ANSWERS TO UNIT REVIEWS Units 12-16 & 18
Unit 12
A. 1. round ones, Cheerios: naturalistic
2. round bowl: naturalistic
3. square window panes: naturalistic
4. signs, windows, vehicles: naturalistic
5. block shapes, rectangular enclosure: naturalistic
6. body shapes: structured
7. cubes, ellipses: naturalistic
8. formboards: naturalistic
9. shape blocks: naturalistic
B. These are examples; responses will vary.
1. Shape discrimination: “This has square corners like a square but it isn’t a square
because two sides are longer.”
2. Labeling—Playing with attribute blocks: “These are hexagons; these are squares;
these are triangles.”
3. Matching: When asked, the child can find another shape like the one the teacher
shows him.
4. Sorting: See 2 above.
C. 1. labeling 2. matching 3. discrimination 4. matching 5. matching, sorting 6.
matching
Unit 13
A. Assessment can be done by noting the child’s use of space words, her use of
organization and pattern arrangement during play activities, her use of construction
materials, and her use of her own body in space.
B. 1. c, e
2. e
3. d
4. d
5. a
9. a 13. a
6. c, f 10. b 14. e
7. d 11. d 15. a, b
8. a 12. d, e
C. The examples in question B are congruent with the NCTM expectations for spatial
relationships: describe, name, and interpret relative positions in space; apply ideas
about relative position; describe, name, and interpret direction and distance in
navigating space and apply ideas about direction and distance; and find and name
locations with simple relationships such as “near” and “far.” Each example in B could be
related to the expectations.
Unit 14
A. 1. c 2. a 3. b 4. c 5. c 6. b 7. a 8. B
B. Answers will vary. Some examples are using part/whole vocabulary, giving children
jobs such as cutting fruits or passing out food equally to a group of children, and asking
students to identify missing parts of broken toys.
C. Children can be observed during their daily activities. Children can be questioned as
they do their daily activities, or they can be interviewed individually.
D. The examples in question A can be categorized into the NCTM expectations for parts
and wholes: a sense of whole numbers and what happens when they are broken into
groups; an understanding that bodies and objects are made up of unique parts.
Unit 15
A. Language is essential to accomplishing all the NCTM guideline goals and to
understanding math and science concepts and reporting the results of math science
investigations.
B. The whole language approach emphasizes immersion in oral and written language
(print). Children talk with each other and the teacher; they write; and they read good
literature. All these activities can support the growth of concept vocabulary.
C. The five mathematics process expectations are the means through which children
learn. Problem solving is the major means through which young children learn
mathematics. Reasoning is important in working with classification and patterning.
Communicating through oral and written language, pictures, and movement tells us how
children have solved problems. Connections between what the child brings to school
and school mathematics make mathematics real. Representation using objects,
drawings, and written language and conventional symbols tells us what children are
thinking.
Unit 16
A. d, f, a, b, c, e, g
B. Children use math concepts and skills as they make observations. Mathematics
concepts and skills are used to quantify information gathered while making
observations. An example would be using measurement to describe the size of a
container. The description would include counting, comparing, classifying, and
measuring.
Unit 18
A.
1. Play and imitation
2. Making comparisons
3. Using arbitrary units
4. Seeing the need for standard units
5. Being able to use standard units
B. The measurement stages are
1. A play stage, in which the child imitates other children or adults, pours objects from
one container to another, lifts things.
2. A comparison stage, in which the child checks to see what is heavier or lighter, longer
or shorter, and so on.
3. An arbitrary unit stage, in which the child uses anything as a unit of measure.
4. An understanding of the need for standard units.
5. The child begins to use and understand units of measurement.
C. 1. stage 2 2. stage 5 3. stage 1 4. stage 4 5. stage 3
D. A young child’s measurement skills can be assessed by observing how he goes
about imitating adult ways of measuring and by noting instances of informal
measurement such as comparing.
E. The NCTM expectations for children in the beginning stages of measurement:
recognizing the attributes of length, volume, weight, and time and comparing and
ordering objects according to these attributes.