CCSS ID 
MathPaths Grade 5 Goals 
CCSS 

NUMBER & OPERATIONS IN BASE TEN

A 
1

Understand the place value system. 
5.NBT.1 
11

Relate place value to multiplying by 10 or 1/10. This problem type includes decimals. In Grade 4, students multiplied and divided whole numbers by 10. Multiplying by 1/10 is the same as dividing by 10. 
5.NBT.2 
12

Multiply and divide whole numbers by powers of 10. 
5.NBT.2 
13

Multiply and divide decimals by powers of 10. 
5.NBT.2 
14*

Write powers of 10 using exponents. 
5.NBT.3a 
15

Read and write decimals to thousandths. 
5.NBT.3a 
16*

Convert between standard and expanded forms of decimals. For example, 0.234 means 2 tenths + 3 hundredths + 4 thousandths, or 0.2 + 0.03 + 0.004. 
5.NBT.3b 
17

Compare decimals to thousandths. 
5.NBT.4 
18

Round decimals to any place. 
B 
2

Perform operations with multidigit whole numbers.* 
5.NBT.5 
21

Multiply whole numbers up to 4digit by 1digit using the standard algorithm. In Grade 4, students multiplied using place value or models but were not required to learn the standard algorithm. 
5.NBT.5 
22

Multiply whole numbers up to 2digit by 2digit using the standard algorithm. 
5.NBT.6 
23

Relate division to multiplication by multiples of 10. For example, to divide 160 by 20, find the missing factor in 20 x __ = 160. 
5.NBT.6 
24

Divide 3digit dividends by multiples of 10 using place value and/or models. 
5.NBT.6 
25

Relate division to multiplication by 2digit factors. For example, students could make a table of the first ten multiples of 47, and then use the table to divide various numbers by 47. 
5.NBT.6 
26

Divide 3and 4digit dividends by 2digit divisors using place value and/or models. The division algorithm is a Grade 6 standard. 
B 
3

Perform operations with decimals to hundredths.*
In CCSS, the whole numbers and decimals are both part of Cluster B. For MathPaths assessments, the cluster has been divided into two parts. 
5.NBT.7 
31

Relate addition and subtraction of decimals. 
5.NBT.7 
32

Add and subtract decimals to hundredths using place value and/or models. At this grade level, it is more important for students to use place value or models than to memorize an algorithm. The algorithms will be emphasized in Grade 6. 
5.NBT.7 
33

Relate multiplication and division of decimals. 
5.NBT.7 
34

Multiply and divide decimals to hundredths using place value and/or models. The algorithms will be emphasized in Grade 6. 
CCSS 

OPERATIONS & ALGEBRAIC THINKING

A 
1

Write and interpret numerical expressions. 
5.OA.1 
11*

Evaluate numerical expressions with parentheses. 
5.OA.2 
12

Write and interpret numerical expressions. 
B 
2

Analyze patterns and relationships. 
5.OA.3 
21

Write and compare two patterns given two rules. 
5.OA.3 
22

Identify features of related patterns in tables or graphs. For example, compare a table of multiples of 0.7 to a table of multiples of 7. How are the patterns alike or different? 
CCSS 

NUMBER & OPERATIONS WITH FRACTIONS

A 
1

Use equivalent fractions as a strategy to add and subtract fractions. 
5.NF.1 
11*

Write equivalent fractions. Students were introduced to equivalent fractions in Grade 4, but may not have become fluent. Fluency is important for adding and subtracting fractions at this grade level. 
5.NF.1 
12

Add and subtract fractions with unlike denominators. Like denominators were emphasized in Grade 4. 
5.NF.1 
13

Add and subtract mixed numbers with unlike denominators. 
5.NF.2 
14

Add and subtract fractions to solve word problems. 
5.NF.2 
15

Add and subtract mixed numbers to solve word problems. 
5.NF.2 
16

Assess reasonableness of answers by using benchmarks and number sense. 
B 
2

Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 
5.NF.3 
21

Interpret fractions as division to solve word problems. For example, if 2 pizzas are shared equally by 5 people each person gets 2/5 pizza. 
5.NF.4a 
22

Multiply whole numbers by fractions. 
5.NF.4b 
23**

Represent products of fractions using area models. 
5.NF.4a, 5a, 5b 
24

Multiply fractions by fractions. 
5.NF.6 
25

Multiply fractions and mixed numbers to solve word problems. 
5.NF.7a 
26*

Divide unit fractions by whole numbers using models. At this level it is very important for students to understand unit fractions. Dividing 1/4 by 5 is the same as making 1/4 into 5 parts. So, the quotient is 1/20. This is an important prerequisite for division of fractions in Grade 6. 
5.NF.7b 
27*

Divide whole numbers by unit fractions using models. Dividing 5 by 1/4 is the same as finding the number of fourths in 5. Since there are 4 fourths in a whole, the quotient is 5 x 4 or 20. This is an important prerequisite for division of fractions in Grade 6. 
5.NF.7b 
28

Relate division to multiplication of fractions. 
5.NF.7c 
29

Divide with unit fractions and whole numbers to solve problems. 
CCSS 

GEOMETRY

A 
1

Graph points on the coordinate plane to solve realworld and mathematical problems. 
5.G.1 
11*

Graph and identify points with positive coordinates on a coordinate system. The standards for previous grades do not call for coordinates. 
5.G.2 
12

Use coordinates (positive only) to represent and solve problems. 
5.G.2 
13

Use coordinates to analyze geometric shapes. For example, if the coordinates for two endoints of a line segment are (3, 4) and (3, 10), students should calculate the length as 6 units. 
B 
2

Classify twodimensional figures into categories based on their properties. 
5.G.3 
21

Classify and identify quadrilaterals. 
5.G.4 
22

Recognize categories and create hierarchies of shapes. 
CCSS 

MEASUREMENT & DATA

A 
1

Convert like measurement units within a given measurement system. 
5.MD.1 
11

Convert metric measurements. In Grade 4, students converted from larger to smaller units. 
5.MD.1 
12

Convert conventional measurements. 
B 
2

Represent and interpret data. 
5.MD.2 
21

Make line plots using data including fractions. 
5.MD.2 
22

Solve problems about line plots. 
C 
3

Understand concepts of volume and relate volume to multiplication and to addition. 
5.MD.3 
31

Identify a cube as a unit of volume. Volume is an important concept at this grade level. 
5.MD.4 
32

Measure volume by counting unit cubes. 
5.MD.5a 
33*

Add and/or multiply to find volumes of rectangular prisms. 
5.MD.5b 
34

Solve problems involving volume of rectangular prisms (with whole numbers as lengths). In Grade 6, students will find volumes of prisms with fractional edge lengths. (See the Geometry domain.) 
5.MD.5c 
35

Solve problems involving volumes of connected prisms. 
*Math card games are available. 
Goals and domain icons were developed by Angie Seltzer. Highlighted parts are from Grade 5 CCSS, Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 