Grade 4 Math blueprint
Course title: Grade 4 Math
Learning Goals (Parenthetical notations are State Frameworks):
1. Create, recognize and extend or complete and compare numerical and geometric sequences.
Classify patterns as growing or repeating. (1.1)
2. Develop and test generalizations based on observable patterns and relationships and describe
the rules for number patterns using equations, e.g., in this sequence 1, 6, 16, 36 …, to get the
next number the current number can be doubled and four added to the product. (1.1)
3. Describe mathematical relationships and situations, involving ratios and computation of whole
numbers, in all four operations with using symbols, number sentences and equations.
If
= ∆∆∆ then
=______.
(1.2)
4. Represent quantities in expressions and number sentences using variables. Use number
sentences to model and solve word problems. (1.3)
5. Solve problems and demonstrate an understanding of equivalence in mathematical situations
that reflect the commutative and associative properties of addition and multiplication of whole
numbers and the distributive property. (1.3)
6. Locate, label, compare and order numbers up to 10,000 using place value models, number lines
and number patterns (including multiples of 100 and 1,000). (2.1)
7. Extend number patterns to determine 100 and 1,000 more and less than a given number in
practical situations. (2.1)
8. Identify, order, round and compare 2-, 3-, and 4-digit whole numbers using place value models,
diagrams, number patterns and number lines. (2.1)
9. Build place value models, draw diagrams and show equivalent representations for 2-, 3-, and 4digit numbers in expanded and regrouped forms. Use the forms to support computational
strategies. (2.1)
10. Relate multiplication and division to number patterns and models of groups and rectangular
arrays. (2.1)
11. Use manipulatives to build and represent factors and multiples of 2-digit numbers to at least 36.
Identify and define prime and composite numbers through the use of models including
rectangular arrays, place value models and pictures. (2.1)
12. Determine, identify, and represent equivalent ratios and fractions (area, linear, and sets) and
mixed numbers using models (including the ruler), pictures and number lines. (2.1)
13. Use concrete manipulatives, models, number patterns, and counting and grouping of objects to
find equal parts of a set of objects and to identify amounts such as ¾ of 12 is 8. (2.1)
14. Compare and order fractional parts of a whole and mixed numbers with like and unlike
denominators of 2, 3, 4, 5, 6, 8, 10 and 12 using fraction sense, models, pictures, number lines
(and rulers.) (2.1)
15. Locate, label and estimate (round) fractions with like and unlike denominators of 2, 3, 4, 5, 6, 8,
10 and 12 by constructing and using models, pictures and number lines. (2.1)
16. Use models to represent tenths and record the representations using equivalent ratio, fraction
and decimal notation (1⁄10, 0.1) (2.1)
17. Develop and use a variety of computation strategies including place value concepts, number
lines and the commutative and associative properties to add and subtract three- and four-digit
numbers and money amounts up to $100.00. (2.2)
18. Solve contextual problems involving addition and subtraction of whole numbers using a variety
of methods. Write appropriate number sentences (equations). Explain the strategies used. (2.2)
19. Recall the multiplication and division facts 1 through 10. (2.2)
20. Write multiplication and division story problems involving basic facts and two- and three-digit by
one-digit numbers to match a given number sentence and vice versa. Solve the problems using
strategies that include models, arrays or pictures, and mental math. Justify the solutions. (2.2)
21. Use arrays, pictures or models of groups, and various story contexts to represent multiplication
and division situations. (2.2)
22. Solve division problems that represent sharing (If I divide 30 pennies equally between 5 people,
how many pennies will each person get?) and grouping (How many groups of 5 can I make if I
have 30 pennies?) (2.2)
23. Interpret the meaning of remainders in division story context problems. (2.2)
24. Determine and explain in writing when an estimate is appropriate and whether a particular
estimation strategy is reasonable or will result in an overestimate or underestimate involving
addition and subtraction with three- and four- digit numbers and money amounts up to $1,000.
(2.2)
25. Use estimation strategies such as front end estimation with adjustments and “think addition”
strategies to estimate solutions to addition/subtraction (comparison) problems. Use the open
number line to represent estimation strategies. (2.2)
26. Use models, pictures and fraction sense to add and subtract fractions with like and unlike
denominators of 2, 3, 4, 5, 6, 8, 10 and 12. Match number sentences or equations to the
problems. (2.2)
27. Estimate a reasonable answer to simple problems involving fractions, mixed numbers and
decimals (tenths). (2.2)
28. Determine and compare the value of a set of coins. Write the values using decimal notation, i.e.
2 quarters = 50 ¢ or $.50. (2.2)
29. Identify, describe, compare, classify, and draw or represent two- or three-dimensional shapes.
(3.1)
30. Describe angles as having a measure of more than, less than, or about the same as a square
corner (right angle.) (3.1)
31. Compare and classify polygons based on relationships such as number of parallel sides,
reflective (mirror) symmetry and congruence. (3.1)
32. Classify and describe 3-dimensional shapes as prisms and pyramids. (3.1)
33. Make and test conjectures about polygons using geometric relationships such as symmetry and
congruence. (3.1)
34. Create simple shapes and designs with at least one line of symmetry. (3.1)
35. Prove that the area of a region remains constant when it is decomposed (taken apart) and then
recomposed (put back together) to form a new shape. (3.1)
36. Interpret simple maps. (3.2)
37. Use calendars and clocks to solve problems and schedule events involving elapsed time. (3.3)
38. Tell time to the minute. (3.3)
39. Solve problems involving the conversion of simple measures of time, e.g., minutes to hours and
vice versa. (3.3)
40. Use simple scales to weigh and order common objects in pounds and ounces and grams and
kilograms. (3.3)
41. Describe the relationships between ounces and pounds and grams and kilograms. (3.3)
42. Use customary and metric tools and units and non-standard units to estimate, measure and
solve problems involving length and perimeter, area, and weight. (3.3)
43. Use estimation strategies to predict reasonable answers to measurement problems and explain
the reasoning used orally and in writing. (3.3)
44. Pose questions and develop a plan to collect data using observations, surveys and experiments
to answer the questions. (4.1)
45. Collect, organize and represent the data that answer the questions using simple circle graphs
and broken line graphs. (4.1)
46. Discuss, make predictions and write about patterns and trends in categorical and numerical data
that have been represented in a variety of ways. (4.2)
47. Determine the range, median, and mode of a set of data and describe characteristics of the data
set as typical or average based on those determinations. (4.2)
48. Conduct probability experiments and describe the probability of an event as ___ out of ___, e.g.
8 out of 10 tiles chosen were red. (4.3)
49. Determine and describe possible combinations, where order does not matter, e.g., when there
is a choice of vanilla (V), chocolate (C) or strawberry (S) ice cream for a two-scoop cone and two
different scoops are desired, the possible combinations are CV, CS, or VS. (4.3)
Course Content :
Graphing
Measurement
Working with Addition and Subtraction
Place Value
Polygons
Fractions
Decimals
Multiplication
Division
Working with Time
Working with Money
Probability
Perimeter and Area
Capacity
Weight
Common Assessments :
Basic Addition, Subtraction, Multiplication and Division Facts (3 times per year)
Balance Scales
Estimation (twice per year)
Fraction Assessment
Comprehensive Assessment
Major Resources :
Growing With Mathematics, Teaching Student-Centered Mathematics