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Introduction to Fourth Grade Everyday Mathematics®
Welcome to Fourth Grade Everyday Mathematics. It is part of an elementary school mathematics curriculum developed by the University of Chicago School Mathematics Project (UCSMP).
Everyday Mathematics offers students a broad background in mathematics. Some approaches may differ from those you used as a student, but the approaches used are based on research, field test results, and the mathematics students will need in this century.
Fourth Grade Everyday Mathematics
emphasizes the following content:
Algebra and Uses of Variables Reading, writing, and solving number sentences
Algorithms and Procedures Exploring addition, subtraction, multiplication, and division methods; inventing individual procedures and algorithms; and experimenting with calculator procedures
Coordinate Systems and Other Reference Frames Using numbers in reference frames: number lines, coordinates, times, dates, and latitude and longitude
Exploring Data Collecting, organizing, displaying, and interpreting numerical data
Functions, Patterns, and Sequences Designing, exploring, and using geometric and number patterns
Geometry and Spatial Sense Developing an intuitive sense about
2- and 3-dimensional objects, their properties, uses, and relationships
Measures and Measurement Exploring metric and U.S. customary measures: linear, area, volume, weight; and exploring geographical measures
Numbers, Numeration, and Order Relations Reading, writing, and using whole numbers, fractions, decimals, percents, negative numbers; and exploring scientific notation
Operations, Number Facts, and Number Systems Practicing addition and subtraction to proficiency; and developing multiplication and division skills
Problem Solving and Mathematical Modeling Investigating methods for solving problems using mathematics in everyday situations
Introduction to Fourth Grade Everyday Mathematics®
Welcome to Fourth Grade Everyday Mathematics. It is part of an elementary school mathematics curriculum developed by the University of Chicago School Mathematics Project (UCSMP).
Everyday Mathematics offers students a broad background in mathematics. Some approaches may differ from those you used as a student, but the approaches used are based on research, field test results, and the mathematics students will need in this century.
Fourth Grade Everyday Mathematics
emphasizes the following content:
Algebra and Uses of Variables Reading, writing, and solving number sentences
Algorithms and Procedures Exploring addition, subtraction, multiplication, and division methods; inventing individual procedures and algorithms; and experimenting with calculator procedures
Coordinate Systems and Other Reference Frames Using numbers in reference frames: number lines, coordinates, times, dates, and latitude and longitude
Exploring Data Collecting, organizing, displaying, and interpreting numerical data
Functions, Patterns, and Sequences Designing, exploring, and using geometric and number patterns
Geometry and Spatial Sense Developing an intuitive sense about
2- and 3-dimensional objects, their properties, uses, and relationships
Measures and Measurement Exploring metric and U.S. customary measures: linear, area, volume, weight; and exploring geographical measures
Numbers, Numeration, and Order Relations Reading, writing, and using whole numbers, fractions, decimals, percents, negative numbers; and exploring scientific notation
Operations, Number Facts, and Number Systems Practicing addition and subtraction to proficiency; and developing multiplication and division skills
Problem Solving and Mathematical Modeling Investigating methods for solving problems using mathematics in everyday situations
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11
Naming and Constructing
Geometric Figures
During the next few weeks, the class will study the geometry of 2-dimensional shapes. Students will examine definitions and properties of shapes and the relationships among them. Students will use compasses to construct shapes and to create their own geometric designs.
Please keep this Family Letter for reference as your child works through Unit 1.
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Naming and Constructing
Geometric Figures
During the next few weeks, the class will study the geometry of 2-dimensional shapes. Students will examine definitions and properties of shapes and the relationships among them. Students will use compasses to construct shapes and to create their own geometric designs.
Please keep this Family Letter for reference as your child works through Unit 1.
Vocabulary
Important terms in Unit 1:
concave (nonconvex) polygon
A polygon in which at
least one vertex is “pushed in.”
convex polygon A polygon in which all vertices are “pushed outward.”
Important terms in Unit 1:
concave (nonconvex) polygon
A polygon in which at
least one vertex is “pushed in.”
convex polygon A polygon in which all vertices are “pushed outward.”
concave polygon
convex polygon
convex polygon
polygon A 2-dimensional figure that is made up
of three or more line segments joined end to end to
make one closed path. The line segments of a
polygon may not cross.
quadrangle (quadrilateral) A polygon that has four sides and four angles.
ray A straight path that extends infinitely from a point called its endpoint.
rhombus A quadrilateral whose sides are all the same length. All rhombuses are parallelograms. Every square is a rhombus, but not all rhombuses are squares.
trapezoid In Everyday Mathematics, a quadrilateral that has exactly one pair of parallel sides.
vertex The point where the rays of an angle, the sides of a polygon, or the edges of a polyhedron meet.
quadrangle (quadrilateral) A polygon that has four sides and four angles.
ray A straight path that extends infinitely from a point called its endpoint.
rhombus A quadrilateral whose sides are all the same length. All rhombuses are parallelograms. Every square is a rhombus, but not all rhombuses are squares.
trapezoid In Everyday Mathematics, a quadrilateral that has exactly one pair of parallel sides.
vertex The point where the rays of an angle, the sides of a polygon, or the edges of a polyhedron meet.
Unit 1: Family Letter cont.
endpoint A point at the end of a line segment
or a ray.
line Informally, a straight path that extends infinitely in opposite directions.
line segment A straight path joining two points. The two points are called the endpoints of the segment.
parallelogram A quadrilateral that has two pairs of parallel sides. Opposite sides of a parallelogram have equal lengths. Opposite angles of a parallelogram have the same measure.
line Informally, a straight path that extends infinitely in opposite directions.
line segment A straight path joining two points. The two points are called the endpoints of the segment.
parallelogram A quadrilateral that has two pairs of parallel sides. Opposite sides of a parallelogram have equal lengths. Opposite angles of a parallelogram have the same measure.
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Do-Anytime Activities
To work with your child on concepts taught in this unit, try these interesting and rewarding activities:
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Do-Anytime Activities
To work with your child on concepts taught in this unit, try these interesting and rewarding activities:
-
Help your child discover everyday uses of
geometry as found in art, architecture, jewelry,
toys, and so on.
-
See how many words your child can think of
that have Greek/Latin prefixes such as tri-, quad-,
penta-, hexa-, and octa-.
-
Help your child think of different ways to draw
or make figures without the use of a compass,
protractor, or straightedge. For example,
you can trace the bottom of a can to make a circle, bend a straw to form a triangle, or make different shapes with toothpicks.
4. Challenge your child to draw or build something, such as a toothpick bridge, using triangular and square shapes. Or show pictures of bridges and point out the triangles used in bridges to provide support.
you can trace the bottom of a can to make a circle, bend a straw to form a triangle, or make different shapes with toothpicks.
4. Challenge your child to draw or build something, such as a toothpick bridge, using triangular and square shapes. Or show pictures of bridges and point out the triangles used in bridges to provide support.
Unit 1: Family Letter cont.
4
Building Skills through Games
In Unit 1, your child will play the following games.
Addition Top-It (Extended-Facts Version) See Student Reference Book, page 263. Have your child play an extended-facts version by attaching a 0 to both cards before finding the sum. This game provides practice with addition fact extensions.
Polygon Pair-Up See Student Reference Book, page 258. This game provides practice identifying properties of polygons.
Sprouts See Student Reference Book, page 313. This game provides practice with simple vertex-edge graphs and developing game strategies.
Addition Top-It (Extended-Facts Version) See Student Reference Book, page 263. Have your child play an extended-facts version by attaching a 0 to both cards before finding the sum. This game provides practice with addition fact extensions.
Polygon Pair-Up See Student Reference Book, page 258. This game provides practice identifying properties of polygons.
Sprouts See Student Reference Book, page 313. This game provides practice with simple vertex-edge graphs and developing game strategies.
Subtraction Top-It (Extended-Facts
Version) See Student Reference Book, pages
263 and 264. Have your child play an extended-
facts version by attaching a 0 to both cards
before finding the difference. This is a variation
of Addition Top-It and provides practice with
subtraction fact extensions.
Sz’kwa See Student Reference Book, page 310. This game provides practice with intersecting line segments and developing game strategies.
Sz’kwa See Student Reference Book, page 310. This game provides practice with intersecting line segments and developing game strategies.
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As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through this unit’s Study Links.
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As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through this unit’s Study Links.
Unit 1: Family Letter cont.
As You Help Your Child with Homework
As You Help Your Child with Homework
Study Link 12
2. a. A B
b. A B
c. The line has arrows on both ends, but the line segment does not.
3. a. D C
b. No. A ray’s endpoint must be listed first when naming a ray.
4. A ruler has markings on it, so it can be used to measure.
2. a. A B
b. A B
c. The line has arrows on both ends, but the line segment does not.
3. a. D C
b. No. A ray’s endpoint must be listed first when naming a ray.
4. A ruler has markings on it, so it can be used to measure.
Study Link 14
1. Sample answer:
2. a. yes b. yes 3. Sample answer:
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2. a. yes b. yes 3. Sample answer:
Study Link 15
c. yes
4. kite
d. no
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1.
2.
2.
Sample answers:
Study Link 16
1. A, B, C, E, F, G, I 3. C,E,F,I
5. A, B, D, F, G, H, I
7. 2
Study Link 18
1. Sample answers: a. square
1. A, B, C, E, F, G, I 3. C,E,F,I
5. A, B, D, F, G, H, I
7. 2
Study Link 18
1. Sample answers: a. square
3. The polygons in Problems 1 and 2 have 4 sides
and at least 1 pair of parallel sides. The Problem
1 polygons have 2 pairs of equal, parallel sides
and all right angles.
1. rectangle
3. rhombus
2. Equilateral triangle
2. B, C
4. A
6.
D, G, H
c. hexagon
c. hexagon
4. a.
5.
K
5.
K
b. E
c. FED
F
E
D
2. Sample answer: Sides are all the same length,
and interior angles are all the same measure.
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