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Math_Mammoth_Grade4A_Samples Flipbook PDF
Math_Mammoth_Grade4A_Samples
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Copyright 2017 - 2020 Maria Miller Edition 1/2020 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, or by any information storage and retrieval system, without permission in writing from the author. Copying permission: For having purchased this book, the copyright owner grants to the teacher-purchaser a limited permission to reproduce this material for use with his or her students. In other words, the teacher-purchaser MAY make copies of the pages, or an electronic copy of the PDF file, and provide them at no cost to the students he or she is actually teaching, but not to students of other teachers. This permission also extends to the spouse of the purchaser, for the purpose of providing copies for the children in the same family. Sharing the file with anyone else, whether via the Internet or other media, is strictly prohibited. No permission is granted for resale of the material. The copyright holder also grants permission to the purchaser to make electronic copies of the material for back-up purposes. If you have other needs, such as licensing for a school or tutoring center, please contact the author at https://www.MathMammoth.com/contact.php Sample worksheet from
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Contents Foreword ........................................................................... 6
Chapter 1: Addition, Subtraction, Patterns and Graphs Introduction ...................................................................... 7 Addition Review ............................................................... 11 Adding in Columns .......................................................... 14 Subtraction Review .......................................................... 15 Subtract in Columns ........................................................ 18 Patterns and Mental Math .............................................. 21 Patterns in Pascal’s Triangle .......................................... 23 Bar Models in Addition and Subtraction ...................... 25 Order of Operations ........................................................ 29 Making Bar Graphs ........................................................ 31 Line Graphs ..................................................................... 33 Rounding .......................................................................... 36 Estimating ........................................................................ 39 Money and Discounts ...................................................... 41 Calculate and Estimate Money Amounts ..................... 44 Review Chapter 1 ............................................................ 47
Chapter 2: Large Numbers and Place Value Introduction ..................................................................... 49 Thousands ........................................................................ 51 At the Edge of Whole Thousands .................................. 54 More Thousands ............................................................. 56 Practicing with Thousands ............................................ 58 Place Value with Thousands .......................................... 60 Comparing with Thousands .......................................... 62 Adding and Subtracting Big Numbers ......................... 65 Rounding and Estimating with Large Numbers .......... 69
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Multiples of 10, 100, and 1000 ...................................... 73 Mixed Review Chapter 2 ............................................... 76 Review Chapter 2 ........................................................... 78
Chapter 3: Multi-Digit Multiplication Introduction .................................................................... 80 Understanding Multiplication ...................................... 84 Multiplication Tables Review ....................................... 87 Scales Problems ............................................................. 90 Multiplying by Whole Tens and Hundreds ................ 94 Multiply in Parts 1 ........................................................ 98 Multiply in Parts 2 ........................................................ 101 Multiply in Parts—Area Model .................................... 103 Multiplying Money Amounts ....................................... 105 Estimating in Multiplication ........................................ 107 Multiply in Columns - the Easy Way .......................... 109 Multiply in Columns - the Easy Way, Part 2 ............. 112 Multiply in Columns - the Standard Way .................. 115 Multiplying in Columns, Practice ............................... 119 Order of Operations Again .......................................... 121 Money and Change ....................................................... 124 So Many of the Same Thing ......................................... 127 Multiplying Two-Digit Numbers in Parts ................... 130 Multiply by Whole Tens in Columns ........................... 135 Multiplying in Parts: Another Way ............................. 137 The Standard Multiplication Algorithm with a Two-Digit Multiplier ......................................... 139 Mixed Review Chapter 3 ............................................... 143 Review Chapter 3 ........................................................... 145
Chapter 4: Time and Measuring Introduction .................................................................... 148 Time Units ...................................................................... 153 Elapsed Time 1 ............................................................... 156 The 24-Hour Clock ........................................................ 159 Elapsed Time 2 .............................................................. 161
Sample worksheetElapsed from Time 3 .............................................................. 164 https://www.mathmammoth.com 4
Measuring Temperature: Celsius ............................... 167 Measuring Temperature: Fahrenheit ......................... 171 Temperature Line Graphs ........................................... 173 Measuring Length ........................................................ 175 More Measuring in Inches and Centimeters ............. 178 Feet, Yards, and Miles ................................................. 180 Metric Units For Measuring Length .......................... 185 Customary Units of Weight ......................................... 188 Metric Units of Weight ................................................ 192 Customary Units of Volume ........................................ 195 Metric Units of Volume ...............................................
198
Mixed Review Chapter 4 ............................................. 201 Review Chapter 4 ......................................................... 203
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Foreword Math Mammoth Grade 4 comprises a complete math curriculum for the fourth grade mathematics studies. The curriculum meets and exceeds the Common Core standards. The main areas of study in Math Mammoth Grade 4 are: 1. Students develop understanding and fluency with multi-digit multiplication, and use efficient multiplication procedures to solve problems. 2. They develop understanding of division to find quotients involving multi-digit dividends (long division), and they solve word problems involving division, including division with a remainder. 3. Students develop an understanding of fraction equivalence and some operations with fractions. They learn to add and subtract fractions with same denominators, and to multiply a fraction by a whole number. 4. Students learn the concept of angle. They draw and identify lines and angles, and classify shapes by properties of their lines and angles. Additional topics we study are place value, time, measuring, graphs, and decimals. This book, 4-A, covers addition and subtraction and graphs (chapter 1), place value (chapter 2), multi-digit multiplication (chapter 3), and time and measuring (chapter 4). The rest of the topics are covered in the 4-B worktext. Some important points to keep in mind when using the curriculum: • The two books (parts A and B) are like a “framework”, but you still have a lot of liberty in planning the child’s studies. Chapters 1, 2, and 3 should be studied in order, and Chapter 3 (multiplication) should be studied before Chapter 5 (division). However, you can be flexible with chapters 4 (time and measuring) and 6 (geometry), and schedule them earlier or later. Also, most lessons from chapters 7 and 8 (fractions and decimals) can be studied earlier; however the topic of finding parts with division should naturally be studied only after mastering division. Math Mammoth is mastery-based, which means it concentrates on a few major topics at a time, in order to study them in depth. However, you can still use it in a spiral manner, if you prefer. Simply have the child study in 2-3 chapters simultaneously. This type of flexible use of the curriculum enables you to truly individualize the instruction for the child. • Don’t automatically assign all the exercises. Use your judgment, trying to assign just enough for the child’s needs. You can use the skipped exercises later for review. For most children, I recommend to start out by assigning about half of the available exercises. Adjust as necessary. • For review, the curriculum includes a worksheet maker (Internet access required), mixed review lessons, additional cumulative review lessons, and the word problems continually require usage of past concepts. Please see more information about review (and other topics) in the FAQ at https://www.mathmammoth.com/faq-lightblue.php I heartily recommend that you view the full user guide for your grade level, available at https://www.mathmammoth.com/userguides/ And lastly, you can find free videos matched to the curriculum at https://www.mathmammoth.com/videos/ I wish you success in teaching math! Maria Miller, the author
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Chapter 1: Addition, Subtraction, Patterns, and Graphs Introduction The first chapter of Math Mammoth Grade 4 covers addition and subtraction, problem solving, patterns, graphs, and money. At first, we review the “technical aspects” of adding and subtracting: mental math techniques and adding and subtracting in columns. We also study some patterns. The lesson on Pascal’s triangle is intended to be fun and fascinating—after all, Pascal’s triangle is full of patterns! In the next lesson, students use bar models (visual models with one or more horizontal “bars”) to help them write addition and subtraction sentences with unknowns and to solve them. They are actually learning algebraic thinking and how to write and solve simple equations. The lesson on the order of operations contains some review. We also connect this topic with real-life situations, such as shopping. The student writes simple expressions (number sentences) for word problems, which, again, practices algebraic thinking, and also helps students learn how to show their work in math problems. As applications of math, the chapter then contains straightforward lessons on bar graphs, line graphs, rounding, estimating, and money problems. Keep in mind that the specific lessons in the chapter can take several days to finish. They are not “daily lessons.” Instead, use the general guideline that fourth graders should finish about 2 pages daily or 9-11 pages a week. Also, I recommend not assigning all the exercises by default, but that you use your judgment, and strive to vary the number of assigned exercises according to the student’s needs. Please see the user guide at https://www.mathmammoth.com/userguides/ for more guidance on using and pacing the curriculum. I also offer free videos matched to the curriculum at https://www.mathmammoth.com/videos/. The Lessons in Chapter 1
page
span
Addition Review ......................................................... 11
3 pages
Adding in Columns ..................................................... 14
1 page
Subtraction Review ....................................................
15
3 pages
Subtract in Columns ...................................................
18
3 pages
Patterns and Mental Math ........................................... 21
2 pages
Patterns in Pascal's Triangle .......................................
23
2 pages
Bar Models in Addition and Subtraction .................... 25
4 pages
Order of Operations ....................................................
29
2 pages
Making Bar Graphs ....................................................
31
2 pages
Line Graphs ................................................................
33
3 pages
Rounding ....................................................................
36
3 pages
Estimating ................................................................... 39
2 pages
Money and Discounts .................................................
41
3 pages
Calculate and Estimate Money Sample worksheet from Amounts .................... Review Chapter 1 ....................................................... https://www.mathmammoth.com
44
3 pages
47
2 pages
7
Helpful Resources on the Internet THE BASIC OPERATIONS Add Like Mad Click on single-digit numbers that add up to the given sum as quickly as you can, clearing the board. http://www.mathnook.com/addlikemad.html Sum Tracks The game board shows square and round tiles with numbers. Drag the square number tiles over the round tiles, so that the sum of the round tiles equals the number on the square tile. http://www.coolmath-games.com/0-sum-tracks A Maze'n Math Move the red piece through the maze and use it to eliminate the other numbers, according to certain rules relating to addition and difference. http://www.hoodamath.com/games/amazenmath.html Minus Mission Practice subtraction facts within your chosen range, such as 0-12 or 0-20 while destroying green slime. http://www.mathplayground.com/ASB_MinusMission.html Pop the Balloons Pop the balloons in the order of their value. You need to use all four operations. http://www.sheppardsoftware.com/mathgames/numberballoons/BalloonPopMixed.htm Math Mahjong Match tiles with the same value. The game uses all four operations and has three levels. http://www.sheppardsoftware.com/mathgames/mixed_mahjong/mahjongMath_Level_1.html PATTERNS AND PASCAL'S TRIANGLE Crack the Code Find the missing numbers in the patterns, and unlock the safe. http://www.sciencekids.co.nz/gamesactivities/math/numberpatterns.html Pascal's Triangle at Maths Is Fun Learn fascinating facts and patterns in Pascal's triangle! http://www.mathsisfun.com/pascals-triangle.html Coloring Multiples Color various multiples (such as multiples of 6 or 10) in Pascal's Triangle, and see the patterns! http://www.shodor.org/interactivate/activities/ColoringMultiples/ BAR MODELS AND PROBLEM SOLVING Thinking Blocks - Addition and Subtraction Model and solve word problems. https://www.mathplayground.com/tb_addition/index.html Jugs Puzzle Fill and pour the water out of the two jugs until you get the desired quantity. Drag the jugs to empty or fill them. A puzzle using logical thinking. https://www.mathsisfun.com/games/jugs-puzzle.html Algebra Puzzle Figure out the values of the objects so that they add up to the target numbers. https://www.mathplayground.com/algebra_puzzle.html
Sample worksheet from https://www.mathmammoth.com
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Calculator Chaos Most of the keys have fallen off the calculator. “Make” numbers using the keys that are left. https://www.mathplayground.com/calculator_chaos.html ORDER OF OPERATIONS Addition Mystery Picture Reinforce your addition skills while uncovering a hidden picture. https://www.mathmammoth.com/practice/mystery-picture#min=20&max=100 Subtraction Mystery Picture Practice subtraction of two-digit numbers while uncovering a hidden picture. https://www.mathmammoth.com/practice/mystery-picture-subtraction#min=11&max=100 Choose Math Operation Choose the operation(s) so that the given number sentence becomes true. https://www.homeschoolmath.net/operation-game.php Order of Operations Quiz A 10-question online quiz that includes two different operations and possibly parentheses in each question. You can also modify the quiz parameters yourself. http://www.thatquiz.org/tq-1/?-j8f-la Order of Ops Choose the expression to be solved in each step, and solve it. The program uses a visual representation of steps to show how the expression gets shorter at each step. https://mrnussbaum.com/order-ops-online-game The Order of Operations Millionaire Answer multiple-choice questions that have to do with the order of operations, and win a million. http://www.math-play.com/Order-of-Operations-Millionaire/order-of-operations-millionaire.html Exploring Order of Operations (Object Interactive) Click on the operation to be done first in the given expression. The program then solves that, and you click on the next operation to be performed, etc., until it is solved. The resource also includes a game. http://www.learnalberta.ca/content/mejhm/html/object_interactives/order_of_operations/use_it.html Order of Operations Practice A simple online quiz of 10 questions. Uses parentheses and the four operations. http://www.onlinemathlearning.com/order-of-operations-practice.html ROUNDING AND ESTIMATING Online Rounding Practice Practice rounding to the nearest ten, hundred, or thousand. https://www.mathmammoth.com/practice/rounding#number-range=0to10000&roundto=ten,hundred,thousand Rounding Sharks Game Round numbers to the nearest hundred by clicking the shark with the correct rounded number. http://www.free-training-tutorial.com/rounding/sharks.html Brain Racer Rounding Round numbers as fast as you can to beat two other walkers in the walking race. Choose to round either to the nearest ten, nearest hundred, or nearest thousand. http://www.mathnook.com/math/brain-racer-rounding.html
Sample worksheet from https://www.mathmammoth.com 9
Ice Ice Maybe Fast estimation game. Help penguins migrate across a perilous ocean patrolled by hungry killer whales. The game uses all operations; addition and subtraction are most appropriate for this level. Start the game from the circular button near the top. https://www.mangahigh.com/en/games/iceicemaybe Estimation Games Find the answer fast! You also get points for being close. Choose “Add 100s” or “Add Tens” “Subtract Tens”, or “Subtract 100s” for 4th graders. https://www.mathsisfun.com/numbers/estimation-game.php MONEY Change Maker Determine how many of each denomination you need to make the exact change. Choose the “hard” level for 4th graders. Playable in US, Canadian, Mexican, UK, or Australian money. https://www.funbrain.com/games/change-maker Cash Out Give correct change by clicking on the bills and coins. It has three levels of difficulty. https://mrnussbaum.com/cash-out-online-game DATA AND GRAPHS Bar Charts Interactive questions about bar charts. First, choose a topic for the graph. Next, choose how the vertical axis is presented; for example, “20 intervals, 10 marked”. Lastly, choose the type of questions asked. http://www.topmarks.co.uk/Flash.aspx?f=barchartv2 Graphs Quiz A 10-question online quiz that involves a variety of types of questions on line graphs, bar graphs, and pictograms. You can also easily change the quiz parameters to your liking. http://www.thatquiz.org/tq-5/?-j50f15-l5-p0 Line Graphs at Maths Is Fun A simple tutorial on line graphs, followed by ten interactive practice questions. https://www.mathsisfun.com/data/line-graphs.html An Interactive Bar Grapher Graph data sets in bar graphs. The color, thickness and scale of the graph are adjustable. You can input your own data or use or alter pre-made data sets. http://illuminations.nctm.org/Activity.aspx?id=4091 Graph Master Create a graph from your own data (you can even make it up). The interactive activity creates the graph, and also makes up multiple-choice questions from your data for you to answer. https://mrnussbaum.com/graphmaster
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Chapter 1: Addition Review
Addition Review The numbers to be added are addends. The result is a sum.
You can write any number as a sum of its different parts: whole thousands, whole hundreds, whole tens, and ones.
5,248 = 5,000 + 200 + 40 + 8 thousands
2,019 = 2,000 +
You can add in parts (hundreds, tens, ones):
hundreds
0
Trick: first add a bigger but easier number, then subtract to correct the error:
7 + 90 + 91 + 3
= 100 + 50 + 20 + 6 + 4
= 7 + 3 + 90 + 91
= 100 + 70 + 10 = 180
= 10 + 90 + 91 = 191
ones
+ 10 + 9
You can add in any order:
56 + 124
tens
76 + 89 = 76 + 90 − 1 = 166 − 1 = 165
1. Add mentally. Compare the problems in each box! a.
b.
c.
d.
70 + 80 = _______
140 + 50 = _______
50 + 60 = _______
80 + 90 = _______
77 + 80 = _______
141 + 50 = _______
54 + 65 = _______
82 + 93 = _______
77 + 82 = _______
144 + 55 = _______
58 + 62 = _______
88 + 91 = _______
2. Write each number as a sum of its parts: thousands, hundreds, tens, and ones. a. 487 =
b. 2,103 =
c. 8,045 =
d. 650 =
3. Solve. a. Emma added three numbers. Two of them were 56 and 90. The sum was 190. What was the third number she added? b. The sum of four numbers is 70 and the sum of five other numbers is 80. What is the sum of all nine numbers?
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Sample worksheet from https://www.mathmammoth.com
Chapter 1: Adding in Columns
Adding in Columns 1. Add in columns. Check by adding the numbers in each column in a different order (for example, starting at the bottom and working up).
a.
b.
3 2 9 2 0 2 +
8 1 0 0 2
c.
2 4 5 1 3 9 3 0 2 9 3 1 5 9 4 4 5 9 3 + 5 2 6
4 2 8 9 6
2. Add. Write the numbers under each other, carefully aligning the ones, tens, hundreds, and thousands. You may use a separate piece of paper if you prefer. a. 5,609 + 1,388 + 89 + 402 + 837 b. 67 + 504 + 1,298 + 492 + 3,288 + 8
3. The map shows some Kentucky cities and distances between them. The two distances that may be hard to read are: from Louisville to Frankfort is 54 miles; from Frankfort to Lexington is 28 miles. Calculate the total driving distance, if a family goes on a trip like this: a. Covington - Lexington - Paducah - Lexington - Covington
b. A trip from Lexington via Covington, Louisville, and Frankfort, and back to Lexington.
Sample worksheet from https://www.mathmammoth.com 14
1 7 3 8 2 3 9 0 1 0 7 8 3 6 4 2 8 0 3 2 1 1 + 9 9
Chapter 1: Subtraction Review
Subtraction Review Compare the methods.
John: “I use a helping problem.”
Marie: “I subtract in parts: first to the previous whole ten, then the rest.”
15 − 7 = 8 is the helping problem for 35 − 7.
35 − 7 = (35 − 5) − 2 =
The answer to 35 − 7 also ends in “8” and is in the previous ten (the twenties). So, 35 − 7 is 28.
30 − 2 = 28
1. Subtract. a.
b.
c.
d.
13 − 7 = ______
12 − 6 = ______
15 − 9 = _______
16 − 8 = _______
63 − 7 = ______
82 − 6 = ______
150 − 90 = ______
1,600 − 800 = _______
2. Subtract from whole hundreds. You can subtract in parts. a.
b.
c.
d.
100 − 2 = _______
200 − 4 = _______
500 − 5 = _______
400 − 7 = _______
100 − 20 = ______
200 − 40 = ______
500 − 50 = ______
400 − 70 = ______
100 − 22 = ______
200 − 45 = ______
500 − 56 = _______
400 − 71 = ______
3. Subtract and compare the results. The problems are “related” — can you see how? a. 12 − 8 = _______
b. 15 − 9 = _______
c. 13 − 7 = _______
42 − 8 = _______
75 − 9 = _______
73 − 7 = _______
120 − 80 = _______
150 − 90 = _______
1,300 − 700 = ______
520 − 80 = _______
650 − 90 = _______
430 − 70 = _______
4. Write here four different subtraction problems that are “related” to the problem 14 − 8 = 6. See the examples above!
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Chapter 2: Large Numbers and Place Value Introduction The second chapter of Math Mammoth Grade 4 covers large numbers (up to 1 million) and place value. The first lessons only deal with thousands, or numbers with a maximum of four digits. These are for review and for deepening the student’s understanding of place value, as understanding place value with four-digit numbers is crucial before moving on to larger numbers. After that we go on to numbers with five and six digits (numbers till one million). Students write them in expanded form, compare them, add and subtract them, and learn more about rounding. Lastly, we briefly study the multiples of 10, 100, and 1000. This lesson prepares the way for some very important ideas in the next chapter (multi-digit multiplication). Please recall that it is not recommended to assign all the exercises by default. Use your judgment, and strive to vary the number of assigned exercises according to the student’s needs. The Lessons in Chapter 2
page
span
51
3 pages
At the Edge of Whole Thousands ............................. 54
2 pages
More Thousands .......................................................
56
2 pages
Practicing with Thousands .......................................
58
2 pages
Place Value with Thousands ....................................
60
2 pages
Comparing with Thousands .....................................
62
3 pages
Adding and Subtracting Big Numbers .....................
65
4 pages
Rounding and Estimating with Large Numbers ......
69
4 pages
Multiples of 10, 100, and 1000 ................................. 73
3 pages
Mixed Review Chapter 2 ..........................................
76
2 pages
Review Chapter 2 .....................................................
78
2 pages
Thousands .................................................................
Helpful Resources on the Internet Teaching Place Value What is the value of the red underlined digit? Answer the questions in this online quiz. http://www.softschools.com/math/place_value/teaching_place_value/TeachingPlaceValue.swf Can You Say Really Big Numbers? Enter a really big number, try to say it out loud, and see it written. http://www.mathcats.com/explore/reallybignumbers.html Place Value Payoff Match numbers written in standard form with numbers written in expanded form in this game. http://www.quia.com/mc/279741.html Base Ten Blocks Click on buttons to make blocks appear. Show a problem to challenge yourself to match the correct number of Sample worksheet fromThe level of difficulty can be adjusted. blocks with a written number. https://www.mathmammoth.com http://www.hoodamath.com/mobile/games/basetenblocks.html 49
Place Value Puzzler Place value or rounding game. Click on the asked place value in a number, or type in the rounded version of the number. https://www.funbrain.com/games/place-value Fruit Splat — Compare Numbers (Choose Level 3) Compare numbers by picking >,