3-1 Models for Numeration with Multibase Pieces
NCTM Standard: Concrete models can help represent numbers and develop number sense; they can
also help to bring meaning to students use of written symbols and can be useful in building place-value
concepts.
9-1 Figures on Rectangular and Circular Geoboards
NCTM Standard: The study of geometry in grades 3-5 requires thinking and doing. As students sort,
build, draw, model, trace, measure, and construct, their capacity to visualize geometric relationships will
1-1 Seeing and Extending Patterns with Pattern Blocks
NCTM Standard: In grades 3-5, students should investigate numerical and geometric patterns and
express them mathematically in words or symbols. They should analyze the structure of the pattern and
how
10-2 Areas on Geoboards
NCTM Standard: Since the customary English system of measurement is still prevalent in the United
States, students should learn both customary and metric systems and should know some rough
equivalences between the metric and custom
MATH 4161
Addition of Integers: Analyzing Students' Work
For each section, decide if the student's work is correct. Show how the student would most likely complete the last exercise. Identify the process the student seems to be using, and write an explana
5-2 Fraction Bar Model for Equality and Inequality
NCTM Standard: By using an area model in which part of a region is shaded, students can see how
fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions.
6-2 Operations with Decimal Squares
NCTM Standard: The approach to decimals should be similar to work with fractions, namely placing
strong and continued emphasis on models and oral language and then connecting this work with
symbols Exploring ideas of te
9-3 Models for Regular and Semiregular Polyhedra
NCTM Standard: The study of geometry in grades 3-5 requires thinking and doing. As students sort,
build, draw, model, trace, measure, and construct, their capacity to visualize geometric relationships will
5-3 Computing with Fraction Bars
NCTM Standard: By using an area model in which part of a region is shaded, students can see how
fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions.
Students who have
3-2 Adding and Subtracting with Multibase Pieces
NCTM Standard: Concrete models can help represent numbers and develop number sense; they can
also help to bring meaning to students use of written symbols and can be useful in building place-value
concepts.
6-1 Decimals Squares Model
NCTM Standard: The approach to decimals should be similar to work with fractions, namely placing
strong and continued emphasis on models and oral language and then connecting this work with
symbols Exploring ideas of tenths and
5-1 Black and Red Tile Model for Integers
NCTM Standard: Negative integers should be introduced at this level [Grades 3-5] through the use of
familiar models such as temperature or owing money. The number line is also an appropriate and helpful
model, and
9-4 Creating Symmetric Figures: Pattern Blocks and Paper Folding
NCTM Standard: The study of geometry in grades 3-5 requires thinking and doing. As students sort,
build, draw, model, trace, measure, and construct, their capacity to visualize geometric rel
1-2 Geometric Number Patterns with Color Tiles
NCTM Standard: In grades 3-5, students should investigate numerical and geometric patterns and
express them mathematically in words or symbols. They should analyze the structure of the pattern and
how it grow
2-1 Sorting and Classifying with Attribute Pieces
NCTM Standard: Being able to reason is essential to understanding mathematics. By developing
ideas, exploring phenomena, justifying results, and using mathematical conjectures in all content areas
and with