Math 5

McGraw Hill My Math 

 

*Note: All problems listed below from the book are in the "Independent Practice" or "Practice It" section of each lesson unless otherwise noted. The "Guided Practice" problems in each lesson are a good place for the student to get assistance from parents, teacher, etc. before trying the "Independent Practice" problems on his or her own. The "My Homework" Practice problems can also be a good place for extra practice or practice with assistance. The lesson's examples and online videos are good resources for guidance. Many answers can be checked in the back of the book and other answers are online.  Extension problems and tasks are for all interested students. They are only listed separately because they are not essential to show a basic understanding of the lesson content. 

 

Week 1: Aug 27- Aug 31

1-1 (Chapter 1 - Lesson 1) #4-7, 9-10 standard form only, 13, 15, 16.  Extension: #16. 

1-2 (Chapter 1 - Lesson 2) #4-13, 16,17, 22

Kahn Academy - Decimals: Expanding Place Value

Task #1: Number Visuals

______________________________________

 

Week 2: Sept 3-7

1-3 #4-18. Extension: #19. 

1-4 #4-11, 16

1-5 Compare $2.00, $0.20, $0.02  Which is the most money? Which is the least? Explain how the position of the "2" affects how much money it is? Discuss other examples of place value and money with a parent, sibling, or teacher.

Task #2: Use all of the digits 0-9 to form one and two digit numbers that make a big addition problem with the goal of the numbers adding up to 100. Keep trying until you get as close to 100 as you can. When you get exactly 100 or very close, show your work as you simplify your problem to get your answer.  Example: 53+92+10+4+7+8+6 ... way to big though!

______________________________________

Week 3: Sept 10-14
 
1-6 #6-17
 
 
1-7 #3-14, 18 
1-8 #5-14, 18
 
 
Task #3: Get at least ten each of pennies and dimes, and then get at least ten each of $1, $10, and $100 bills by cutting paper to make fake money or getting bills from a game like Monopoly. Have a parent make up an amount of money, like $629.04, or $301.70. Gather the appropriate amount, and put it in separate piles according to type. Keep making up different amounts to gather. Then, switch the task so the parent just presents you with a pile of money and you have to total it. Discuss the importance of place value with your parent in terms of money. For example, why would you never get ten pennies back (ignoring nickels of course)? Would you rather have 70 pennies or 9 dimes? How many times more money is 5 tens than 5 pennies? Would you rather have $10 or $9.99?
______________________________________
 
Week 4: Sept 17-21
 
1-9 #1-4, 6. Extension: #5,9
 
Chapter 1 Review (pg 67-69) #12, 13, 16-23
Page 73 #1-17
 
Task #4: Create your own word problem that involves money that is being earned and money that is being spent on one day. The answer to your problem must be: "At the end of the day, you have $4.70 remaining." Your task is to create the situation and math word problem that will result in that answer. 
______________________________________
 
Week 5: Sept 24 – Sept 28
 
Page 73 #1-17
If necessary, review “Prime Numbers.”
 
 
2-1 #3-9odd. Extension #17.
2-3 #2-11, 18. Extension #12-15.
2-4 Guided Practice #1, 2.
2-4 #3, 5, 8, 10, 11, 15.
 
 
Page 104 #9.
 
Task #5: Try 3,000 times 40,000 using the standard multiplication method by hand. Then think about powers of 10 and the number of zeros to determine the answer much more quickly. Compare how much time and effort was saved!
______________________________________
 
Week 6: Oct 1 – Oct 5
 
Note: Times Tables from 1-10 ideally need to be memorized before these lessons.
Page 106  all
Page 107-108 #1-3, 5-7. Extension #8.
2-6 #4-7,11.
 
Go through all the videos in this thread.
 
2-7 #3-13odd.
2-8 #3-13odd.
2-9 #3-13odd, 16. Extension #17.
 
Task #6: Why does it work to regroup or break down 42 * 6 into (40 * 6) + (2 * 6)? Why is it helpful? Why is 40 * 6 so convenient to work with? How does it help estimate the answer ?
______________________________________
 

Week 7: Oct 8 – Oct 12

Note: Times Tables from 1-10 ideally need to be memorized before these lessons.

2-10 #3-15odd.

Kahn Academy - Multiplying Multi Digit Numbers

Page 142 #5-7.

Optional: Page 143 #1-20. Page 144 #1-10. Do only if you need the extra practice.

Extension: Page 143 Identify some problem you can do in your head by regrouping numbers. For example, for #3, you could do 30*3 and then add 1*3.

3-1 #9-17

Page 162 #11-14.

Task #7: Determine as many different pairs of whole numbers as you can that multiply to equal 360. (Assume that 1*360 is the same as 360*1, so it only counts as one pair.) How can you organize your answers so that you can be sure that you have tried all of the possibilities? Hint: there are 12 pairs of numbers.

______________________________________

Week 8: Oct 15 – 29

3-2 #2-11. (Drawing out not mandatory, but can be fun to do and very helpful for some students.)

3-3 #3-15. Extension: #16, 17.

3-4 #2-17.

Kahn Academy - Intro to Long Division

Task #8: Determine all of the different ways you can divide 24 granola bars into piles that would have an equal number of granola bars. Show the piles as circles and the number of granola bars as tick marks. (If you don’t want to draw out 24 circles with one tick mark each you can skip that one.)

______________________________________

Week 9: Oct 22 – 26

3-5 #2-16. (This estimation with mental math is very important. When we do these problems for exact answers later, a rough estimate helps us know if our answer is reasonable. For example, if you do 545 divided by 5 and get 10.9 (because of simply putting the decimal in the wrong place), we need to know that this answer is not reasonable! Note: It doesn’t matter if a student rounds 545 to 550, 500, or 600… the rounding is flexible.

Optional: 3-6 #2-5.

3-7 #2-5, 9-11. The “bar diagrams” (also called “area models”) are very helpful, regularly used, and connect to the concept of rectangle area. Do not skip the bar diagrams! Ignore the confusing partial quotients method on pg 196.

Kahn Academy - Division with Area Models

Task #9: Use a sheet of graph paper. Make a rectangle that has 30 squares inside of it and a width of 5 units. Then, determine the length of your rectangle. What does this have to do with division? Try this again by making a rectangle that has 42 squares inside of it and a width of 3 units. Finally, determine the length of a rectangle that has 408 squares and a width of 4? Extension: Divide 12,488 by 4 using an area model or bar diagram. Hint: to start, first divide 4 into 12,000. Then divide 4 into 400. Then 4 into 80, etc…

______________________________________

Week 10: Oct 29 – Nov 2

3-8 #1-13odd. Extension #17.

3-9 #1-15odd. Extension #18.

3-10 #1-15odd. Extension #17.

Kahn Academy - Intro to Division

Kahn Academy - Intro to Long Division

Task #10A Look for patterns that help you do the problem faster when you divide the following problems. #1: 88,888 divided by 2. #2: 77,777 divided by 7. #2: 100,000 divided by 9.  #3: 252,525 divided by 5.  #4: 777,777 divided by 3.

Task #10B Explain why you would not want to bother doing long division if you were going to divide 820 by 10. What about 820 divided by 20? You also don’t really need long division. Talk with an adult about how the answer to 820 divided by 20 is related to 820 divided by 10. 

______________________________________

Week 11: Nov 5 – 9

3-11 #3-8.

3-12 #2-7. Extensions #8-9.

Page 240-241 #7-26.

Task #11: Write three different word problems that ask a question which you will make up. The first word problem should not have enough given information and so you won’t actually be able to solve it. Make a note about what information is needed. The second word problem will have a question that is solvable by multiplication or division. The third word problem should have extra (too much) information, but will still be solvable by multiplication or division. (See pages 233-236 for examples.)

______________________________________

 

Week 12: Nov 12 – 16

Page 245 #1-9.

4-1 #2-13.

4-3 #2-10, 14-18.

Kahn Academy - Dividing by 2 Digits

Task #12:  Roll three dice to make a three-digit number (or roll one three times), then roll one die and have that number be the divisor. Try to divide the three-digit number by the single-digit number in your head. Discuss mental math strategies with an adult or older sibling. Try an estimate if an exact answer is hard to do in your head. Record some of your results and/or strategies. Hint: a good way to start is to quickly determine if the divisor goes in more than 10 or 100 times. 

______________________________________

Week 13: Nov 26 – Nov 30
 
Page 269-270 #1-16.
 
Extension Lesson: 4-5 #3-13odd.
 
4-6 #1-8, 10. Extension #9.
 
Task #13: Use each of the numbers from 0 to 5 exactly once to create division problems that would equal a number between 0-10. Then, create a new problem that would equal a number from 10-20, then 20-30, then 30-40, then 40-50. Remainders are fine and can be ignored. Example: 1234 divided by 50 equals 24 (remainder34).
______________________________________
Week 14: Dec 3 – Dec 7
 
5-1 #2-18.
5-2 #3-18.
5-3 Page 317 #2-5.
5-3 Page 320 #1,3.
 
Task #14:  Discuss with a parent/adult the assigned problems on pages 317 and 320. What is necessary for a good estimate depending on the situation? What do adults care about when estimating when it comes to money. Then, consider something that costs $449.99 . What place makes the most sense to round to? Why? In other words, if an adult was going to tell someone what they paid for it, what would they actually say? What would happen if you rounded to the nearest hundred? Nearest thousand? 
______________________________________
 
Week 15: Dec 10 – Dec 14
 
Optional Lesson 5-4 #2-7. Could also be done with one dollar bills, dimes, and pennies as well.
Optional Lesson 5-5 #3-7. Primary purpose of this is estimation so student recognizes a mistake when adding by hand. Make sure you can estimate the sums. Drawings are optional.
 
5-6 #6-17, 19.
5-7 #5-8. Page 345-346 #1-4. This lesson is short but very important. Looking to group two numbers that make whole numbers or multiples of ten is an essential math practice.
 
 
Task #15: Write an addition problem with at least six numbers that looks difficult but can actually be solved reasonably easily with just mental math because groups of two numbers can be paired nicely together.  Show or explain how to solve your problem.
______________________________________
 
Week 16: Dec 17 – Dec 21
 
5-8 #3-10 & 5-9 #2-7. This is essential practice. Could be done with money (dollar bills, dimes, and pennies) instead of base ten blocks and grid diagrams. Goal here is to build more proficiency with place value, “borrowing” or “regrouping, and the use of visuals to justify and understand the difference between two numbers. Eventually, we want students to have strong enough number sense to do these problems “visually” in their heads and not rely on the rule of lining up the decimals.
 
5-10 #3-13odd, 15-18.
 
 
Task #16: Write three different addition problems that would all have the answer of 1.72
______________________________________
 
 
Week 17: Jan 7 – Jan 11
 
6-1 #5-16. Talk through these with an adult.
Optional Lesson 6-2 #3-8.
 
6-3 #3-17odd, 18.
6-4 #4-11.
 
 
Task #17: Write at least five different multiplication problems that would all equal 0.24 . Explain a rule or pattern you used or show a strategy that helps you come up with more solutions.  
______________________________________
 

Week 18: Jan 14 – Jan 18

6-5 #5-15odd, 16-21.

6-6 #4-19.

6-7 #2-6. Extensions: 1, 7, 9.

Page 422 #1-4.

6-8 #4-7. Discuss why the parenthesis can be moved or ignored and how these problems can be done entirely in your head. Remember, we don’t approach all math problems from left-to-right, we strategize when we can!

Kahn Academy - Intro to Multiplying Decimals

Task #18: Write a multiplication problem with at least four numbers (all being multiplied) that looks difficult but can actually be solved reasonably easily with just mental math because groups of two numbers can be paired nicely together. Explain and show how it works out nicely.

______________________________________

Week 19: Jan 21 – Jan 25

6-9 #4-15. Estimating these answers is probably more important than being able to get the correct exact answer by hand. Spend time considering and discussing reasonable estimates!

6-10 #3-6. Work through with visual or manipulative.

Think Central

6-11 #3, 4, 6-11, 17-19. Extensions: 5, 12-15.

Kahn Academy - Building a Decimal by a Whole Number

6-12 #3-7. This models another way of “seeing” division. 2.4 divided by 0.3 means “how many 0.3s will fit into 2.4? or “how times will 30 cents go in to $2.40?” or “how many sets of 3 tenths bars will make two unit squares and 4 tenths bars?”

Task #19:  Should the answer to the problem 2.945 ÷ 0.06 be really big (in the tens or hundreds) or really small (almost zero)? Explain. What about the problem 0.42 ÷ 68? Explain or show how you know. Do not solve for an exact answer.

______________________________________

Week 20: Jan 28 – Feb 1
 
6-13 #2-5, 7, 8, 13-15, 17. Extensions: 6, 9-11, 16.
 
6-14 #4-16. Learn and use the shortcut of moving the decimal place. Do NOT divide out the long way by hand.
Page 468-469 #7-17, 21-24.
 
Task #20:  Explain why the problem 12,345.67 times 1,000 is a relatively easy problem to do. What is the answer and why? What about 12,345.67 divided by 1,000?
 
Mid-Year Assessment: Take Mid-Year Tests (Ch 1-3 & Ch 4-6) and use the Mid-Year Test Answer Keys to do some test corrections and further practice on the more important skills/problems with your parent, teacher, or tutor.
 
______________________________________ 
 
Week 21: Feb 4 – Feb 8
 
7-2 #2-15. Show work step-by-step.
7-3 #2-4, 7-10.
 
 
Task #21: Use three or four 3s, any operations (addition, subtraction, multiplication, and division), and parenthesis (if necessary) to create an expressions that equal each of the integers from 0 to 5. For example, 3*3+3= 6, so this one doesn’t work since it doesn’t equal 0, 1, 2, 3, 4, or 5. Here’s another example:  3+3+3/3= 7. Make up at least one expression for each number 0-5. Hint: you will need to use division for some and may need parenthesis as well.
______________________________________  
 
 
Week 22: Feb 11– Feb 15
 
7-4 #1-10.
7-5 Do pg 507-508 with toothpicks or similar object and #1-8 on pages 508-510.
7-6 #2-13, 15.
 
 
Task #22: Write five different patterns that end up with the number 24 as the 4th number in your pattern. If you start with some “easy” ones, try to come up with one or two “trickier” patterns that involve a different type of rule.
______________________________________  
Week 23: Feb 18 – Feb 22
 
7-7 (Page 521) #6-9.
7-8 #3-20
7-9 #2-4. Page 536 #1-2. 
 
 
Task #23: On graph paper, draw an x and a y axis. Then, mark five different points that would make a straight line if they were connected with a line through them. Write down the coordinates of all five points. What do you notice about the coordinates of the points? Do you see a pattern? Explain. 
______________________________________
Week 24: Feb 25 – Mar 1
 
8-1 #2-7.
8-2 #3-10. I recommend using the method shown in Example 2 on page 558.
 
Task #24A:  Justifying Half
 
Task #24B: Talk with a parent or adult about where you and he or she has encountered fractions in your daily lives. What are some of the most important fractions? In what situations do fractions regularly come up? Do you normally think of a fraction as a part out of a whole or as a situation that involves division? Write a paragraph that answers these questions and includes some of your own examples.  
______________________________________
 
Week 25: Mar 4 – Mar 8
 
8-3 #3-17.
 
8-4 Do this section on a separate sheet of paper. Choose any four from #s 1-8. Set up guess and check tables similar to the one on page 569. Try to NOT solve the problem initially so you can try out some different possibilities and get a feel for how the guess and check tables work. The more guesses, the better practice for the brain. But do focus on organizing your work as neatly as possible.
 
 
Task #25: Talk with a parent or adult about situations when it might make more sense to know the reduced or simplified fractions. Come up with an example that you would want to know the simplified fraction, and also an example or situation where it might make more sense to actually have the original fraction that is not simplified. Are there also other types of way of conveying fraction information? Brainstorm other ways that our culture has for communicating fraction information. 
______________________________________
 
Week 26: Mar 11 – Mar 15
 
8-5 #3-13. Extension #14.
 
 
8-6 #2-10, 15, 17. Extension #14.
 
 
 Task #26: Claire wants to go to see a Giants game, but she wants to go with people who are also big Giants fans like herself so they have great energy and enthusiasm in the stands. One group of 5 friends is going on one day and 4 of them are big fans. 10 of her classmates are also going another day and 6 of them are big fans. Claire’s brother says, “Well, you should go with your classmates because there will be two more people who are big fans.” But Claire isn’t so sure. How might Claire approach her decision? What does this situation have to do with math? How might fractions, decimals, or percents help her make her decision?  
______________________________________
Week 27: Mar 25 – Mar 29
 
8-7 #1-10.
 
 
8-8 #3-14. Extensions #15-17.
 
Task #27: Hector wants to change 3/20 to be out of 100 so he can know the decimal equivalent. He decides to multiply the 3 by 5 and the 20 by 5, and he gets an equivalent fraction of 15/100. He then knows the decimal is 0.15. Why is Hector allowed to multiply the 3 by 5 and the 20 by 5? Isn’t that going to change the number or value and therefore change the original amount to something different? Explain. 
______________________________________
Week 28: April 1 – 5
 
9-1 #2-18.
9-2 #3-17.
9-3 #4-19.
 
 
 Task #28A: Explore what is different about adding fractions with unlike denominators. Why can’t you use the same rule for adding fractions with like denominators? What if you added the numerators and the denominators separately? Try creating two different fractions with all different numbers and then see what happens when you add the numerators and add the denominators. Does the answer look correct? Why or why not? Use visual models like pie slices if that helps.
 
 Task #28B:  Alice gave Brian ¾ of a candy bar. Alice also gave Cindy ¾ of a candy bar. Dave thinks that Alice has given away a total of 6/8 of a candy bar. Use written explanations and/or visuals to show why Dave is incorrect. 
______________________________________
 
Week 29: April 8 – 12
 
9-4 #4-9, 12, 13.
 
 
This is an important concept to understand. Some questions to consider: How can we show and justify our thinking visually? Is a fraction one number or two numbers? How are fractions related to a whole? How can I estimate if my answer is reasonable? Why can't 1/2 and 1/3 add to 2/5? 
 
9-5 #3-17.
9-7 #2-17.
 
 
 Task #29: What kinds of unlike denominators make it easier to add and subtract two fractions? For example, why would 1/13 + 1/29 be a harder problem than 1/10 + 1/30? Explain or clearly show your thinking as it relates to these examples or your own examples. 
______________________________________
Week 30: April 15 – 19
 
9-9 #4-19.
9-10 #2-10.
9-11 #2-17.
9-12 #3-11, 15-17.
 
 
Optional Extension Lesson 9-13 #2-17.
 
Task #30: Page 697 #25, 26. 
______________________________________
Week 31: Apr 22 – 26
 
10-1 #3-12.
10-2 #2-13. Discuss these estimations with your parent/teacher/etc. We are just looking for a reasonable estimate or a range of reasonable answers…there is definitely NOT one best answer for an estimate, but there are unreasonable estimates… so talk through some options for these.
 
10-3 #3-8,11.
10-4 #2-10, 14-17.
 
 
Task #31: Make up or determine with your parent/teacher a real-world problem that would require you to multiply a whole number by a fraction. Show work or explain how you can determine the answer. 
______________________________________
 
Week 32: Apr 29 – May 3
 
10-5 #4-11.
10-6 #5-10.
10-8 #3-10.
 
 
10-9 #3-6, 11. Do NOT use a rule… think about what division means and count! For example, for #4, two pizzas can be divided into how many 1/5ths? Or in other words, how many 1/5th will fit into 2 wholes?
 
10-10 #2, 3, 5, 6, 10.
 
 
Optional: 10-7 #2-10even,14-16.
Optional: 10-11 #2-10.
 
Task #32: No extra task this week. 
______________________________________
 
Week 33: May 6 – 10
 
11-1 #4, 5, 10-12, 15.
11-2 #3-17odd, 18, 19.
11-3: Choose any 5 of the 10 problems on pages 815-816.
11-9: #4-5, 10-12, 15
.
Task #33: For sections 11-4 to 11-8, we’re headed outside of the book and inside of the home. Look around the house for units of volume (canning jars, boxes, measuring spoons, etc), units of weight, or or units of length. Ask a parent/teacher what conversions they have memorized, if any. (oz to pints? quarts? gallons? cm to m?) How do Google and cell phones help us with tricker conversions? Discuss with a parent/teacher and record at least three separate examples of how to convert from one unit of measurement to another.
______________________________________  
Week 34: May 13 – 17
 
12-1 #2-11.
12-2 #4, 5, 7, 12. 
12-5: #3-10.
 
 
Task #34:  Find examples of at least four of the following shapes around your home or city: equilateral triangle, right triangle, square, rectangle, rhombus, parallelogram, or trapezoid. Name each example, sketch it, and explain how you know for sure that it is the shape you claim. Note: “It looks like it” or “I can tell from the sides” are not explanations—focus on the lengths of the sides and the degrees or congruence of any angles.
______________________________________
Weeks 35 & 36: May 20 – June 7
 
Complete any two of the three Year-End Project Tasks and turn in to your supervising teacher. 
Task #35: Take Year-End Test and use the Year-End Test Answer Key to do some test corrections with your parent, teacher, or tutor. 
______________________________________