Accelerating Students in
Mathematics
Bringing Students to Grade Level
in a Standards-Based World
Strand Trace
What mathematical ideas are
embedded in this standard?
Grade 3: Order and compare unit fractions
and fractions with like denominators by
using models and an understanding of the
concept of numerator and denominator.
How did we learn these ideas?
Conceptual Thought Patterns
for Comparing Patterns
• With a partner, read through each of the
examples. Make up some fractions that
provide an example of the description.
• Table sharing.
• Finish these fractions so they are close to
but greater than one-half.
9
15
12
21
• Finish these fractions so they are close to
but less than 1 whole.
11
24
16
30
Reflect:
Through these two activities:
What would students be
understanding about fractions?
Conceptual Thought Patterns
for Comparing Fractions
• More of the same-size parts.
• Same number of parts but different sizes.
• More or less than one-half or one whole.
• Distance from one-half or one whole (residual
strategy–What’s missing?)
Comparison of Fractions
Consider ways to reason with benchmarks
when comparing these fractions.
•
5/7 or
•
3/8
or
3/4
•
5/4 or
8/9
•
15/16 or 9/10
•
1 1/3 or 6/3
3/7
Fraction Cards
3/8
3/10
6/5
7/47
7/100
25/26
8/15
13/24
14/30
16/17
6/9
5/3
1/3
17/12
Ordering Fractions
on the Number Line
Gr. 3 Everyday Math
(1) Make fraction cards using the post it notes. One
fraction per card.
(2) Allow quiet time to think about placements.
(3) Taking turns, each person:
•
•
•
Make a number line with benchmark numbers; 0, 1,
2, 3.
Places one fraction on the number line, and
Explains his/her reasoning using benchmarks and
conceptual thought patterns.
Reflect
As you placed the fractions on
the number line, summarize
some new reasoning or
strengthened understandings.
Fraction Kit
Gr. 4 Everyday Math
Fold paper strips
• Purple: Whole strip
• Green: Halves, Fourths, Eighths
• Gold: Thirds, Sixths, Ninths,
Twelfths
Fraction Strip Observations
• With your partner, make a few observations
about ways to use your fractions strips. Make
up two problems for each observation.
• Present a problem for the class to solve.
Task:
Estimation with Benchmarks
• Table facilitator reveals one problem at a time.
• Each individual silently estimates.
• On the facilitator’s cue:
– Thumbs up = greater than benchmark
– Thumbs down = less than benchmark
– Wavering “waffling” = unsure
• Justify reasoning.
Reflection
What are some of the big
ideas about fractions you are
learning?
Minnesota Standards
Fraction Strand Trace
Make connections between the big ideas in the
fraction standards and the activities for today.
Day 2
• Estimating Fractions Operations with
Benchmarks
• Fraction Strand Trace
• 2 D Geometry
Tricky Triangles
Consider: What will students learn? What are the
big ideas?
1. Triangles have three sides, three vertices, and
three angles.
2. Triangles can be oriented in many different
ways.
3. Angles may have the same size or very different
sizes. Side lengths may be the same or different.
What idea is important?
What question will you ask?
• Shapes A, C, H, M.
• Shapes F and O
• Shapes P and B
• Shapes E, G, and K
Power Polygons
• Clear off the table.
• Find the polygons that are triangles. Put the
rest back in the bucket.
• Take out 8 triangles from each of the bags.
(save the plastic bags).
Power Polygons
• Use your polygons to find pairs of triangles
that have an attribute in common.
• Draw two more triangles that share the
attribute and one that does not.
Include the following words in your discussion:
Acute, obtuse, scalene, isosceles, equilateral
Before you start, write a definition for these
words on a sheet of paper.
Guess My Rule (5 of each polygon)
1) One person thinks of a rule and, without
telling anyone the rule, places two of the
polygons that fit the rule on a piece of paper.
2) The same person then picks up a polygon
that does not fit the rule and places it off the
paper.
3) The other players take turns choosing a new
polygon that either fits the rule or does not fit
the rule.
4) A rule can be guessed after each player has
had a turn to place their polygons.
Important Mathematical Ideas
•
•
•
•
•
Have three/four/ five sides
Have sides that are all the same size
Have angles that are all the same size
Have angles that are different sizes
Have no right angles
Quadrilaterals
• Mystery Rings
• Ring Labels
• All or Some Quadrilaterals
• Criteria for Sorting Quadrilaterals
Strand Trace
Make connections back to the standards.
Shape Cards
• Study the quadrilaterals
• Discuss the similarities and the differences in
the quadrilaterals. List properties.
• Construct a table chart.
All Quadrilaterals
Some Quadrilaterals
What mathematical ideas does the teacher
listen for?
What are the mathematical ideas that children
need to develop with these 2 D shapes?