David Wasdin

4th Grade Teacher
2014 - 2015

OVERVIEW

In this unit students will: 

Fractions and Decimals ∙ Unit 5

• ●  express fractions with denominators of 10 and 100 as decimals

• ●  understand the relationship between decimals and the base ten system

• ●  understand decimal notation for fractions

• ●  use fractions with denominators of 10 and 100 interchangeably with decimals

• ●  express a fraction with a denominator 10 as an equivalent fraction with a denominator 100

• ●  add fractions with denominators of 10 and 100 (including adding tenths and hundredths)

• ●  compare decimals to hundredths by reasoning their size

• ●  understand that comparison of decimals is only valid when the two decimals refer to the same whole

• ●  justify decimals comparisons using visual models

   

STANDARDS
Understand decimal notation for fractions and compare decimal fractions.

MGSE4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/1001.

MGSE4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

MGSE4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of the comparisons with the symbols >, =, or <, and justify the conclusions, e.g. by using a visual model.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MGSE4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

• ●  Recognize and represent that the denominator determines the number of equal sized pieces that make up a whole.

• ●  Recognize and represent that the numerator determines how many pieces of the whole are being referred to in the fraction.

• ●  Compare fractions with denominators of 2, 3, 4, 6, 10, or 12 using concrete and pictorial models.

• ●  Understand that a decimal represents a part of 10

   

• Vocabulary

  The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them.

  Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, and numbers.

  The websites below are interactive and include a math glossary suitable for elementary children. It has activities to help students more fully understand and retain new vocabulary. (i.e. The definition for dice actually generates rolls of the dice and gives students an opportunity to add them.) Note – At the elementary level, different sources use different definitions. Please preview any website for alignment to the CCGPS. http://www.corestandards.org/Math/Content/mathematics-glossary/glossary

  The terms below are for teacher reference only and are not to be memorized by the students.

  ● decimal
  ● decimal fraction ● decimal point
  ● denominator
  ● equivalent sets ● increment
  ● numerator
  ● term
  ● unit fraction
  ● whole number 

Geometry ∙ Unit 6

OVERVIEW

In this unit, students will:

 

• ●  Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines

• ●  Identify and classify angles and identify them in two-dimensional figures

• ●  Distinguish between parallel and perpendicular lines and use them in geometric figures

• ●  Identify differences and similarities among two dimensional figures based on the absence or presence of characteristics such as parallel or perpendicular lines and      

•     angles of a specified size.

• ●  Sort objects based on parallelism, perpendicularity, and angle types

• ●  Recognize a right triangle as a category for classification

• ●  Identify lines of symmetry and classify line-symmetric figures

• ●  Draw lines of symmetry 

STANDARDS 

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

MGSE4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

MGSE4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

MGSE4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. 

Vocabulary

• •     acute angle

• ●  angle

• ●  equilateral triangle

• ●  isosceles triangle

• ●  line of symmetry

• ●  obtuse angle

• ●  parallel lines

• ●  parallelogram

• ●  perpendicular lines

• ●  plane figure

• ●  polygon

• ●  quadrilateral

• ●  rectangle

• ●  rhombus

• ●  right angle

• ●  scalene triangle

• ●  side

• ●  square

• ●  symmetry

• ●  triangle

• ●  trapezoid

• ●  vertex (of a 2-D figure) 

 

Unit 7

In this unit students will:
● investigate what it means to measure length, weight, liquid volume, time, and angles
● understand how to use standardized tools to measure length, weight, liquid volume, time, and angles.

● understand how different units within a system (customary and metric) are related to each other.

● know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; L, ml; hr, min, sec.

● solve word problems involving distances, intervals of time, liquid volumes, masses of 111

● make a line plot to display a data set of measurements in fractions of a unit ( 2 , 4, 8 ) objects, and money, including problems involving simple fractions or decimals.

● solve problems involving addition and subtraction of fractions by using information presented in line plots

● apply the area and perimeter formulas for rectangles in real world and mathematical problems.

● decompose rectilinear figures into non-overlapping squares and rectangles to find the total area of the rectilinear figure

● recognize angles as geometric shapes that are formed when two rays share a common endpoint, and understand concepts of angle measurement

● measure angles in whole number degrees using a protractor
● recognize angle measurement as additive and when an angle is decomposed into non-

overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. 

 

STANDARDS 

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MGSE4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.

1. Understand the relationship between gallons, cups, quarts, and pints.

2. Express larger units in terms of smaller units within the same measurement system.

3. Record measurement equivalents in a two column table. 

 

MGSE4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

 

MGSE4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

 

MGSE4.MD.8 Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.  Represent and interpret data.

 

MGSE4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (2, 4, 8). Solve problems involving addition and subtraction of fractions with common denominators by using information presented in line plots. For example, from a line plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.  Geometric Measurement - understand concepts of angle and measure angles.

 

MGSE4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

 

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

 

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

 

MGSE4.MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

 

MGSE4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol or letter for the unknown angle measure. 

 

Vocabulary

• ●  centimeter(cm)

• ●  cup (c)

• ●  customary

• ●  foot (ft)

• ●  gallon (gal)

• ●  gram (g)

• ●  kilogram (kg)

• ●  kilometer (km)

• ●  liquid volume

• ●  liter (L)

• ●  mass

• ●  measure

• ●  meter (m)

• ●  metric

• ●  mile (mi)

• ●  milliliter (mL)

• ●  ounce (oz)

• ●  pint (pt)

• ●  pound (lb)

• ●  quart (qt)

● relative size

● ton (T)
● weight
● decompose

● yard (yd)

● data
● line plot
● intersect
● acute angle
● angle
● arc
● circle
● degree
● measure
● obtuse angle
● one-degree angle

● protractor
● rectilinear figure

● right angle
● straight angle