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.

Category 
Concept 
Stndrd 
Objective 
Algebra 




Describe simple relationships by creating and analyzing tables, equations, and expressions 
II 
1a 

Draw a graph and write an equation from a table of values 
II 
1b 

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 

Recognize that expressions in different forms can be equivalent; rewrite an expression to represent a quantity in different way 
II 
2b 

Evaluate, simplify expressions & formulas, substituting values for variables 
II 
2c 

Explore how a change in one variable affects a second variable 
II 
Explore 

Develop understanding of slope as constant rate of change 
II 
Explore 
Compare Fractions, Decimals, and Percents 




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 %s less than 1% or greater than 100% to equivalent fractions, decimals, whole #s and mixed #s 
I 
2d 
Computation Estimation 




Use estimation to determine whether results obtained using a calculator are reasonable 
I 
5b 

Use estimation or calculation to compute results, depending on the context and #s involved in the problem. 
I 
5c 
Data 




Describe simple relationships by creating and analyzing tables, equations, and expressions 
II 
1a 

Extend data display and comparisons to include scatter plots and circle graphs 
V 
1b 

Compare 2 similar sets of data on the same graph; compare 2 graphs representing the same set of data 
V 
1c 

Recognize that changing the scale influences the appearance of a display of data 
V 
1d 

Propose and justify inferences and predictions based on data 
V 
1e 
Decimals 




Place rational #'s on a number line 
I 
2a 

Compare & order rational numbers, including positive & negative mixed fractions and decimals 
I 
2b 

Use estimation or calculation to compute results, depending on the context and #s involved in the problem. 
I 
5c 

Multiply & divide a multi digit # by a 2 digit #, including decimals 
I 
6a 
Division 




Give mixed number and decimal solutions to division problems with whole #s 
I 
4c 

Use estimation or calculation to compute results, depending on the context and #s involved in the problem. 
I 
5c 

Multiply & divide a multi digit # by a 2 digit #, including decimals 
I 
6a 

Solve single variable linear equations using a variety of strategies 
II 
2a 

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 




Place rational #'s on a number line 
I 
2a 

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 

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 




Identify midpoint of line segment & center and circumference of a circle 
III 
1a 

Identify angles as vertical, adjacent, complementary, or supplementary; provide descriptions 
III 
1b 

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 

Translate polygon horizontally or vertically on coordinate grid; identify the location of new vertices 
III 
2b 

Reflect a polygon across the x or y axis; identify the location of the new vertices 
III 
2c 

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 




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 




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 

Find circumference using a formula 
IV 
1b 

Describe pi as the ratio of the circumference to the diatmeter of a circle 
IV 
1c 

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 

Find the area of a circle using a formula 
IV 
1e 

Recognize that measurements are approx.; describe how the size of the unit used in measuring affects the precision 
IV 
2a 

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 

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 

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 




Multiply & divide a multi digit # by a 2 digit #, including decimals 
I 
6a 
Number Concepts 




Determine whether whole #s to 100 are prime, composite or neither 
I 
3a 

Prime factorization of numbers to 100 
I 
3b 

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 




Find equivalent forms for common fractions, decimals, %s, ratios, including repeating or terminating decimals 
I 
2c 

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 




Write results of a probability experiment as a fraction between zero and one, or an equivalent % 
V 
2a 

Compare experimental results with theoretical results 
V 
2b 

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 




Explore the distributive property of multiplication over addition of double digit multipliers 
I 
Explore 
Ratios & Proportions 




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 




Select appropriate methods to solve a multistep 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 


I. Students will expand number sense to include operations with rational numbers 



1. Represent rational numbers in a variety of ways 



2. Explain relationships and equivalencies among rational numbers. 



3. Use number theory concepts to find prime factorizations, least common multiples and greatest common factors. 



4. Model and illustrate meanings of operations and describe how they relate 



5. Solve problems involving multiple steps 



6. Demonstrate proficiency with the 4 operations, with positive rational numbers and with addition and subtraction of integers. 


II. Use patterns, relations, algebraic expressions to represent, analyze mathematical problems & # relationships. 


1. Analyze algebraic expressions, tables, graphs to determine patterns, relations, rules. 



2. Write, interpret and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations. 


III. Use spatial & logical reasoning to recognize, describe, analyze geometric shapes and principles. 



1. Identify and analyze attributes and properties of geometric shapes to solve problems. 



2. Visualize and identify geometric shapes after applying transformations on a coordinate plane. 


IV. Understand and apply measurement tools and techniques and find the circumference and area of a circle. 


1. Describe and find the circumference and area of a circle. 



2. Identify and describe measurable attributes of objects and units of measurement and solve problems involving measurement. 


V. Analyze, draw conclusions, make predictions based upon data and apply basic concepts of probability. 



1. Design investigations to reach conclusions using statistical methods to make inferences based on data. 



2. Apply basic concepts of probability and justify outcomes. 






IMPORTANT MATHEMATICAL LANGUAGE & SYMBOLS STUDENTS SHOULD USE: 


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 


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 


Standard III 
midpoint, circumference, complementary and supplementary angles, rotate, translate, reflect, transformation 


Standard IV 
cylinder, radius, diameter, circumference, area, surface area, volume, pi (π) 


Standard V 
data display, scatter plot, circle graph, scale, predict, justify, probability, experimental results, theoretical results 

