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Singapore Math Dimensions Math Teaching Notes and Textbook Solutions 7A

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Singapore Math Dimensions Math Teaching Notes and Textbook Solutions 7ADimensions Math Textbook 7A Chapter 1: Factors and Multiples 1. 1 Factors and Multiples A. Factors B. Multiples 1. 2 Prime Factorization and Exponential Notation A. Prime Factorization B. Exponential Notation 1. 3 Greatest Common Factor (GCF) 1. 4 Least Common Multiple (LCM) 1. 5 Square Roots and Cube Roots A. Square Roots B. Cube Roots In A Nutshell Extend Your Learning Curve Write In Your Journal Chapter 2: Real Numbers 2. 1 Idea of Negative Numbers

Dimensions Math® Textbook 7A

Chapter 1: Factors and Multiples

1.1 Factors and Multiples

A. Factors
B. Multiples

1.2 Prime Factorization and Exponential Notation

A. Prime Factorization
B. Exponential Notation

1.3 Greatest Common Factor (GCF)
1.4 Least Common Multiple (LCM)
1.5 Square Roots and Cube Roots

A. Square Roots
B. Cube Roots

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Chapter 2: Real Numbers

2.1 Idea of Negative Numbers and the Number Line

A. Negative Numbers
B. The Number Line
C. Absolute Value

2.2 Addition and Additive Inverse

A. Addition of Integers
B. Additive Inverse

2.3 Subtraction and Absolute Value of the Difference

A. Subtraction of Integers
B. Absolute Value of the Difference

2.4 Multiplication, Division, and Combined Operations of Integers

A. Multiplication of Integers
B. Division of Integers
C. Combined Operations of Integers

2.5 Rational Numbers

A. Definition
B. Addition and Subtraction of Rational Numbers
C. Multiplication and Division of Rational Numbers

2.6 Real Numbers and Use of Calculators

A. Real Numbers
B. Use of Calculators

2.7 Rounding Numbers to Decimal Places

A. Idea of Rounding
B. Rounding Numbers to Decimal Places

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Chapter 3: Introduction to Algebra

3.1 The Use of Letters in Algebra

A. The Use of Letters
B. Basic Notations in Algebra
C. Exponential Notation

3.2 Evaluation of Algebraic Expressions and Formulas

A. Evaluation of Algebraic Expressions
B. Formulas

3.3 Writing Algebraic Expressions to Represent Real-world Situations

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Chapter 4: Algebraic Manipulation

4.1 Like Terms and Unlike Terms
4.2 Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

A. Use of Parentheses
B. Addition and Subtraction of Linear Algebraic Expressions

4.3 Simplification of Linear Algebraic Expressions
4.4 Factorization by Extracting Common Factors
4.5 Factorization by Grouping Terms

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Chapter 5: Simple Equations in One Variable

5.1 Simple Linear Equations in One Variable
5.2 Equations Involving Parentheses
5.3 Simple Fractional Equations
5.4 Forming Linear Equations to Solve Problems

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Chapter 6: Ratio, Rate, and Speed

6.1 Ratios Involving Rational Numbers

A. Meaning of Ratio
B. Simplification of Ratios
C. Ratio of Three Quantities
D. Problems Involving Ratios

6.2 Average Rate
6.3 Speed

A. Uniform Speed and Average Speed
B. Conversion of Units

In A Nutshell
Extend Your Learning Curve

Chapter 7: Percentage

7.1 Meaning of Percentage

A. Introduction
B. Expressing One Quantity as a Percentage of Another

7.2 Reverse Percentages
7.3 Percentage Increase and Decrease

A. Percentage Increase
B. Percentage Decrease

7.4 Discount and Sales Tax

A. Discount
B. Sales Tax

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Chapter 8: Angles, Triangles, and Quadrilaterals

8.1 Points, Lines, and Planes
8.2 Angles

A. Angles and Measurements
B. Types of Angles
C. Complementary, Supplementary, and Adjacent Angles
D. Properties of Angles

8.3 Perpendicular Bisectors and Angle Bisectors

A. Use of Compasses
B. Perpendicular Bisectors
C. Angle Bisectors

8.4 Triangles

A. Classification of Triangles
B. Construction of Triangles

8.5 Quadrilaterals

A. Types of Quadrilaterals
B. Properties of Special Quadrilaterals
C. Construction of Quadrilaterals

In A Nutshell
Extend Your Learning Curve
Write In Your Journal

Answers 

Note: The answer key in the first printing of Textbook 7A has some errors in it. Please download revised key from here. Please note that not all the answers are incorrect in the first printing answer key, and incorrect answers are highlighted in this corrected answer key. We apologize for the inconvenience caused. 

Click here to view Dimensions Math® Teaching Notes and Solutions 7A samples.

Dimensions Math® G6-8 Textbooks are designed for middle school students. Developed in collaboration between Star Publishing and Singapore Math Inc®, this series follows the Singapore Mathematics Framework and covers the topics in the Common Core State Standards.

The emphasis of this series is on empowering the students to learn mathematics effectively and independently. Depending on the topics covered, different approaches are adopted for the presentation of concepts to facilitate easy understanding by students to internalize concepts and instill in them an interest to explore the topics further.

Each book includes appropriate examples, class activities and diagrams to understand the concepts and apply them. IT skills and values are incorporated as appropriate.

Some features of this series include the following:

  1. Class activities which allow the student to learn mathematics through discovery. Some of the class activities make use of Geometer’s Sketchpad (available at keypress.com).
  2. Worked examples are followed by a similar question (Try It!) so that students can check if they have understood the concepts presented earlier.
  3. An exercise for each lesson including questions in the following sequence:
    • Basic Practice (simple questions involving a direct application of the concepts)
    • Further Practice (more challenging questions on direct application)
    • Maths@Work (questions that apply mathematical concepts to real-life situations)
    • Brainworks (questions involving higher order thinking or an open-ended approach to problems)
  4. Each chapter is followed by a review exercise; the Extend Your Learning Curve activity encourages students to explore mathematical concepts further or apply mathematics in real-life situations, with some questions requiring sentence or paragraph answers to encourage students to reflect on their learning experiences.
  5. The right margins contain remarks on important information, concepts or definitions covered earlier related to the current material to help students recall them, discussion questions, interesting puzzles or facts that are related to mathematics, and some website references.

The answer key at the back of the book provides answers to the Try It! and the problems in the exercises for the Basic PracticeFurther Practice, and Maths@Work questions. It does not include answers to the class activities or the Extend Your Learning Curve activities. 

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C
Verified Purchase
C
West Palm Beach, US
★★★★★ 5
Delightful little device now that I've had a practice run with it
Color: Silver
I just picked this up to make my own cappuccino and breve and I must say that I've fallen in love with the thing. My first use was a bit of a misfire owing to my inexperience with it, but the second time worked like a champ. The trick is to ensure that you have plenty of empty head space in the container to develop a good vortex and foam volume while still having a tall enough fluid column to keep the mixing head mostly submerged while generating the vortex. My first attempt involved using about half a cup of half and half in a small saucepan. I had more than enough head space, but I was only barely able to keep the mixing head (it comes with two: a single turn coil and a 3-turn coil of coil) submerged and that went poorly, leaving me with a bit of a mess to clean up on my rangetop as the lack of fluid column ended up slinging the fluid around and out of the saucepan. The second attempt went far better, as I transferred the barely-simmered half and half back into the Pyrex two-cup mixing cup in which i initially measured the 4 fl. oz. This time it worked beautifully. There was just enough unfoamed column height to keep the mixing head well covered prior to powering up and it just barely kept me sufficiently covered while powered up to maintain a very vigorous yet controlled vortex. This method also had the advantage of telling me exactly how much total foamed volume I had generated. The resulting breve had a wonderfully thick and frothy head in my mug and resulted in a delightfully topped beverage which, if anything, had a bit too much foam and a bit too little liquid. That's on me, however, since I wanted to get a feel for the device under better conditions to build my own experience; I'll just run the frother for less time next time. Cleanup of the device itself is quite easy: simply detach the mixing head and shaft from the motor base and rinse. I always hand-wash my dishes, so I'm not in a good position to speak to its machine wash compatibility, but I suspect that it would come out just fine, provided that care is taken not to bend the shaft or coil head out of shape. The device itself is small enough to fit in a purse and should travel quite nicely, though you'll need to commit to a single mixing head, which will almost certainly turn out to be the smaller one. It's really nice to be able to make cappuccino/breve at home any time I see fit now. It's going to make a well-loved addition to my kitchen.
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Reviewed in the United States on December 6, 2018
C
Verified Purchase
C. Day
Los Angeles, US
★★★★★ 4
Worked well, fast, then overheated. Contacted Vomelon and they were quick to help me replace unit.
Color: Silver
Update ***Vomelon customer service is great! I contacted them about my issue, they responded quickly and worked to resolve it. They're giving me a new one! Hope this one works out. I'm adding back a star for their service. Update 4/18/20 While making whipped Dalgona coffee today the unit slowed down the completely shut off. I pressed the power button again to restart and same thing, it starts at high speed then slows down and shuts off. I will be contacting seller. I’m taking away a star, can’t believe this is happening. First day using this frother with the batteries provided and the body became very hot. Used it for about 3 minutes and the heat became uncomfortable in my hands. Took out the AAA alkaline batteries “Nai Li Wang” brand made in China and replaced them with some Kirkland AAA that I had on hand. Problem solved! No overheating with the new batteries. Throwing away the China made batteries. Would’ve been 5 stars if it weren’t for the overheating. Other than that mishap, the frother was easy to use and pretty powerful. Whipped up my coffee with maple syrup (making Dalgona coffee) really quick. I like that it has a cover for storage. I don’t have much space so having a compact size with a cover is convenient, I can put it in a drawer or storage box without damage to the whisk. Update: Day 2 of use Body of unit became warm but not hot as with original batteries provided. I used new batteries. Had the unit on for 4-5 minutes to whip my dalgona coffee. Not sure if the unit is supposed to get warm? Is it normal? I will contact seller. Besides that, my coffee got whipped pretty quick. I want to upload a photo but seems that Amazon has taken away that function for me? I could upload photos for my previous reviews on other products.
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Reviewed in the United States on April 16, 2020
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Verified Purchase
Guy E. Wolek
Chelsea, US
★★★★★ 5
Great Little Frother.
Color: Silver, Color: Silver
I really like this this little frother. What I noticed first is that it comes with a cover for the frothing arm. That’s very practical if you travel with it. I have traveled with a frother before and I put it in a toothpaste box, not much protection there. I use this 2 to 4 times a day. I can come pretty close to creating a Starbucks flat white at home. That saves $$$. The next thing I really like is that I can remove the arm for cleaning. If the arm does not come off clean up is a bit tricky. How does it work? Great! It has one speed, Fast. The power button is on the base of the handle so I just had to adjust the way I hold the frother when I turn it on. One thing, make sure the froth head is all the way into the liquid when you start it, lol. This little machine whips up a thick froth fast. It comes with 2 frothing heads, a three spring version as well as a standard one spring. There is a lot of plastic, but it doesn’t look or feel cheap. Actually I think it helps keep the weight down. I travel some and I appreciate when things are light. Over all, this is really nice it’s light portable and works great. I highly recommend this product. I was given this product for review and I am so glad they choose to contact me. I have been frothing milk for my coffee for the last few years. This has now became my go to frother.
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Reviewed in the United States on July 12, 2019
J
Verified Purchase
JSS
Belleville, US
★★★★★ 5
Great Frother
Color: Silver
The best frother I’ve owned! Love that the whisk is removable for washing, the end is flat so it stands up on its own and it’s pretty powerful.
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Reviewed in the United States on February 20, 2026
T
Verified Purchase
Toga
Lexington, US
★★★★★ 1
Almost right but connector sucks
Color: Silver
I much prefer a frother with swappable batteries and always use rechargeable AAA's and never disposable one's. The power button is in a comfortable spot as opposed to everyone else's odd and very uncomfortable side placement. Placing the power button on the side make you have to twist your entire arm to have your thumb facing down to be able to press anything whereas this one is right on top and can hold it like a simple joystick with no twisting of my arm. However, these plastic attachment points crack waaay too easily. I've already bought 3 of these and this is the part that breaks on all of them. I have designed and printed new attachments but the installation of them can damage the motor if I'm not careful. The motor also looses torque after only a few months. The windings need to be improved. Even though I really hate the plastic attachment, the button on top and the ability for it to stand up on its own without some stupid fiddly stand are the ONLY reasons I come back to this design. The moment someone makes a fully metal attachment (like I've seen) a power button on top and self standing, I'll throw this one away. Updated April 2025: I am about to buy my 4th one since 2019. This is NOT an endorsement for it, I just haven't found anything design wise that's better. The motor in these are short lived and they give out with no warning. Ergonomically this design make more sense than a side mounted button or switch, but I'm still dropping a star for the fact I've had to buy 4 of these darn things in such a short time Update: Oct 2025 I just bought this replacement in April and this things motor is already dead. I'm done with this item/seller. Just an overly cheap product. Product no longer worthy of even 2 stars
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Reviewed in the United States on May 27, 2024

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