Argyle ISD 2014-2015

Third Grade Mathematics Curriculum Guide

Second Quarter (October 20- December 19) This guide provides a timeline and suggested resources for teaching the third grade TEKS. It is expected that a minimum of 90 minutes a day be hands-on/minds-on active investigation that utilize the tools and resources available to you.

TEKS Mathematical Process skills will be integrated throughout all units and concepts

Integrated in ALL Concepts

3.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: 3.1A apply mathematics to problems arising in everyday life, society, and the workplace 3.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 3.1C select tools, including real objects, manipulatives, paper/pencil, and technology as appropriate techniques, including mental math, estimation and number sense, as appropriate to solve problems. 3.1D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 3.1E create and use representations to organize, record and communicate mathematical ideas 3.1F analyze mathematical relationships to connect and communicate mathematical ideas 3.1G display, explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communications

3.4K solve with fluency one and two –step problems involving multiplication and division, including interpreting remainders 3.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity.

Unit 1 – Multiplication & Division (Continued)

TEKS/Student Expectations

3.4D determine the total number of objects when equally-sized groups of objects are combines or arranged in arrays up to 10 by 10. 3.4E represent multiplication facts by using a variety of approaches such as repeated addition, equal sized groups, arrays, area models, equal jumps on a number line and sip counting 3.4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts 3.4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products and the commutative, associative and distributive properties. 3.4H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally. 3.4I determine if a number is even or odd using divisibility rules 3.4J determine a quotient using the relationship between multiplication and division 3.4K solve one and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area 3.5B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams and equations 3.5C describe a multiplication expression as comparison such as 3x24 represents 3 times as much as 24 3.5D determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing product or factor

TEKS Clarification 1. Students use repeated addition to find the total number of objects represented in equal

groups.

2. Use arrays to develop meaning of multiplication 3. Apply multiplication in multiple scenarios and not just in a single, familiar scenario. 4. Emphasize the use of a number line to aid in multiplication 5. Make a connection between multiplication and division. 6. Use multiplication strategies to multiply up to two-digit by one-digit numbers 7. In order to use partial products, students must understand expanded notation. 8. Grouping and fair sharing is the focus for division. 9. Students will understand the meaning of division and develop their own models, not just

apply a model.

Sample Problems

 4 X 3 can be represented as follows: 3+3+3+3 

                    

 

  

                    

 3+3+3+3 

 

 

 

 

Guiding Questions

1. How are multiplication and addition related? 2. How can an array model be used to represent multiplication? 3. How can multiplication be used in daily life? 4. How are multiplication and division related? 5. How can multiplication and division improve your life? 6. How can finding patterns in numbers help solving problems?

Common Misconceptions

Students see multiplication and division as discrete and separate operations. Their conception of the operations does not include the fact that they are linked as inverse operations.

Key Academic Vocabulary Product Quotient

Array Dividend Factor Divisor

Vertical Alignment

2nd Grade

Before

After

4th Grade 2.6A model, create and describe contextual multiplication situations in which equivalent sets of concrete objects are joined 2.6B model, create and describe contextual division situations in which a set of concrete objects is separated into equivalent sets.

4.4B determine products of a umbers and 10 or 100 using properties of operations and place value understandings 4.4C represent the product of 2 two-digit numbers using arrays, area models or equations, including perfect squares through 15 by 15 4.4D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative and distributive properties.

4.4E represent the quotient of up to a four-digit whole number by a one-digit whole number using arrays, area models or equations 4.4F use strategies and algorithms, including the standard algorithm,, to divide up to a four-digit dividend by a one-digit divisor 4.4H solve with fluency one and two-step problems involving multiplication and division, including interpreting remainders

Suggested Resources

EnVision Lessons: Units 5 – 8 Motivation Math/Mentoring Minds: Units 15-21

Unit 2 – Numbers, Operations &Algebraic Reasoning

TEKS/Student Expectations

3.3A- represent fractions greater than zero and less than or equal to one with denominators of 2,3,4,6 and 8 using concrete objects and pictorial models, including strip diagrams and number lines 3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6 and 8 given a specified point on a number line. 3.3C- explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

3.3D- compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b 3.3E- solve problems involving a set of objects among two or more recipients using pictorial representation of fractions with denominators of 2, 3, 4 ,6 and 8 3.3F- represent equivalent fractions with denominators of 2, 3, 4, 6 and 8 using a variety of objects and pictorial models, including number lines 3.3G- explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model 3.3H- compare two fractions having the same numerator or denominator in problems by reasoning about their size and justifying the conclusion using symbols, words, objects and pictorial models 3.7A- represent fractions of halves, fourths, and eights as distances from zero on a number line 3.5E- represent real-world relationships using number pairs in a table and verbal descriptions

TEKS Clarifications

● Students can write fractions based on a concrete and pictorial model.

● Students use strip diagrams and number lines to write fractions using the fractions

symbols.

● Students will locate points on a number line that represent fractions less than 1

● Understand that ¼ is the unit fraction of 4. Understand that the denominator tells you the

parts of the whole and that the unit fraction is one part of that whole. Students understand

parts and wholes and equal partitioning of fractions.

● Students can identify that 2/4 is 1/4 plus 1/4. They understand that the numerator is a sum

of all the equal parts.

● Students apply fraction knowledge to solve problems involving partitioning objects or a set

of objects.

● Students must be able to create a fraction that is equivalent to another fraction in concrete

and pictorial numbers and number lines. Students should use many objects for finding

equivalent fractions.

● Students must recognize that comparisons are valid only when the two fractions refer to

the same whole. For example half is a half, but the fractions are only equivalent if the

objects are the same size. Half of one object might be a whole of another object

● Students develop the number sense of knowing the importance of numerators and

denominators in fractions. Students must know that fractions are different sizes and be

able to justify why one fraction is greater than or less than another based on the number

sense and understanding of the partitioning of the whole.

● Students need a deep understand of function tables. They will need to categorize and

create subsets of information from a given table. They must take an abstract description of

a situation and create a concrete model of what the situation is representing.

Sample Problems

Emily answered 2 questions correct on a test that had 3 questions. What fraction of the questions did she answer correctly?

What is the fraction represented in the following picture?

Which letter represents 3/6 on the number line?  

Explain why ¾ is greater than 3/8 based on the number of parts of a whole.

Guiding Questions

1. What does “equal shares” mean and why it is important when working with fractions?

2. Is ½ always equal to ½ ?

3. Tell me some fractions that are equivalent to ½. How do you know? Are there others? Repeat

for fractions like ¼ and ¾, 1/3 and 2/3.

4. Tell me some fractions that are greater than ½. How do you know? What about fractions that

are greater than 1?

5. How do fractions on a number line relate to measurement?

Common Misconceptions

● Demonstrate using visual and kinaesthetic resources how and why fractions can be

equivalent sizes but be split into different numbers of parts.

● Often students are unsure of the meaning of the value of the denominator and the

numerator, particularly where the numerator is greater than 1. ● Patterns and rules are related. A pattern is a sequence that repeats the same process over

and over. A rule dictates what that process will look like. Students investigate different

patterns to find rules, identify features in the patterns, and justify the reason for those

features.

Key Academic Vocabulary

Fraction Numerator Partitionin

g

Half Denominato

r

Equal Parts

Whole Table Output Portion Input

Vertical Alignment 2nd Grade

Before

After

4th Grade 2.3A partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words 2.3B explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part 2.3C use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole 2.3D identify examples and non-examples of halves, fourths, and eighths 2.5A determine the value of a collection of coins up to one dollar 2.6A model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined 2.6B model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

4.2B- represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals 4.2E- represent decimals, including tenths and hundredths, using concrete and visual models and money 4.2F- compare and order decimals using concrete and visual models to hundredths 4.2G- relate decimals to fractions that name tenths and hundredths 4.2H- determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line 4.3A- represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b>0, including when a>b 4.3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recordings results with symbolic representations. 4.3C -determine if two given fractions are equivalent using a variety of methods 4.3D -compare two fractions with different numerators and different

denominators and represent the comparison using the symbols >, = or < 4.3E- represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties operations 4.3F- evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0. ¼, ½, ¾, and 1. Referring to the same whole 4.3G- represent fractions and decimals to the tenth or hundredths as distances from zero on a number line 4.5B- represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

Suggested Resources

EnVision Lessons: Topic 11 –Fractions Lesson 1-7 – Money 10-4, 10-5 – Tables/Relationships Mentoring Minds/Motivation Math: Unit 5 – Unit 11