Click on the concept to access interventions for each concept. Interventions include listings of instruction and practice in Everyday Mathematics and/or Houghton Mifflin. (All Houghton Mifflin Practice, Reteach, Enrichment, Homework, Problem Solving and English Learners sheets are online here.) Also on each page for each concept is a listing of websites that are specific to the concept - both for teacher instruction and student practice.
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| Category |
Concept |
Stndrd |
Objective |
| Algebra |
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Describe simple relationships by creating and analyzing tables, equations, and expressions |
II |
1a |
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Draw a graph and write an equation from a table of values |
II |
1b |
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Draw a graph and create a table of values from an equation |
II |
1c |
|
Solve single variable linear equations using a variety of strategies |
II |
2a |
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Recognize that expressions in different forms can be equivalent; rewrite an expression to represent a quantity in different way |
II |
2b |
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Evaluate, simplify expressions & formulas, substituting values for variables |
II |
2c |
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Explore how a change in one variable affects a second variable |
II |
Explore |
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Develop understanding of slope as constant rate of change |
II |
Explore |
| Compare Fractions, Decimals, and Percents |
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Compare & order rational numbers, including positive & negative mixed fractions and decimals |
I |
2b |
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Find equivalent forms for common fractions, decimals, %s, ratios, including repeating or terminating decimals |
I |
2c |
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Relate %s less than 1% or greater than 100% to equivalent fractions, decimals, whole #s and mixed #s |
I |
2d |
| Computation Estimation |
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Use estimation to determine whether results obtained using a calculator are reasonable |
I |
5b |
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Use estimation or calculation to compute results, depending on the context and #s involved in the problem. |
I |
5c |
| Data |
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Describe simple relationships by creating and analyzing tables, equations, and expressions |
II |
1a |
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Extend data display and comparisons to include scatter plots and circle graphs |
V |
1b |
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Compare 2 similar sets of data on the same graph; compare 2 graphs representing the same set of data |
V |
1c |
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Recognize that changing the scale influences the appearance of a display of data |
V |
1d |
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Propose and justify inferences and predictions based on data |
V |
1e |
| Decimals |
|
|
|
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Place rational #'s on a number line |
I |
2a |
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Compare & order rational numbers, including positive & negative mixed fractions and decimals |
I |
2b |
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Use estimation or calculation to compute results, depending on the context and #s involved in the problem. |
I |
5c |
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Multiply & divide a multi digit # by a 2 digit #, including decimals |
I |
6a |
| Division |
|
|
|
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Give mixed number and decimal solutions to division problems with whole #s |
I |
4c |
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Use estimation or calculation to compute results, depending on the context and #s involved in the problem. |
I |
5c |
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Multiply & divide a multi digit # by a 2 digit #, including decimals |
I |
6a |
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Solve single variable linear equations using a variety of strategies |
II |
2a |
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Convert units of measurement within metric system; convert units of measurement within the customary system |
IV |
2b |
|
Design investigations to answer questions |
V |
1a |
| Fractions |
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Place rational #'s on a number line |
I |
2a |
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Compare & order rational numbers, including positive & negative mixed fractions and decimals |
I |
2b |
|
Find equivalent forms for common fractions, decimals, %s, ratios, including repeating or terminating decimals |
I |
2c |
|
Relate fractions to multiplication & division; use to explain procedures for multiplication & division of fractions |
I |
4a |
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Add, subtract, multiply and divide fractions and mixed numbers |
I |
6b |
|
Explore addition and subtraction of positive & negative fractions. |
I |
Explore |
|
Solve single variable linear equations using a variety of strategies |
II |
2a |
|
Identify & draw shapes & figures from different views/perspectives |
III |
Explore |
| Geometry |
|
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|
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Identify midpoint of line segment & center and circumference of a circle |
III |
1a |
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Identify angles as vertical, adjacent, complementary, or supplementary; provide descriptions |
III |
1b |
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Develop and use properties of complementary & supplementary angles and the sum of angles of a triange to solve problems w/unknown angle in a triangle or quadrilateral |
III |
1c |
|
Rotate a polygon about the origin by a multiple of 90 degrees; identify the location of new vertices |
III |
2a |
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Translate polygon horizontally or vertically on coordinate grid; identify the location of new vertices |
III |
2b |
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Reflect a polygon across the x or y axis; identify the location of the new vertices |
III |
2c |
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Use manipulatives & technology to model geometric shapes |
III |
Explore |
|
Investigate tessellations |
III |
Explore |
|
Explore angles formed by intersecting lines |
III |
Explore |
|
Identify & draw shapes & figures from different views/perspectives |
III |
Explore |
| Integers |
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|
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Recognize a rational # as a ratio of two integers, a to b, where b is not equal to zero |
I |
1a |
|
Add & subtract integers |
I |
6c |
|
Sum of an integer and its additive inverse is 0 |
I |
2e |
| Measurement |
|
|
|
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Identify & draw shapes & figures from different views/perspectives |
III |
Explore |
|
Explore relationship between radius and diameter of circle to circle's circumference to develop formula for circumference |
IV |
1a |
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Find circumference using a formula |
IV |
1b |
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Describe pi as the ratio of the circumference to the diatmeter of a circle |
IV |
1c |
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Decompose a circle into a number of wedges and rearrange the wedges into a shape that approx. parallelogram to develop formula for area of circle |
IV |
1d |
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Find the area of a circle using a formula |
IV |
1e |
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Recognize that measurements are approx.; describe how the size of the unit used in measuring affects the precision |
IV |
2a |
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Convert units of measurement within metric system; convert units of measurement within the customary system |
IV |
2b |
|
Compare a meter to a yard, a liter to a quart, a kilometer to a mile |
IV |
2c |
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Determine when it is appropriate to estimate or use precise measurement when solving problems |
IV |
2d |
|
Derive and use the formula to determine the surface area and volume of a cylinder |
IV |
2e |
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Investigate volumes and surface areas of a variety of 3D objects |
IV |
Explore |
|
Recognize that changing the scale influences the appearance of a display of data |
V |
1d |
| Multiplication |
|
|
|
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Multiply & divide a multi digit # by a 2 digit #, including decimals |
I |
6a |
| Number Concepts |
|
|
|
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Determine whether whole #s to 100 are prime, composite or neither |
I |
3a |
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Prime factorization of numbers to 100 |
I |
3b |
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Find the GCF, LCM for 2 #s using variety of methods (list of multiples, prime factorization) |
I |
3c |
| Number Lines |
|
|
|
|
Place rational #'s on a number line |
I |
2a |
| Percents |
|
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|
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Find equivalent forms for common fractions, decimals, %s, ratios, including repeating or terminating decimals |
I |
2c |
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Relate %s less than 1% or greater than 100% to equivalent fractions, decimals, whole #s and mixed #s |
I |
2d |
| Place Value |
|
|
|
|
Change whole #s w/exponents to standard form |
I |
1b |
|
Any # to the zero power equals 1 |
I |
1b |
|
Write a whole # in expanded form using exponents |
I |
1c |
|
Express #s in scientific notation using positive powers of ten |
I |
1d |
|
Recognize that expressions in different forms can be equivalent; rewrite an expression to represent a quantity in different way |
II |
2b |
| Probability |
|
|
|
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Write results of a probability experiment as a fraction between zero and one, or an equivalent % |
V |
2a |
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Compare experimental results with theoretical results |
V |
2b |
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Compare individual, small group, and large group results of a probability experiment in order to more accurately estimate the actual probabilities |
V |
2c |
|
Investigate the notion of fairness in games |
V |
Explore |
| Properties |
|
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|
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Explore the distributive property of multiplication over addition of double digit multipliers |
I |
Explore |
| Ratios & Proportions |
|
|
|
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Recognize that ratios derive from pairs of rows in the multiplication table and connect with equivalent fractions |
I |
4b |
|
Solve problems using ratios and proportions |
I |
5d |
|
Model situations with proportional relationships & solve problems |
II |
Explore |
| Word Problems |
|
|
|
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Select appropriate methods to solve a multi-step problem involving multiplication and division of fractions and decimals |
I |
5a |
|
Design investigations to answer questions |
V |
1a |
| |
|
|
|
| New Math Core Standards & Objectives |
|
|
|
| STANDARDS |
OBJECTIVES |
|
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| I. Students will expand number sense to include operations with rational numbers |
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1. Represent rational numbers in a variety of ways |
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2. Explain relationships and equivalencies among rational numbers. |
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3. Use number theory concepts to find prime factorizations, least common multiples and greatest common factors. |
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4. Model and illustrate meanings of operations and describe how they relate |
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5. Solve problems involving multiple steps |
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6. Demonstrate proficiency with the 4 operations, with positive rational numbers and with addition and subtraction of integers. |
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| II. Use patterns, relations, algebraic expressions to represent, analyze mathematical problems & # relationships. |
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1. Analyze algebraic expressions, tables, graphs to determine patterns, relations, rules. |
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2. Write, interpret and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations. |
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| III. Use spatial & logical reasoning to recognize, describe, analyze geometric shapes and principles. |
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1. Identify and analyze attributes and properties of geometric shapes to solve problems. |
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2. Visualize and identify geometric shapes after applying transformations on a coordinate plane. |
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| IV. Understand and apply measurement tools and techniques and find the circumference and area of a circle. |
|
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1. Describe and find the circumference and area of a circle. |
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2. Identify and describe measurable attributes of objects and units of measurement and solve problems involving measurement. |
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| V. Analyze, draw conclusions, make predictions based upon data and apply basic concepts of probability. |
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1. Design investigations to reach conclusions using statistical methods to make inferences based on data. |
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2. Apply basic concepts of probability and justify outcomes. |
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| |
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| IMPORTANT MATHEMATICAL LANGUAGE & SYMBOLS STUDENTS SHOULD USE: |
|
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| Standard I |
prime, composite, exponent, least common multiple, least commondenominator, greatest common factor, decimals, percents, divisible, divisibility , equivalent fractions, integer, dividend, quotient, divisor, factor, simplest terms, mixed numberal, improper fraction |
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| Standard II |
order of operations, sequence, function, pattern, algebraic expression, approximately equal to, notation for exponents: 43 or 4^3, a number in front of a variable indicates multiplication, formula, generalization |
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| Standard III |
midpoint, circumference, complementary and supplementary angles, rotate, translate, reflect, transformation |
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| Standard IV |
cylinder, radius, diameter, circumference, area, surface area, volume, pi (π) |
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| Standard V |
data display, scatter plot, circle graph, scale, predict, justify, probability, experimental results, theoretical results |
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