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Bringing knowledge to children,
and children to God.
Upper-grade Math
Online Ministry to the Christian Homeschool Community.
NUMBER SENSE
Reading and Writing Whole Numbers
Watch this animated math lesson on reading and writing whole numbers.
- Comparing Numbers
- Rounding
Adding Roman numerals.
Subtracting Roman numerals.
Comparing Numbers
1.2 Order and compare whole numbers and decimals to two decimal places.
ASSESSMENT: Ordering and Compring Whole Numbers - Level 4
Rounding
1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
Watch this animated math lesson on rounding using a number line.1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate.
Students have direct instruction on how to estimate whole numbers and how it applies to the real world.
Students apply knowledge of estimating with whole numbers.
Fractions
1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0).
1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).
1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
Figure out which is the larger fraction
- Negative Numbers
- Number Mining
- Decimal Numbers
- Rounding Decimal Numbers
More Fractions
Students will predict and extend existing numerical patterns using addition.
- Subtraction
- Multiplication
- Division
- Factoring
- Prime Numbers
1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0).
1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).
Write tenths and hundredths in decimal and fraction notations
Draw lines to match each fraction with its equivalent decimal
1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
Negative Numbers
1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").
Number Line
1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.
2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals:
Decimal Numbers
2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places.
2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.
Rounding decimals to the nearest whole number.
Rounding decimal numbers
3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations:
Computing Numbers
3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
Subtract whole numbers through thousands using place-value models.
3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.
We don't multiply this way in "The States."
3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.
3.4 Solve problems involving division of multidigit numbers by one-digit numbers.
4.0 Students know how to factor small whole numbers:
Factoring
4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).
4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.
Click on the apples with prime numbers as they fall from the tree.
ALGEBRA & FUNCTIONS
1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:
Variables
1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).
Watch this animated math lesson on finding the value of a variable.
Students use algebra to solve for unknown numbers.
Order of Operations
1.2 Interpret and evaluate mathematical expressions that now use parentheses.
1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.
Formulas
1.4 Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships.
1.5 Understand that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given.
2.0 Students know how to manipulate equations:
2.1 Know and understand that equals added to equals are equal.
2.2 Know and understand that equals multiplied by equals are equal.
MEASURE-
MENT & GEOMETRY
Dena McElligott demonstrates a manipulative that helps students see the relationships among the customary units of liquid measure.
Karen Cribbs, Hanover County Public School secondary mathematics specialist, demonstrates a hands-on introduction to volume and surface area.
Estimate and Measure with Chef Pierre Students use non-standard units to estimate and measure.
PERIMETER & AREA:
1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2).
Finding the area of plane figures using grids and formulas.
1.2 Recognize that rectangles that have the same area can have different perimeters.
1.3 Understand that rectangles that have the same perimeter can have different areas.
1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.
A visual approach to the concepts of linear, square and cubic units.
TWO-DIMENSIONAL COORDINATE GRID:
2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3 x and connect them by using a straight line).
Click on the lesson that says: Ordered Pairs.
Click on Lesson 18: Using Ordered Pairs.
Select Lesson 36: Coordinate Graphs.
Click on the arrow keys to guide Billy to the coordinates of the hidden grub ten times.
Find the Hurkle in as few guesses as possible.
2.2 Understand that the length of a horizontal line segment equals the difference of the x- coordinates.
2.3 Understand that the length of a vertical line segment equals the difference of the y- coordinates.
Sample video from linear equations and inequalities in two variables. (Double-click on the play button.)
PLANE GEOMETRIC FIGURES:
Planes
Lines
Circles
Congruence
3.3 Identify congruent figures.
Bitesize math lesson
Drag a shape to each work area and use the tools to rotate and/or reflect the second shape to try to match the first.
(More advanced conceptualizations.)
Polygons
3.7 Know the definitions of various polygons, including the definition of different triangles (e.g., equilateral, isosceles, scalene, acute, right, and obtuse) and identify their attributes.
Classify each triangle by the relative lengths of its sides.
3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).
Summary of figures and polygons
Drag all of the polygons to the left and any non-polygons to the right.
Take this quiz on the various shapes.
SYMMETRY
3.4 Identify figures that have bilateral symmetry and rotational symmetry.
ANGLES:
3.5 Know the definitions of each kind of angle, including a right angle, an acute angle, and an obtuse angle. Understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, 3/4, and full turns.
Summary of angles and angle terms.
Identify and classify angles as right, obtuse, or acute.
Sort (click and drag) the angles into the appropriate containers.
Use the figures to answer the questions.
Measuring Angles
Using a protractor to measure angles.
Take this quiz on measuring turns.
Calculate angles and units to get as many hole-in-ones as possible.
SOLID GEOMETRIC FIGURES:
3.6 Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids, cylindars, cones, cubes, spheres, and tetrahedrons) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.
Identifying speres, cylindars, cones and cubes.
Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices.
Use nets to recognize the relationship between planes and solids.
Interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.
Click on the solid figure created when the net is folded.
Rotate the building until you get the right side view (see the same shape).
More Shapes
Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.
Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).
DATA &
STATISTICAL
ANALYSIS
Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings:
Representing Data
1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.
How to read a line graph.
Circle graphs.
1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.
Mean, median, and mode
1.3 Interpret one-and two-variable data graphs to answer questions about a situation.
Chance, Odds, Etc...
2.0 Students make predictions for simple probability situations:
2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3/4).
PROBABILITY
2.0 Students make predictions for simple probability situations:
2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
Determining the probability of an event and showing it as a fraction.
2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3 /4).
Use manipulatives to help sixth-grade students grasp the concept of ratio.
MATHEMATI-CAL REASONING
Making Decisions about How to Solve Word Problems
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
(choose "Strategies"), and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.
How to approach multi-step problems with data presented in a table.
MATH RESOURCES
Worksheets
To access the Lesson and Practice Sheet combinations I mentioned yesterday, go to http://www.sadlier-oxford.com.
There you will find a sky blue column on the left-hand side of the web page with topics listed in navy blue.
Click on the first topic: Mathematics.
The blue column (panel) will then be replaced by a white panel inside of a red border. Click on the link for your grade level (beginning with Grade 1).
Now the white column (panel) inside of the red border will be replaced by a white panel inside of a purple border. Click on the Skills Update link and this will take you to the page with the Lesson / Practice combination worksheets we are using in Grade 4.
On-line math workseet generator.
Illustrated glossary of math terms
IMAGES site map of instructional activities.
NutShell Math
Eduplace activity search
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