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Build deep math reasoning
Math Tasks uses open-ended tasks and manipulatives to apply deep
conceptual understanding to real-life challenges and deepen math
reasoning. Each Teacher Guide focuses on a single manipulative and
offers countless ways to use them. Flexible activities can be fit into
your math curriculum to preview, support, to reteach important concepts.
Present a possible scenario for introducing
the students to the activity. The aim of this
brief introduction is to help you give student
the tools they will need to investigate
independently and grow their own mathematical
These hands-on explorations have the potential
for bringing student to new mathematical ideas
and deepening skills as well as make sense of
problems and persevere in solving them.
Several prompts are provided to promote discussion.
Prompts are designed to encourage student
to describe what they notice, tell how they found
their results, and give the reasoning behind
The Extension takes the essence of the main
activity and either alters or extends its
parameters. These activities are well used
with a class that becomes deeply involved
in the primary activity, or for student who
finish before the others.
Feature 18 rich tasks that teach
content and practice standards
using the most common manipulatives.
Includes the grade-appropriate
Teachers Guides for: Base Ten
Blocks, Color Tiles, Cuisenaire®
Rods, Pattern Blocks, Geoboards,
and Snap Cubes®.
Maximize your investment with a
Math Task Teacher Guide, a
classroom manipulative kit, 8
math cooperation mats, and a
virtual manipulative bundle.
Allow students to work collaboratively
on a task. The mats remind the
students of the problem-solving
Each Teacher Guide includes 18 lessons that incorporate the
appropriate manipulative into math activities in meaningful
ways that help students grasp concepts with greater ease and
apply this conceptual understanding to real-world tasks and
challenges. Lessons teach perseverance that will benefit K-8
students in solving other math problems using other manipulatives
and connect to the core of mathematics learning that is important
to every K–8 student.
Base Ten Blocks provide students with ways to physically represent
the concepts of place value and addition, subtraction, multiplication,
and division of whole numbers. By building number combinations
with Base Ten Blocks, students ease into the concept of regrouping,
or trading, and are able to see the logical development of each
operation. The blocks provide a visual foundation and understanding
of the algorithms students use when doing paper-and-pencil computation.
Older students can transfer their understanding of whole numbers
and whole-number operations to an understanding of decimals and
Cuisenaire Rods can be used to develop a wide variety of
mathematical ideas at many different levels of complexity.
Initially, students use the rods to explore spatial
relationships. This introductory exploration will lead
students to discover how some combinations of rods are equal
in length to other, single rods. Older students who have no
previous experience with Cuisenaire Rods may explore by
comparing and ordering the lengths of the rods and then
recording the results on grid paper to visualize the inherent
“structure” of the design. In their early work with the
rods, students have a context in which to develop their
communication skills through the use of grade-appropriate
arithmetic and geometric vocabulary.
Pattern Blocks help students explore many mathematical topics,
including congruence, similarity, symmetry, area, perimeter,
patterns, functions, fractions, and graphing. In the beginning
students work with Pattern Blocks to explore spatial relations.
Young students have an initial tendency to work with others and
to copy one another’s designs. Yet even duplicating another’s
pattern with blocks can expand students’ experience, help them develop
the ability to recognize similarities and differences, and provide
a context for developing language related to geometric ideas.
Throughout their investigations, student should be encouraged
to talk about their constructions. Expressing their thoughts
out loud helps students to clarify and extend their thinking.
Although Color Tiles are simple in concept, they can be used
to develop a wide variety of mathematical ideas at many
different levels of complexity. Young students who start using
Color Tiles to make patterns may be likely to talk about
numbers of different-colored tiles. Some students may even
spontaneously begin to count and compare numbers. The fact
that the tiles are squares means that they fit naturally
into a grid pattern, so the tiles can be used to discover
many number patterns.
Snap Cubes are very suitable for developing understanding
of the meaning of addition. The colors can also broaden
students’ understanding of subtraction. Snap Cubes are
also ideal for developing the concept of multiplication,
both as equal grouping and as an array. In addition,
Snap Cubes are suitable for exploring area, perimeter,
volume, and surface area relations.
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