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## Math — Fractions — 5th Grade Polo Ridge

Topic 9- Dividing Fractions
In this topic, your student is learning how to interpret a fraction as division of the numerator by the denominator and show quotients as fractions and mixed numbers. He or she is solving real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. A unit fraction is a fraction with a numerator of one. The end of topic test will be given by March 13th.

Topic 10- Volume
Throughout this topic, your student is learning about volume. He or she will learn how to find the volume of a rectangular prism, and then use that understanding to formulate a plan to find the volume of a solid figure that is a combination of two or more rectangular prisms. Your student will also use models to develop the formula for volume and to recognize a cube with a side length of one unit as a unit cube having one cubic unit of volume. This will give him or her the skills necessary to solve problems involving volume, the area of the base of a prism multiplied by the height of the prism. ### Fraction Lessons

• ﻿Add and subtract fractions with unlike denominators (including mixed numbers) with fraction bars
• Add and subtract fractions and mixed numbers with unlike denominators using area models
• Add and subtract fractions with unlike denominators
• Add and subtract mixed numbers

### Multipliction and Division

• Interpret a fraction as division and answer division problems using fractions
• Interpret fractions as division and solve problems leading to answers in the form of fractions
• Multiply a whole number times a fraction
• Multiply a fraction times a fraction
• Solve problems involving multiplication of fractions and mixed numbers

### ath Resources:

We Love Math!

Visit the following website to select challenging math problems for 1-6th grade. You will find plenty of math challenges at Mathtop10.com.

www.mathtop10.com

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## Teaching Volume — (Free Volume Hands-on Activity and Posters) —

| 6 Comments | Filed Under: Geometry & Measurement, Math

When we moved to the Common Core standards this year, volume was a new skill for my 5th graders. Also, since there were three standards that addressed some aspect of volume, it was assessed more frequently than the other standards. I knew I needed to find or create some quality and engaging resources for teaching volume. This post shares my go-to activities, video, and resource for teaching volume (including a few free resources).

### Introducing Volume: Study Jams Video

When I introduce Volume for the first timel, I always like to start with this Study Jams video on volume. My students always love Study Jams video and this video is great for showing visuals to help the students conceptually understand the concept of volume.

### Teaching Volume with Hands-On Volume Activities

After introducing the skill through this video, we do a lot of building prisms and practicing the skill in a hands-on manner. One way that we do this is by building different rectangular prism using linking cubes. Here are some of the activities we do when building prims and calculating volume (by counting the cubes and not using the formula – more about how we transition to the volume formula in the next section):

• We build a variety of prisms based on lengths, widths, and heights that I tell the students. • The students “free build” rectangular prisms and then record the length, width, height, and the volume of the prism.
• The students build different prisms that have the same volume. Grab the free printables for this hands-on volume activity by clicking here!

### Moving to the Volume Formula

After a few days of practice building prims and calculating volume, we are ready to move to the volume formula (length x width x height). I do this through an exploratory lesson where the students (at my guidance) use their unit cube prisms to derive the formula. Then, we test it out several times with new prisms before we officially decide that it is an effective and efficient formula for determining volume.

Grab these free posters for introducing and teaching volume by clicking here.

### Hands-On Volume Activity Using the Formula

Even though we move to using the formula for calculating volume, we are not done with hands-on activities. One of our favorite activities is measuring actual boxes and then determining the volume of those boxes. This also helps the students check the reasonableness of the volume they calculate, which helps with estimating volume.

For this hands-on volume activity, we ask students and other teachers in the school to bring in boxes and we collect them from year to year. The students use rulers (they choose inches or centimeters) to measure the length, width, and height. Then they use the formula that we derived in the previous lesson to determine the volume.

### My Go-To Resource for Teaching Volume

Hands-on activities are very important to ensure students have a conceptual understanding of volume, but we also use paper to pencil practice as well. I use the resources in my Teaching Volume Unit from TPT.

Here are some of the key resources in this Volume Resource:

• Volume Practice Printables – The printables have a variety of different volume skills for the students to practice. There are also a few printables that are activities that require the students to build and draw prisms. There is also a printable that has the students solving a performance based task involving cracker boxes with specific dimensions. There are three parts to this task and the students get to design their own cracker and cracker box design.

• Volume Math Centers – My favorite part of this resource are the volume math centers. The math centers include a little of everything: building prisms and calculating the volume of the prisms, spinning dimensions and then calculating volume, and then task cards that review a variety of volume skills.

• Additive Volume – One of the trickiest skills for the volume standards is additive volume. This resource includes a math task that is perfect for introducing the skill and then a separate printable for continued practice. Additive volume practice problems are also included in the task cards, exit slips, and assessments.

• Volume Assessments – The biggest key to success with this unit (besides all the hands-on practice) is regular formative assessment to see how the students are progressing. Since this is a new skill for 5th graders, it is important that we build a strong foundation and conceptual understanding without misconceptions or errors in thinking. In order to regularly monitor my students’ progress, this resource includes a variety of exit slips that address all the skills and get progressively more difficult. A two-page post assessment is also included that can be used as  a summative assessment.

If you are interested in more printables, math centers, and assessments to help you teach volume, click here or on the image below to purchase the unit from my TeachersPayTeachers store.

Do you have any great ideas or resources for teaching volume? Let us know in the comments!

6 Comments | Filed Under: Geometry & Measurement, Math

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Welcome friends! I’m Jennifer Findley: a teacher, mother, and avid reader. I believe that with the right resources, mindset, and strategies, all students can achieve at high levels and learn to love learning. My goal is to provide resources and strategies to inspire you and help make this belief a reality for your students. Learn more about me.

Theme of the lesson: Luch. Plane. Image of basic geometric shapes.

Geometry and arithmetic are important parts of mathematics. In arithmetic, we are mainly concerned with calculations, that is, operations with numbers. And the very name «arithmetic» comes from the Greek word «arithmos», which means number in translation. Let’s analyze the word «geometry» in parts: «geo» and «metry». What famous words start with geo? (Geography, geology, geodesy, etc.)

All these sciences study the earth. Indeed, the word «geo» in ancient Greek means «earth». What does the word «metric» mean? Let’s remember why we need a meter, and in what cases we use a meter. ( For measuring). Therefore, the word «geometry» can be translated as «surveying». Paper had not yet been invented in antiquity, so drawings were then often made on the ground. You will draw in notebooks.

The surface of the chalkboard and the pages of a notebook are flat surfaces or, as they say in geometry, planes. More precisely, they are only finite parts of infinite planes.

— Which of the following surfaces — a floor, a ceiling, a curtain, a flower petal, a tree leaf, a handle — can be considered flat?

— Give examples of your flat surfaces.

In geometry, we deal with drawings — drawings, which depict geometric shapes. — By what rule were the figures combined into groups?
(Hint* Plane figures and three-dimensional bodies)

— Name the plane figures you know
(Hint* square, triangle, circle, rectangle)

— Name three-dimensional bodies you know.
(Hint* Cube, cylinder, cone, pyramid, ball)

The word «figure» in Latin means «appearance», «image». Name objects that have the shape: ball, circle, square, cube.

— You are already familiar with the basic geometric shapes. This is a point, a segment, a ray, a straight line, an angle, a triangle, a rectangle, a polygon, a circle.

1. Reference. The figure shows a line, a segment, a ray, an angle, a triangle, a circle, a rectangle, a circle, a rectangle, a quadrilateral, a pentagon, a circle.

— List each of these shapes.

— What drawing tools do you need to draw these figures?
All these figures, except for the dot, are drawn using lines. 2. Job. Performed independently.

1) Draw line segment AB. Mark points so that point:

a) K did not belong to segment AB;
b) L belonged to segment AB;
c) N was between points A and L;
d) M was on the segment between points N and L.

2) How many segments were formed on the segment AB?

CHECK:.

3. There are infinitely many lines that can connect points A and B. Line AMNB is called a broken line, it consists of three links — segments AM, MN, NB. Imagine that all three of our lines are threads. Then both the broken line and AMNB, and the curve AB can be straightened by pulling, for example, the end of B. But the segment AB cannot be stretched. This means that it is the shortest of all the lines connecting points A and B. Therefore, the length of the segment is considered the distance between points A and B.

4. RULES for reading equalities and inequalities with segments.
In equality, everything on the left side is read in the nominative case, and everything on the right side is read in the dative case. EX. AB \u003d 7 cm — the length of the segment AB is seven centimeters.

In the inequality, everything on the left side is read in the nominative case, and everything on the right side is read in the genitive case.

EX. AB

Point K lies between points C and B, and point N lies between points K and C. Compare the lengths of the segments and write down the result using inequality signs:

1) CB and NK; 2) CN and SC; 3) VN and VK; 4) SW and SC.

CHECK:

1) CB NK; 2) СN ВК; 4) SV SK.

6. Oral work.

a) AB = CD; e) pH = 5 m 6 dm;
b) EF c) MN OS; g) XY = XE — EY;
d) RT = 3mm; h) DF = CD 5.

— Which points belong to the segment KL?

— Between which points is located:
a) point L? b) point A?

— Which point is located between:
a) points K and B?;
b) points B and L?.

— Find the length of the segment KL if it is known that KD = 15cm, LW = 9cm, BA = 21cm, AL = 7cm. 7. Homework.

1) Practice in drawing segments with ends at given points.

2) Assignment — for strong students. Conclude that the sum of the distances from the point to the ends of the segment is equal to the length of the segment if the point belongs to the segment, and more than the length of the segment if the point does not belong to the segment.

Complete the sentence.
I can…
I can…
I know…

## IRO DISTANCE LEARNING SYSTEM › Mathematics. Geometry around us (grade 5) (template)

The e-learning course «Geometry around us» is designed to accompany the study of the basic mathematics course in grade 5 or as additional tasks in the mathematics course of grades 5-6.

target course : organize through a system of tasks the intellectual, practical and research activities of students aimed at:

— the development of spatial representations, figurative thinking, visual and graphic skills, methods of constructive activity, the ability to overcome difficulties in solving mathematical problems, geometric intuition, cognitive interest of students , development of an eye, memory training of correct geometric speech;

— the formation of logical and abstract thinking, the formation of personality traits (responsibility, conscientiousness, discipline, accuracy, perseverance). Course objectives introduce students to the properties of geometric shapes at the level of practical research,

teach how to apply acquired knowledge in solving various problems. The main techniques for solving problems are: observation, design, experiment.

Authors of the course :

— Mathematics teacher of the Moscow Autonomous Educational Institution Lyceum No. 21, Pervouralsk Sushintseva Irina Anatolyevna

— Specialists of the SAEI DPO SO IRO

For technical support, please contact the Center for Distance Educational Technologies of the IRO at mail [email protected]

Thematic planning

Technological map of the course «Geometry around us» Grade 5

Section/Topic

Contents

Control forms

Lesson 1. Introduction

Getting to know the specifics of working in course

Lesson 2.

First steps in geometry

1. Solve the crossword puzzle

Lesson 3.

Space and dimension

Part 1

1. The concept of three-two- and one-dimensional space
2. Image of a cube by dots
3. Image of a box by points
4. Dotted Pyramid

Part 2

1. Exercise 1. Flat and three-dimensional geometric shapes
2. Exercise 2. Filling in the blanks «Elements of a cube, box, pyramid»
3. Exercise 3. Dividing into groups «Pyramids» and «Other geometric shapes»
4. Exercise 4. Dividing geometric shapes into groups «One-dimensional production», «Two-dimensional production», «Three-dimensional production»
5. Exercise 5. Geometric Lotto
1. Studying the materials of the training module
2. Making drawings in a notebook
3. Exercise

Lesson 4.

Section. Cut length

1. Point concept
2. The concept of a segment, its designation.
3. The concept of a straight line, its designation
4. Mutual arrangement of a point and a segment
5. Length of cut, units of length

Learning Module

Lesson 5.

Problems about calculating the length of a segment

1. Exercises for calculating the length of a segment (part 1)
2. Problems about calculating the length of a segment (part 2)
1. Exercise (Part 1)
2. Completion of a creative practical task (compose and solve a problem) (part 2)

Lesson 7. Luch. Angle

1. Beam concept
2. Concept of an angle, types of angles
3. Types of angles according to their degree measure
1. Learning Module Materials (Part 1)
2. Performing exercises to determine the type of angle (part 2)

Lesson 8.

Protractor Measuring and plotting angles

Part 1

1. Drawing tools (protractor, ruler, compasses)
2. The concept of the degree measure of an angle
3. Rule for measuring angles with a protractor
4. Examples of measuring the degree measure of an angle with a protractor
5. Rule for constructing angles of a given value

Part 2

Practical exercises on the topic «Measuring and constructing angles with a protractor»

1. Learning Module Materials (Part 1)
2. Performing practical tasks on the topic «Measuring and constructing angles with a protractor» (part 2)

Lesson 9. Angle Finding Problems

Practical lesson on solving problems of finding the magnitude of the angle

Performing practical tasks on the topic «Problems of finding the magnitude of the angle»

Lesson 11.

Construct an angle equal to the given one. Dividing an angle in half. Practical work No. 1

Part 1

1. Algorithm for constructing an angle equal to a given one
2. Algorithm for bisecting an angle

Part 2

Performing practical tasks for constructing an angle equal to a given one, dividing the angle in half

1. Learning module
2. Practice #1

Lesson 12.

Triangle

Part 1

1. Polygon concept
2. Polygon examples
3. Triangle, triangle elements
4. Types of triangles

Part 2

Research practical work

1. Learning Module Materials (Part 1)
2. Performing research practical work (part 2)

Lesson 13. Polygon circumference

Exercises for calculating the perimeter of a rectangle, square and triangle

Performing exercises on the topic «Perimeter of a polygon»

Lesson 15. Research work. The sum of the angles of a triangle

1. Research work «Measuring angles with a protractor»
2. Research work «The sum of the angles of a triangle»
1. Research practical work «Measuring angles with a protractor» (part
2. Research practical work «The sum of the angles of a triangle» (part 2)

Lesson 16.

Sum of the angles of a triangle

Solving problems on finding the degree measure of the angles of a triangle

Lesson 18. Construction of a triangle equal to the given one. Practical work №2

Part 1

1. Algorithm for constructing a triangle given two sides and an angle between them
2. Algorithm for constructing a triangle given a side and two adjacent angles
3. Algorithm for constructing a triangle on three sides

Part 2

Practical work on solving building problems

1. Learning Module Materials (Part 1)
2. Implementation of practical work No. 2 (part 2)

Lesson 20.

Triangle area

1. The concept of the area of ​​a figure
2. Area units
3. Area properties
4. Square area
5. Area of ​​a rectangle
6. Triangle area

Studying the materials of the training module

Lesson 21. Area units

1. Area units
2. Area unit ratio

Studying the materials of the training module

Lesson 22.

Problems for finding the areas of shapes

Exercises for finding the area of ​​shapes (rectangle, square, triangle)

Exercise

Lesson 24. Polygons in painting

2. Geometric Drawings by Tim Biscap

Studying the materials of the training module

Lesson 25.

Triangle elements

Elements of a triangle exercise

Performing exercises on the topic «Elements of a triangle»

Lesson 26. Practical work No. 3. Triangle parquet

Practical work «Parquet of triangles»

Implementation of practical work No. 3

Lesson 28.

Surface area of ​​the parallelepiped

Exercises on the topic «Surface area of ​​a parallelepiped»

Performing exercises on the topic «Surface area of ​​a parallelepiped»

Lesson 29.

Box Volume

1. Concept of volume
2. Volume units
3. Volume properties
4. Volume of box, cube
5. The concept of a prism
6. Prism Volume

Learning Module

Lesson 30.

Volume. Volume units

1. Volume units
2. Correlation of volume units

Learning Module

Lesson 32.  Similar Posts