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 Patternsfor 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 FractionsConsider ways to reason with benchmarks

when comparing these fractions.

• 5/7 or 3/7

• 3/8 or 3/4

• 5/4 or 8/9

• 15/16 or 9/10

• 1 1/3 or 6/3

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 KitGr. 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?