7.1: New Page - Mathematics

7.1: New Page - Mathematics

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7.1: New Page - Mathematics

Overview of Randall Holmes's Home Page

Just so you know who you are really dealing with.

I'm (Melvin) Randall Holmes, a professor of mathematics at Boise State University in Boise Idaho since 1991. My research is in systems of set theory or combinatory logic related to Quine's set theory New Foundations, with a sideline in computer-assisted reasoning. I have a general somewhat more than amateur interest in the history and philosophy of mathematics, particularly mathematical logic.

This is a version of my home page under my own control. It largely mirrors but does not exactly mirror my former university home page. It will contain some material found in my page at the university which will appear familiar other material (either outdated or inconvenient to import to the new location) will not be reproduced. The original page is now redirected to here (queries to most subdirectories of the original page will come right here, because the internal structure of this page is different). Queries to my Loglan resources at Boise State will go to the root Loglan page here.

Here is my very ancient personal data page, which is not very serious and has a lot of broken links because it is ancient and needs to be fixed.

Here is the universal set bibliography (an expansion of the bibliography of Forster's NF book). I have an obligation to do some updating here.

Here is a largely outdated blurb about my NF activities, which I preserve for revision.

Here is my old home page for New Foundations, which is referenced here just so I can go in and fix it. It is very old.

Here is my new separate page on the artificial language Loglan.

Set theory textbook

Teaching Stuff

Theorem Proving Projects

  • Marcel: Here is the page for my current theorem proving project Marcel. There is access to documents from the latter two sections.

New York State Math Curriculum

Curriculum modules in mathematics are marked by in-depth focus on fewer topics. They integrate the CCLS, rigorous classroom reasoning, extended classroom time devoted to practice and reflection through extensive problem sets, and high expectations for mastery. The time required to complete a curriculum module will depend on the scope and difficulty of the mathematical content that is the focus of the module (first priority cluster area for a given grade level). For example, the curriculum module relating to Grade 3 multiplication and division introduces initial ideas of multiplication and division in a brief period at the start of the year, continues to develop strategies and problem solving throughout the year, and includes materials to be used throughout the year for helping students reach fluency by the end of the year with single-digit multiplication and related division.

Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.

Table of contents

This is quite self-­explanatory *

The TE and Student books are color coded according to the critical areas in the standards.

When you pick up the first chapter in a color set you will find that it has an extra tool. The Critical Area at a Glance gives you a more in depth view of the skills and activities across all the chapters included in that particular critical area.

Here you have the Chapter at a Glance and it does exactly what its name suggests. This can be used in your planning, to help you see the:

  • essential questions,
  • objectives and vocabulary,
  • needed material and manipulatives
  • print resources to gather for you lessons,
  • digital options known as the Digital Path and
  • response to intervention (RTI).

In the lower grades TE you will occasionally find a section with a Math Story that will connect your lesson to other subjects. In this case, the story is designed to connect to Social Studies. Before you use any of these literature *connections be sure to preview them for appropriateness for your classroom.

Next in your TE you will come to the section Teaching for Depth.This is an area that shows how Go Math! is very different from prior math series. Because our NAD Math Standards focus on greater depth and less breadth, these pages will serve to help us strengthen our supporting knowledge of the skills being taught. A very helpful part of this section is the Professional Development Videos for Podcasting. They are short videos, designed as a review of standards and skills for use by the teachers. You will find them to be a short, practical explanation of the concepts and recommended manipulatives. This is a very valuable tool for teachers: much like having your very own math expert at your fingertips. HOUGHTON MIFFLIN HARCOURT is continually adding to its bank of podcasts. If the lesson does not show the podcast icon, check on Think Central.

Your TE now takes you to the Daily Classroom Management page. This page reminds us of the ways we can differentiate instruction using Go Math! materials. We see Whole Group and Small Group Activities. We are reminded of the Response to Intervention, RtI, components that provide support for the students who

Now we turn to the section where we can Review Prerequisite Skills . At the bottom of the page you will find the standard that is being taught in this chapter. At a glance, you can see what skills and standards were taught in the previous grade that support the present concept being addressed and what skills will be taught at the next grade level to build on what is being taught now. *

At the top of this page you will see a list of activities that can be used to refresh the students&rsquo memory on the prerequisite skills needed for the current chapter. As this series is being adopted there are bound to be areas where students are not yet as prepared as we would like them to be. This page will give suggestions on how to support them. Over time, as Go Math! is taught from grade level to grade level, this problem should become a moot point. The Assessment Guide has a Prerequisite Skill Inventory that can be given to the students to help further identify the missing skills.

The following page is a very important component in teaching with Go Math!. Developing Math Language is every bit as essential to student success as problem solving and computation. Here you will find the vocabulary for this chapter listed. These words and concepts can be used in word walls, math bulletin boards and even in math journals created by the students for future reference.

And now we come to Introduce the Chapter. In this section you will find pages that are in the student text. In first and second grade you will find an introductory page for the unit, Show What You Know, Vocabulary Builder and a Game. This section will have a picture of a send home letter that can be found in the Standards Practice book.

In grades 3-­6, Introduce the Chapter begins with Show What You Know and Vocabulary Builder. Show What You Know is a quick assessment tool to help the teacher determine if students need intensive or strategic intervention. Vocabulary Builder helps set the tone for the conversations that will follow.

Earlier we looked at the Chapter at a Glance. Now we come to the Lesson at a Glance page. The red section at the top of the page will have much of the same information found *in the Chapter at a Glance with the expanded Common Core Standard written out. We should pay special attention to the Lesson Objective and the Essential Question as we plan our lessons.

The red section at the bottom of the page, Mathematical Practices, will give quick explanations for the teacher that are pertinent to this lesson. This is where a Pod Cast icon will be placed if there is one available. The pod casts can be downloaded to your computer for easy viewing later without the need for an internet connection. There will be Daily Routine activities that support the skills taught and used in this lesson.

On the facing page are resources for Differentiated Instruction Activities. These will help you meet the needs of the learners in your classroom at a variety of levels. And now we have come to the lesson pages. Always look for the white numbers in red circles, 1-­4.

&ldquo1&rdquo Engage will be a short part of the lesson to catch the interest of the students,

&ldquo2&rdquo Teach and Talk will include activities such as Unlock the Problem, Listen and Draw and Investigate. As you work toward the end of Teach and Talk section 3 will have Share and Show which is used as a quick assessment for RtI (Response to Intervention). &ldquo3&rdquo continues with On Your Own and Problem Solving. Each lesson ends with &ldquo4&rdquo, Summarize. Here you will be prompted to review by using the Essential Question. Suggestions for supporting the student Math Journals are found here.

The lessons continue on in the same format until you come to the Mid-­Chapter Checkpoint. Formative and Summative Assessments are conveniently labeled with a red *tab for easy reference. Simply feather the TE&rsquos pages to see the red tabs. At the bottom of the assessment pages you will find direction as to how to address the specific needs of each student. There will also be a description of common errors. This is a quick tool that can be used for helping our students master the standards being taught.

After the Mid-­chapter Checkpoint lessons continue again to the end of the chapter and the Summative Review/Test. The Summative Assessments have a form A and B. The answer key for Form A is found in the TE. You will find the Form B answer key in the on-­line Assessment Guide, TE.

The Go Math! TE is a very valuable tool. It does much more than simply show an example of the student text with answers. When fully utilized, along with the ePlanning Guide, the tools for streamlining and supporting the teacher&rsquos work are varied and numerous. As you use it for planning and daily math classes remember that this is simply a tool used in the hands of a professional teacher. We were not called to teach math. We are commissioned to teach His children. With the touch of the Master Teacher our efforts can reach farther than we can begin to imagine. Go with God.

Sample Grade 1 Math Worksheet

K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5. We help your children build good study habits and excel in school.

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K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5. We help your children build good study habits and excel in school.

Fourth Grade Math

Educators may find the fourth grade math curriculum covers a lot of ground. Fourth graders begin to incorporate algebraic thinking, understand the place value of numbers up to 1,000,000, the basic shapes and their angles in geometry, among other higher-level challenges. Coming up with lesson plans and homework assignments in all these areas is a lot of work, but's Learning Library provides resources that encompass all of Common Core's fourth grade math standards.

Parents and teachers can choose from a large selection of professionally-created lesson plans that provide clear, straightforward instruction. The plans include divisibility practice, geometric angle exercises, fraction teachings, word problem challenges, metric measurements and more.

Imaginative hands-on activities reinforce math concepts. Exercises such as Play Pantry Math, Dividing by Fractions with Graham Crackers and Math in the Kitchen use treats to engage fourth graders in math. A selection of online games like Galactic Space Fractions: Comparing Like Denominators, serves a similar reinforcement purpose, plus, the visuals add an extra method for memorization.

The Learning Library resources accommodate whatever educators may need when teaching the broad spectrum of the fourth grade math curriculum.

Customer reviews

Top reviews from the United States

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This book has ADHD. It's a disaster from beginning to end. Whoever wrote it clearly has no idea about how to present algebra so that students actually understand it. If you're a student stuck with this book and are confused, don't feel bad. It's not your fault that your book jumps from one idea to another like a pinball bouncing off bumpers.

I prefer a book like Algebra: Structure and Method, Book 1 or Modern Algebra - Structure and Method: Book One . These books go in order and present one idea at a time. The Prentice Hall book, on the other hand, mashes up three ideas into one section and assumes that students know stuff they can't possibly know. For example:

Section 3.3: Hi kids! Today's lesson is about solving equations with variables on both sides of the equals sign. Here's an example. Look, here's a pretty picture of some people rollerblading! Solve the word problem about rollerblading. BTW, vertical angles are congruent! Solve the problem about vertical angles (consult diagram showing crossed lines. [6x+3 degrees] is above the point where they cross and [8x-21 degrees] is below it. Figure out what all this means and solve.).

My daughter: "Okay, what the HECK are vertical angles? And what does *congruent* mean? I do NOT get this."

Me: I'll explain it. You don't get it because you haven't taken geometry yet.

Book: Swell! Now here are two word problems about someone's salary. Do them. Next, use a graphing calculator to solve the following problems.

My college-student son: "What the HECK? A graphing calculator? In Chapter 3 of Algebra 1? They haven't even learned that there *is* such thing as graphing an equation yet. What's the point of a graphing calculator?

Book: Great job! Here's picture of a teddy bear! Now let's fill in some tables. Moving right along, let's go back to graphing calculators. Finally, Joey made the spreadsheet at right to solve the following equation. Did he make a mistake?

In the next section, we will work with ratios and proportions. We will include pictures of cheetahs and Lance Armstrong!

Seriously, I do NOT know how any student, no matter how talented, could emerge from a course based on this book with anything resembling literacy in algebra and without significant help from a parent and/or a tutor. As in, doing a completely different course with said parent or tutor.

Most read

M. O. Korpusov et al 2021 Izv. Math. 85 111

We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when there is a local weak solution.

S. D. Glyzin et al 2021 Izv. Math. 85 177

We study a quite natural class of diffeomorphisms on , where is the infinite-dimensional torus (the direct product of countably many circles endowed with the topology of uniform coordinatewise convergence). The diffeomorphisms under consideration can be represented as the sums of a linear hyperbolic map and a periodic additional term. We find some constructive sufficient conditions, which imply that any in our class is hyperbolic, that is, an Anosov diffeomorphism on . Moreover, under these conditions we prove the following properties standard in the hyperbolic theory: the existence of stable and unstable invariant foliations, the topological conjugacy to a linear hyperbolic automorphism of the torus and the structural stability of .

V. D. Sedykh 2021 Izv. Math. 85 279

We prove that the manifold of non-singular points of a stable real caustic germ of type and the manifolds of points of transversal intersection of its smooth branches consist only of contractible connected components. We also calculate the number of these components.

Yu. G. Prokhorov and C. A. Shramov 2020 Izv. Math. 84 978

We classify uniruled compact Kähler threefolds whose groups of bimeromorphic selfmaps do not have the Jordan property.

S. A. Nazarov 2020 Izv. Math. 84 1105

We describe and classify the thresholds of the continuous spectrum and the resulting resonances for general formally self-adjoint elliptic systems of second-order differential equations with Dirichlet or Neumann boundary conditions in domains with cylindrical and periodic outlets to infinity (in waveguides). These resonances arise because there are &ldquoalmost standing&rdquo waves, that is, non-trivial solutions of the homogeneous problem which do not transmit energy. We consider quantum, acoustic, and elastic waveguides as examples. Our main focus is on degenerate thresholds which are characterized by the presence of standing waves with polynomial growth at infinity and produce effects lacking for ordinary thresholds. In particular, we describe the effect of lifting an eigenvalue from the degenerate zero threshold of the spectrum. This effect occurs for elastic waveguides of a vector nature and is absent from the scalar problems for cylindrical acoustic and quantum waveguides. Using the technique of self-adjoint extensions of differential operators in weighted spaces, we interpret the almost standing waves as eigenvectors of certain operators and the threshold as the corresponding eigenvalue. Here the threshold eigenvalues and the corresponding vector-valued functions not decaying at infinity can be obtained by approaching the threshold (the virtual level) either from below or from above. Hence their properties differ essentially from the customary ones. We state some open problems.

Yu. A. Neretin 2020 Izv. Math. 84 1161

We consider a tree all whose vertices have countable valency. Its boundary is the Baire space and the set of irrational numbers is identified with by continued fraction expansions. Removing edges from , we get a forest consisting of copies of . A spheromorphism (or hierarchomorphism) of is an isomorphism of two such subforests regarded as a transformation of or . We denote the group of all spheromorphisms by . We show that the correspondence sends the Thompson group realized by piecewise -transformations to a subgroup of . We construct some unitary representations of , show that the group of automorphisms is spherical in and describe the train (enveloping category) of .

7.1: New Page - Mathematics

Practice Worksheets
Worksheets can help students practice basic math facts for speed and accuracy.

Algebra Worksheets - Generate your own algebra worksheets to print and use. Includes many options and types of equations, systems, and quadratics.

No software to download - this works right from your browser.

Just fill in the number of problems of each type and click "Generate". Answer sheet included! (click here to begin)

Customizable Basic Skill Worksheets . Create and print your own worksheets, multiple levels and formats. Includes negative numbers, fractions and decimals.

Word Problem Worksheets Word problem sheets to print out (4th to 7th grade)

Math Stories - Print out word problem worksheets based on popular stories and books (for grades 1-6).

Other Print Materials
Grid with numbers 1 - 100 to print out. Requires PDF plug-in.

Geoboard dot paper to print out. Requires PDF plug-in.

Activity Sheets Customizable. Print out practice worksheets, tips, and tricks for K-12. Adjusts to different browsers for accurate printing.

Basic Math Practice- Addition, subtraction, multiplication and division.

Middle School Math workouts - quizzes and interactive exercises at the end of every lesson.

Even Seven

How do you make the number 7 even without addition, subtraction, multiplication, or division?

Eight Eights

Can you write down eight eights so that they add up to one thousand?

Strange Subtraction

How can you take 2 from 5 and leave 4?


Remove the 2 letters F and E from five and you have IV.

What About Circles

How many sides does a circle have?

Two. The inside and the outside.


How many times can you subtract the number 5 from 25?

Once, because after you subtract it's not 25 anymore.

A Growing Tree

When John was six years old he hammered a nail into his favorite tree to mark his height. Ten years later at age sixteen, John returned to see how much higher the nail was. If the tree grew by five centimeters each year, how much higher would the nail be?

The nail would be at the same height since trees grow at their tops.

Watch the video: Μαθαίνουμε στο Σπίτι: Μαθηματικά Ε Δημοτικού - Πράξεις με κλάσματα. 08042020. ΕΡΤ (June 2022).


  1. Brys

    There are of course a couple of beautiful moments, but I expected more !!!

  2. Mazulkis

    I congratulate, what necessary words ...

  3. Ignatius

    and how to find out - to pozon and run over?

  4. Breandan

    I am better, perhaps, promolchu

  5. Daudi

    You are absolutely right. There is something in this and I think this is a good idea. I agree with you.

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