao |
|12(a) | |3x > 2 – 12 |x > -10/3 oe |2 |M1 for 3x > 2 – 12 |
| | | | | |A1 for x > -10/3 or better |
| | | | | | |
|12(b) | |x2 – 7x + 3x – 21 |x2 – 4x – 21 |2 |M1 for 3 correct out of 4 terms or 4 correct terms ignoring signs |
| | | | | |A1 for x2 – 4x – 21 oe |
|13 | |165 ÷ 82 > 2 |Since 165 ÷ 82 > 2 |3 |M1 for considering 165 ÷ 82 or 133 ÷ 82 oe |
| | |133 ÷ 82 < 2 |and 133 ÷ 82 < 2, the scale factors are| |A1 for correct estimated answers |
| | | |different; so not similar | |C1 for a correct conclusion based upon their answers |
| | | | | | |
|14 | | |Triangle with coordinates (-3,-1.5), |3 |B3 for a correct triangle |
| | | |(-4.5,-1.5) and (-3,-4.5) | |[B2 for an enlargement of 1.5 about (0,0) or for an enlargement of -1 about |
| | | | | |(0,0) |
| | | | | |B1 for an enlargement of 1.5 about any point] |
|15(a) | |[pic] − 5 = 3x – 6 |3/8 |4 |M1 for 3x – 6 |
| | | | | |M1 for x − 15 = 9x – 18 |
| | | | | |M1 for rearranging so that numbers and x-terms or on opposite sides of the |
| | | | | |equation |
| | | | | |A1 for 3/8 oe |
| | |(x – 6)(x + 3) | | | |
|15(b) | | |x= 6 and x = -3 |3 |M1 for (x ± 6)(x ± 3) |
| | | | | |A1 for x = 6 and |
| | | | | |A1 for x = -3 |
|16(a) | |26 |64 |1 |B1 cao |
| | | | | | |
|16(b) | | |3 |1 |B1 cao |
| | | | | | |
|16(c) | |√(24x32) = 22 x 3 |12 |2 |M1 for 22 x 3 oe |
| | | | | |A1 cao |
| | | | | | |
|16(d) | |1/42 |1/16 |1 |B1 cao |
| | | | | | |
|17(a) | |4 = k/32 |9 |4 |M1 for F = k/x2 |
| | |F = 36/x2 | | |M1 for 4 = k/32 |
| | |36/22 | | |M1 for ‘36’/22 |
| | | | | |A1 cao |
| | | | | | |
|17(b) | |64 = 36/x2 |3/4 |2 |M1 for 64 = 36/x2 |
| | |√(36/64) | | |A1 cao |
|18 | |[pic] |10/21 | |M1 for [pic] |
| | |[pic] | | |M1 for [pic] |
| | | | | |M1 for [pic] |
| | | | | |A1 for 10/21 oe |
|19 | |√8(√5 + √20) - √5 × √2 |83.33… |4 |M1 for √8(√5 + √20) - √5 × √2 oe |
| | |=2√2(√5 + 2√5) - √5 × √2 | | |M1 for 2√2(√5 + 2√5) - √10 |
| | |=2√2×3√5 - √5 × √2 | | |M1 for 5√10 / 6√10 x 100 |
| | |=6√10 - √10 = 5√10 | | |A1 for 83.33… |
| | |5√10 / 6√10 x 100 | | | |
| | |500/6 | | | |
|20(i) | |q + ½ (p – q) |½ (p+q) |5 |M1 for QP = q – p |
| | | | | |M1 for OS = q + ½ QP |
|(ii) | |RS = ½ (p+q) – ½ p = ½ q |Proof | |A1 for ½ (p+q) |
| | |RS = ½ OQ parallel | | |M1 for RS = ½ (p+q) – ½ p |
| | | | | |C1 for conclusion of proof; ie RS = ½ q and relating this to OQ = q |
|21(a) | | |πx2/3 |2 |B1 for πx2/3 oe |
| | | |2πx/3 | |B1 for 2πx/3 oe |
| | | | | | |
|21(b) | |A = 2πx/3 = 2πr |27 |3 |M1 for 2πx/3 = 2πr |
| | |r = x/3 | | |M1 for 1/3 x π x (x/3)2 x h = 3 x πx2/3 |
| | |V = 1/3 x π x (x/3)2 x h = 3 x πx2/3 | | |A1 cao |
| | |1/3 (1/3)2 x h =1 | | | |

Similar Documents

Premium Essay

Gbfs Paaper

...animation. How to apply it on a text present in a slide. 13) How will you change the case of characters from lowercase to uppercase in Msword? 14) Differentiate between Web page and Website. 15) How will you use AutoSum feature of MS Excel. 16) What are the uses of Header and Footer in MS Word? 17) Mention any two uses of bullets and numbering? 18) Define custom Path with an example. 19) Discuss the use of Min () function? Give the Syntax and explain with the help of suitable example. 20) List all the steps required to perform a mail merge. Explain with the help of an example. 21) Answer the following questions from the given table below: | A | B | C | D | E | F | G | 1 | Sl.no | Name | English | Math | Computers | Total | Average | 2 | 1001 | Karan | 66 | 73 | 71 | -- | -- | 3 | 1002 | Sanu | 70 | 98 | 87 | -- | -- | 4 | 1003 | Mohan | 67 | 95 | 82 | -- | -- | 5 | 1004 | Rohit | 68 | 89 | 83 | -- | -- | 6 | 1005 | Priya | 90 | 77 | 60 | -- | -- | 7 | Max | | | | -- | | | 8 | Count | | | | | | | a) Write the formula to calculate the Total marks and display them in column F. b)...

Words: 1466 - Pages: 6

Free Essay

Stereotyping

...powerful tool. Governments and organizational leaders charged with the distribution of these positions and resources often use stereotyping and discrimination as a process of elimination. Therefore, negative stereotyping exists in almost every sphere of participation. It exists in schools, in financial institutions, in nearly every industrial and societal sector. Sometimes, negative stereotyping is less obvious than others are. As demonstrated by the University of Toronto 2010 article, “Stereotyping has a lasting negative impact,” innuendo can yield detriment. In fact, the University of Toronto (2010) explains how one group of women taking a math test were subjected to negative stereotyping. According to the University of Toronto (2010) article, the test monitor told these women this test would prove whether they were smart in math....

Words: 938 - Pages: 4

Premium Essay

Verizon Inspire Her Mind Analysis

...use power tools. All of these activities are shut down by her parents. Her parent say, don't get mud on your dress and let your brother use the power tools. Since all of her activities involving science and math are not encouraged she starts to listen to her parents and stop exploring. When she is in Middle School she stops at a science fair poster. Instead of signing up she uses the window to put on lipgloss. Society does not make science or math ‘cool’ for girls to enjoy, so girls stop finding excitement in science and math. The commercial is...

Words: 465 - Pages: 2

Free Essay

Social Studies Teacher

...Homework – Grade 7 Week of 10/21 – 10/25 Monday, 10/21 Tuesday, 10/22 Wednesday, 10/23 Thursday, 10/24 Wksh: Power to a Power (p 2) Wksh: Division with Exponents (p 3) Wksh: Mixed Review (p 4) Study for test. Complete review sheet. Friday, 10/25 Test in class. Print out next week’s hw assignments. Have a great weekend.   Topics covered for the week Power to a power Division with exponents Textbook Additional help can be found in Chapter 1: pp 10 – 13 Chapter 4: pp 194 – 203 Chapter 9: pp 453 – 457 and p 822 Chapter 12: pp 674 – 678       Test Topics Intro to exponents/meaning of exponents Exponents with a zero power Negative exponents Exponents with similar bases Power to a power Division with exponents 1 Name _________________________ Date __________________________ Math Period ______ Power to a Power Expand each of the following expressions. 1) (2rm3)2 2) (– 4a2) – 3 3) (– 3m2p3)2 ____________________________________________________________________________________ Simplify. Write all exponents as positive if necessary. 4) (5x2)3 5) (xy3) – 5 (x2)4 • (– 3x6)4 6) ____________________________________________________________________________________ 7) (6x2y3)3 8) (– 2mn5)5 9) (4x2)2 • (3y)2 Mixed Review. Simplify. (All answers must have positive exponents) 10) – (m4)3 11) – 3x0 12) – (xy)0 ____________________________________________________________________________________ 13) xy0 14) (– m4)3 15) ( ) –3 _______...

Words: 451 - Pages: 2

Free Essay

None

...GMAT Math Refresher – Diagnostic Test GMAT Math Refresher Diagnostic Test Please take the time to complete the following diagnostic test. If you have difficulty with any of the topics, you will be directed to one of several short refresher lessons available. 1 GMAT Integer Arithmetic Evaluate the following (without a calculator) a) Math Refresher – Diagnostic Test ( −5 ) + ( −8 ) = ( −2 ) − 10 = b) c) 5 × ( −2 ) × 3 = d) ( 10 )( −2 )( 4 ) = ( −8 )( 1) e) 4 − ( −4 ) = f) If you had difficulty with any of these questions, you may want to print and complete the Math Refresher lesson “Integer Arithmetic.” b) -12 j) ( −5 ) − 9 − ( −10 ) = d) 10 i) 8 − 14 = f) 1 h) ( −6 )( −1)( −8 ) = ( −2 )( −12 ) h) -2 g) ( −10 ) − 8 + 2 = j) -4 i) -6 g) -16 e) 8 c) -30 a) -13 2 ( −5 ) + ( −1) − ( −7 ) = Answers: GMAT Decimal Arithmetic Evaluate the following (without a calculator) a) 5.278 + 0.0544 + 17.65 = Math Refresher – Diagnostic Test b) 1.2074 + 11.809 = c) 6.0287 – 4.55 = d) 1.542 – 0.9438 = e) 8.5 × 16.3 = Answers: h) 8.8 g) 1.35 f) 304.512 e) 138.55 d) 0.5982 c) 1.4787 b) 13.0164 a) 22.9824 3 f) 6.24 × 48.8 = g) 57.78 ÷ 42.8 = h) 27.5 ÷ 3.125 = If you had difficulty with any of these questions, you may want to print and complete the Math Refresher lesson “Decimal Arithmetic.” GMAT Fractions Math Refresher – Diagnostic Test Evaluate the following and express...

Words: 765 - Pages: 4

Free Essay

Math Facts

...“Memorizing math facts is the most important step to understanding math. Math facts are the building blocks to all other math concepts and memorizing makes them readily available” (EHow Contributor, 2011). To clarify, a math fact is basic base-10 calculation of single digit numbers. Examples of basic math facts include addition and multiplication problems such as 1 + 1, 4 + 5, 3 x 5 and their opposites, 2 – 1, 9 – 4, 15/5(Marques, 2010 and Yermish, 2011). Typically, these facts are memorized at grade levels deemed appropriate to a student’s readiness – usually second or third grade for addition and subtraction and fourth grade for multiplication and division. If a child can say the answer to a math fact problem within a couple of seconds, this is considered mastery of the fact (Marques, 2010). Automaticity – the point at which something is automatic- is the goal when referring to math facts. Students are expected to be able to recall facts without spending time thinking about them, counting on their fingers, using manipulatives, etc (Yermish, 2011). . In order to become a fluent reader, a person must memorize the sounds that letters make and the sounds that those letters make when combined with other letters. Knowing math facts, combinations of numbers, is just as critical to becoming fluent in math. Numbers facts are to math as the alphabet is to reading, without them a person cannot fully succeed. (Yermish, 2011 and Marquez, 2010). A “known” fact is one that is “answered...

Words: 1902 - Pages: 8

Free Essay

Effective Curriculum

...creating engaging lessons that supports all areas of the child development and the program purpose. Teachers are allowed to be flexible in their creation of their lesson plans. Regardless of how the themes or topics are selected, the early childhood administrator must continually review and monitor the curriculum plans that teachers select or create, making sure that the curriculum is aligned with the program's philosophy(Gadzikowski, A., 2013). Ole Faithful program curriculum allows teachers to create their own lesson plans based on the theme for the week but it is reviewed by the administrator before it is applied in the classroom. Teachers play such an important role in helping making sure that the programs curriculum is implemented. If math is an integral part of a programs curriculum then the administrator will create opportunities for teachers to teach the appropriate skill with the appropriate materials. A teacher’s role includes giving input on what materials and activities that may be beneficial to teaching their students how to count. Among the school staff, teachers spend the most time with the students which are why teachers are a vital part of the decision-making process because they know what works and what needs improvement. In a well built curriculum teachers are allowed to make small changes as long as they are meeting the standards....

Words: 2297 - Pages: 10

Free Essay

Lesson Plam

...Mathematics overview: Stage 7 Unit | Hours | Mastery indicators | Essential knowledge | Numbers and the number system | 9 | * Use positive integer powers and associated real roots * Apply the four operations with decimal numbers * Write a quantity as a fraction or percentage of another * Use multiplicative reasoning to interpret percentage change * Add, subtract, multiply and divide with fractions and mixed numbers * Check calculations using approximation, estimation or inverse operations * Simplify and manipulate expressions by collecting like terms * Simplify and manipulate expressions by multiplying a single term over a bracket * Substitute numbers into formulae * Solve linear equations in one unknown * Understand and use lines parallel to the axes, y = x and y = -x * Calculate surface area of cubes and cuboids * Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines | * Know the first 6 cube numbers * Know the first 12 triangular numbers * Know the symbols =, ≠, <, >, ≤, ≥ * Know the order of operations including brackets * Know basic algebraic notation * Know that area of a rectangle = l × w * Know that area of a triangle = b × h ÷ 2 * Know that area of a parallelogram = b × h * Know that area of a trapezium = ((a + b) ÷ 2) × h * Know that volume of a cuboid = l × w × h * Know the meaning of faces, edges and vertices * Know the names of special triangles and quadrilaterals...

Words: 4838 - Pages: 20

Free Essay

Cheating on Exams

...2009) Internet based classes are experiencing a growth surge. With the recent employment crisis, and the increased weight on academic achievement, more adults are now able to enroll in online classes, and still maintain full time jobs and meet the demands of busy families. In a study conducted by Oskar Harmon and James Lambrinos they used a “model that predicts exam scores from independent variables of student characteristics. In one course, the final exam was proctored, and in the other course, the final exam was not proctored. In both courses, the first three exams were un-proctored. If no cheating took place, the authors expected the prediction model to have the same explanatory power for all exams, and conversely, if cheating occurred in the un-proctored exam, the explanatory power would be lower. Their findings are that both across and within class, variations in the R-squared statistic suggest that cheating...

Words: 621 - Pages: 3

Premium Essay

Communication Styles Worksheet

...problems you may have in school. You also have an academic councilor and a financial advisor helping you out as well as checking on you throughout your college experience. The CWE helps you develop essential written communication skills. Good writing skills are important to academic and professional success. If you have excellent written communication skills when you graduate you’ll have an advantage in most professional work environments. The CWE also provides a write point program. The write point processes your paper and reviews it and provides feedback there’s also a plagiarism checker which make sure the papers you submit aren’t plagiarized. The CME helps build math confidence by providing tutorials, videos, practice problems, tip sheets, power points, web links, and other resources to help you get ready for your math class. You asked your facilitator to review your e-mail draft. She liked what you wrote and asked you to write a summary to post in the class forum for the other students to read. Write a 150- to 200-word summary for your class of the resources available to students. Remember to write using an academic tone. The University of Phoenix Online Learning System has lots of different programs and services...

Words: 461 - Pages: 2

Premium Essay

Alexander The Great's Legacy

...The Legacy of Alexander the Great Alexander the Great came to power when he was just twenty years old. One vital part of Alexanders legacy was the spread of Hellenism across his widely spread empire. His reign lasted from 336 to 323 B.C. After the father of his death is when he gained his power. He went on to conquer Persia and Egypt, he had expanded his kingdom from the Mediterranean to India. His reign ended at the age of 32 when he was killed by an unknown illness. Alexander’s legacy was marked by the cities he founded, the new roles he created for women, new schools of philosophy, and his well-known advancements in math and science. Alexander the Great founded 24 cities in his short lived reign of power. His most recognized city is Alexandria in Egypt. Alexandria was founded in 331 B.C. and quickly grew to be one of the greatest cities of the Hellenistic world. Rome was slightly more superior to Alexandria in size and wealth. The cities were based off of a grid plan which creates easy access to the cities. All Greek cities had 5 essentials a theatre, being the most important of the city, a temple, a gymnasium, a marketplace (Agora), and a mall. Alexander the Great had finally managed to give power to women. In most early civilizations women had...

Words: 618 - Pages: 3

Premium Essay

Summary Of What Is A Life Worth By Amanda Ripley

...claim that there shouldn’t be a price tag on someone’s life and that the simple formula is not the right thing to do. Ripley also describes this simple formula as “cold hearted math,” making us feel some type of negative emotion for this. I on the other hand, am with this “cold hearted math.” The way the government determined the amount to pay the victim's family following the 9/11 tragedy was the right decision. The government came up with a simple way to calculate the amount of money each person got: the salary at the time of death X years of work until retirement = the amount of money the family receives. First of all, the government had not limit to the federal fund. In other words, the government could have easily gave each victim's family the same amount of money regardless of their background or position. Instead, the government was clever enough to make the simple formula. This way, fairness is the base, giving each victim what they deserve and equality gets eliminated....

Words: 563 - Pages: 3

Premium Essay

Number Sense in Children

...elementary level. The idea that students should already have some number sense is controversial. Struggling students in today’s classroom in the area of math seem to lack a major concept, which is a basic math skill or understanding numbers. What is number sense? Number sense refers to a person's general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving complex problems. Number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. Most children acquire this conceptual structure informally through interactions with parents and siblings before they enter kindergarten (Marshall 2010) . Other children who have not acquired it require formal instruction to do so. For example, one child may enter school knowing that 8 is 3 bigger than 5, whereas a student with less well-developed number sense may know only that 8 is bigger than 5. Other children may have very well-developed number sense and may have a strategy for figuring out how much bigger 8 is than 5 using fingers or blocks. This number sense not only leads to automatic use of math information, but also is a key ingredient in the ability to...

Words: 1428 - Pages: 6

Premium Essay

Gender Discrimination In The United States

...For many centuries, discrimination has been a problem all around the world. Discrimination is not stationed in one spot, it happens in all countries.Human right laws prohibited discrimination against race,sex,religion, marital status, age, and pregnancy this happened in 2011 in European Union Legislation, United Nations Legislation, and United States Federal Legislation. (Custers,1) Women are considered to be a minority group because they do not share the power, privilege, and rights as men. This problem is just not a problem in the United States discrimination of gender happens globally. The discrimination for any minority group goes in a vicious cycle that repeats over and over again. Discrimination of women happens all the time in society....

Words: 861 - Pages: 4

Premium Essay

Art of Conversation

...Nine Ways How do we help floundering students who lack basic math concepts? Marilyn Burns aul, a 4th grader, was struggling to learn multiplication. Paul’s teacher was concerned that he typically worked very slowly in math and “didn’t get much done.” I agreed to see whether I could figure out the nature of Paul’s difficulty. Here’s how our conversation began: P MARILYN: Can you tell me something you know about multiplication? PAUL: [Thinks, then responds] 6 x 8 is 48. MARILYN: Do you know how much 6 x 9 is? PAUL: I don’t know that one. I didn’t learn it yet. MARILYN: Can you figure it out some way? PAUL: [Sits silently for a moment and then shakes his head.] MARILYN: How did you learn 6 x 8? PAUL: [Brightens and grins] It’s easy—goin’ fishing, got no bait, 6 x 8 is 48. connects to addition. Paul wasn’t the only student in this class who was floundering. Through talking with teachers and drawing on my own teaching experience, I’ve realized that in every class a handful of students are at serious risk of failure in mathematics and aren’t being adequately served by the instruction offered. What should we do for such students? Grappling with Interventions My exchange with Paul reminded me of three issues that are essential to teaching mathematics: I It’s important to help students make connections among mathematical ideas so they do not see these ideas as disconnected facts. (Paul saw each multiplication fact as a separate piece of information to memorize.) I It’s important to...

Words: 3526 - Pages: 15