D691 – Elementary Mathematics Curriculum
D691 – Elementary Mathematics – Practice Questions With Answers
Boost your test performance with Ulosca’s D691 Elementary Mathematics review. This guide is designed for education students preparing to demonstrate mastery of foundational mathematical concepts, operations, and problem-solving skills required for effective teaching at the elementary level.
Everything you need to answer with confidence:
- Covers all key D691 exam topics including number sense and operations, fractions and decimals, ratios and proportions, algebraic thinking, geometry, measurement, and data analysis.
- Features timed practice sets with computation, application, and multi-step word problems modeled after the real exam structure.
- Strengthens your ability to explain concepts clearly, apply multiple solution strategies, and connect mathematics instruction to real-world contexts in the elementary classroom.
- Fully aligned with D691 course objectives and elementary mathematics teaching standards.
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Free D691 – Elementary Mathematics Curriculum Questions
If you have the numbers 2, 3, and 4, how can you use the associative property to simplify the expression (2 + 3) + 4?
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You can only add the first two numbers together.
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You can regroup it as 2 + (3 + 4).
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You must calculate (2 + 3) first and cannot change the grouping.
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You cannot use the associative property with addition.
Explanation
Explanation:
The associative property of addition states that the way addends are grouped does not change the sum: (a + b) + c = a + (b + c). So (2 + 3) + 4 can be regrouped as 2 + (3 + 4). Both give the same total: (2 + 3) + 4 = 5 + 4 = 9 and 2 + (3 + 4) = 2 + 7 = 9. Regrouping can make mental computation easier.
Correct Answer:
You can regroup it as 2 + (3 + 4).
Why Other Options Are Wrong:
You can only add the first two numbers together.
This ignores the associative property, which allows regrouping. You are not restricted to adding the first pair; you can change grouping without changing the result.
You must calculate (2 + 3) first and cannot change the grouping.
This contradicts associativity. While evaluating left to right is fine, the property explicitly permits regrouping to 2 + (3 + 4).
You cannot use the associative property with addition.
Addition is one of the classic operations where associativity holds. Saying you cannot use it is false; addition is associative.
A teacher has 6 boxes with 4 markers in each box. Which expression correctly finds the total number of markers?
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6 + 4
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6 × 4
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6 − 4
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6 ÷ 4
Explanation
Correct Answer:
6 × 4
Explanation:
When there are equal groups (6 boxes) with the same amount in each group (4 markers), multiplication models the total: number of groups × amount per group. Thus, 6 × 4 gives the total markers, which equals 24. Multiplication is the most efficient way to combine equal groups without repeated addition.
Why Other Options Are Wrong:
6 + 4
This finds the sum of two numbers, not the total from 6 equal groups of 4. It would yield 10, which does not represent 6 groups of 4.
6 − 4
Subtraction compares or removes quantities; it does not combine equal groups to find a total. The result (2) is unrelated to the total number of markers.
6 ÷ 4
Division would tell how many are in each group if the total were known, or how many groups can be made—neither matches this context. We already know groups and size; we need the total, so division is inappropriate here.
If the digit 5 is in the hundreds place of the number 5,432, what is its value and how does it contribute to the overall number?
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5, contributing to the total value of 5,432
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5,000, contributing to the total value of 5,432
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500, contributing to the total value of 5,432
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50, contributing to the total value of 5,432
Explanation
Explanation:
In base ten, a digit’s value equals the digit multiplied by the place value. The hundreds place represents 100s, so a 5 in the hundreds place is 5 × 100 = 500. Thus, it contributes 500 to the overall number.
Correct Answer:
500, contributing to the total value of 5,432
Why Other Options Are Wrong:
5, contributing to the total value of 5,432
A value of 5 corresponds to the ones place, not the hundreds place.
5,000, contributing to the total value of 5,432
5,000 would be the value if the 5 were in the thousands place.
50, contributing to the total value of 5,432
50 corresponds to the tens place, not the hundreds place.
Describe why knowing the length of a cube's edge is essential for calculating its volume.
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The length of the edge is only needed for measuring the cube's weight.
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Knowing the length of a cube's edge allows us to use the formula for volume, which is edge length cubed.
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The length of the edge helps in determining the surface area, not the volume.
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The edge length is irrelevant for volume calculations.
Explanation
Explanation:
A cube’s volume depends solely on its edge length because all three dimensions are equal. The volume formula is V =s3, where sss is the edge length. Once you know sss, you multiply it by itself three times to find the amount of space the cube occupies. Without the edge length, you cannot compute the volume.
Correct Answer:
Knowing the length of a cube's edge allows us to use the formula for volume, which is edge length cubed.
Why Other Options Are Wrong:
The length of the edge is only needed for measuring the cube's weight.
Weight depends on both volume and material density; edge length alone doesn’t measure weight. Here we’re concerned with geometric volume, for which edge length is directly required via s3.
The length of the edge helps in determining the surface area, not the volume.
Edge length does determine surface area (6s2), but it also determines volume (s3). Saying it’s only for surface area ignores the volume relationship.
The edge length is irrelevant for volume calculations.
This is false. The edge length is the sole geometric input for a cube’s volume; without sss, you cannot compute V.
In a classroom activity, students are asked to quickly identify the number of dots on a dice without counting. What mathematical concept are they practicing?
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Substizing
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Subtraction
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Addition
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Estimation
Explanation
Explanation:
This activity targets subitizing—the ability to recognize the quantity of a small set instantly, without counting one by one. Standard dot patterns on a die are designed to support this rapid recognition. Practicing subitizing strengthens number sense, helps children see parts and wholes, and builds a foundation for efficient mental arithmetic. It is different from computing; it’s about immediate perception of quantity.
Correct Answer:
Substizing
Why Other Options Are Wrong:
Subtraction
Subtraction involves finding how many are left or the difference between two quantities. In this activity, students are not removing dots or comparing two sets; they are naming the exact quantity shown. The cognitive demand is perceptual recognition, not computation. Therefore, subtraction is not the focus of this task.
Addition
Addition combines two or more groups to find a total. The dice task does not ask students to join separate groups or compute a sum; it asks them to instantly recognize a known arrangement. While subitizing can later support quick addition, that is not what students are being asked to do here. The activity centers on immediate quantity recognition, not calculating.
Estimation
Estimation is making a reasonable guess without determining an exact count. With die faces, students are expected to state the exact number of dots accurately and quickly, not to approximate. The dot configurations are small and standardized precisely to enable exact recognition. Thus, estimation is neither necessary nor intended in this context.
At a certain school, the ratio of the number of female teachers to male teachers is 5 to 2. Which of the following could be the total number of female and male teachers at the school?
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35
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37
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52
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20
Explanation
Explanation:
If the ratio of females to males is 5:2, the total must be a multiple of 5 + 2 = 7. Only totals divisible by 7 can be split into whole numbers keeping the 5:2 ratio (females = 5/7 of total, males = 2/7 of total). Among the choices, 35 is the only multiple of 7, giving females = 25 and males =10, which matches 5:2.
Correct Answer:
35
Why Other Options Are Wrong:
37
Not divisible by 7, so (5/7) × 37 and (2/7) × 37 are not whole numbers; the ratio cannot be satisfied with whole teachers.
52
52 is not a multiple of 7; splitting 52 in a 5:2 ratio would not yield whole numbers for both groups.
20
20 is not divisible by 7, so it cannot be partitioned into whole numbers in a 5:2 ratio.
If Ben had bought 2 more watermelons at the same price, how much change would he receive from a $20 bill?
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$3.50
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$2.50
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$4.50
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$1.50
Explanation
Explanation:
Using the same price per watermelon from the original scenario ( $3.50 each ), buying 2 more means Ben would have 5 watermelons total. The cost is 5 × $3.50 = $17.50. Change from $20 is $20 − $17.50 = $2.50.
Correct Answer:
$2.50
Why Other Options Are Wrong:
$3.50
Would imply a total cost of $16.50, which is not 5 × $3.50.
$4.50
Would imply a total cost of $15.50, not consistent with 5 × $3.50.
$1.50
Would imply a total cost of $18.50, again not equal to 5 × $3.50.
Describe how the activity of surveying favorite shapes helps students develop their mathematical skills.
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The activity helps students develop their skills in collecting and representing data through graphing.
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The activity teaches students about the properties of geometric figures.
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The activity introduces students to basic probability concepts.
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The activity focuses on understanding spatial relationships between shapes.
Explanation
Correct Answer:
The activity helps students develop their skills in collecting and representing data through graphing.
Explanation:
When students survey classmates about favorite shapes, they generate categorical data, practice tallying, and organize results into tables or simple graphs. They interpret counts, compare frequencies, and draw conclusions from the displays. This work strengthens vocabulary such as “most,” “least,” and “equal to,” while connecting real-world questions to mathematical representations. It directly targets early data collection and graphing standards.
Why Other Options Are Wrong:
The activity teaches students about the properties of geometric figures.
While shapes are mentioned in the survey, the task does not analyze attributes like side lengths, angles, or symmetry. Students are choosing preferences, not classifying by properties. Any discussion of why someone prefers a shape is incidental to the data goal. Therefore, it does not systematically build knowledge of geometric properties.
The activity introduces students to basic probability concepts.
A preference survey records what students like; it does not model random events or sample spaces. Without random selection or chance processes, the results do not represent probabilities. Treating the class’s favorites as probabilities confuses frequency with likelihood in a chance context. Thus, probability is not the mathematical focus of this activity.
The activity focuses on understanding spatial relationships between shapes.
Spatial reasoning involves position, orientation, and relationships like “above,” “inside,” or “congruent.” The survey does not require manipulating shapes in space or analyzing how they relate. Students are counting responses, not exploring transformations or spatial arrangements. Consequently, spatial relationships are not the primary learning outcome here.
What does the conservation of number principle state?
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Numbers can be rearranged without changing their value
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Physical arrangement affects the total quantity
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Quantity does not change with physical arrangement
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The sum of numbers remains constant regardless of order
Explanation
Explanation:
The conservation of number principle means that the number of objects in a set stays the same even if their spatial arrangement changes, as long as no objects are added or removed and none are hidden. Rearranging them closer together or farther apart does not alter the set’s cardinality. This idea supports stable counting and one-to-one correspondence in early math.
Correct Answer:
Quantity does not change with physical arrangement
Why Other Options Are Wrong:
Numbers can be rearranged without changing their value
This statement is vague and can be misread as moving digits in numerals or reordering terms in an equation. Conservation is specifically about the count of concrete objects being invariant under spatial rearrangement, not about symbolic manipulation of numbers.
Physical arrangement affects the total quantity
This is the opposite of conservation. Spreading objects out or clustering them does not change how many there are; only adding or removing objects changes quantity.
The sum of numbers remains constant regardless of order
This describes the commutative property of addition, not conservation. Commutativity concerns arithmetic with symbols; conservation concerns the cardinality of a set of objects under rearrangement.
A customer pays for a meal with a $20.00 bill. The total for the meal was $17.74. The change due, using the fewest number of coins and bills, would be
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two $1.00 bills, one dime, and one penny
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two $1.00 bills, one quarter, and one penny
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three $1.00 bills, one quarter, and one penny
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three $1.00 bills, one dime, and one penny
Explanation
Explanation:
Compute the change: $20.00 − $17.74 = $2.26. Using the fewest pieces, give two $1 bills ($2.00), leaving $0.26. The minimal coin combination for 26¢ is one quarter (25¢) and one penny (1¢), totaling 26¢ in just two coins. Thus the least-count set is two $1 bills, one quarter, and one penny.
Correct Answer:
two $1.00 bills, one quarter, and one penny
Why Other Options Are Wrong:
two $1.00 bills, one dime, and one penny
Totals only $2.11, which is 15¢ short of the required $2.26 change.
three $1.00 bills, one quarter, and one penny
Totals $3.26, which is $1.00 too much change.
three $1.00 bills, one dime, and one penny
Totals $3.11, also too much by $0.85 compared to the correct $2.26.
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D691 – Elementary Mathematics – Comprehensive Study Notes
This D691 exam review prepares education students to demonstrate mastery of foundational concepts in elementary mathematics, emphasizing number sense, operations, algebraic thinking, geometry, measurement, and data. Students will be expected to apply both conceptual understanding and procedural fluency, design developmentally appropriate instruction, and connect mathematics learning to real-world classroom contexts.
1. Number Sense and Operations
Place Value: Understanding base-ten structure, expanded notation, and value of digits.
Whole Numbers: Addition, subtraction, multiplication, and division as operations with multiple models (equal groups, arrays, repeated addition/subtraction, area).
Fractions and Decimals: Interpreting fractions as parts of a whole, on a number line, and in relation to division; connecting decimals to fractions and place value.
Properties: Commutative, associative, distributive, and identity properties as tools for mental math and flexible strategies.
2. Ratios, Proportions, and Algebraic Thinking
Patterns: Identifying, extending, and creating repeating and growing patterns.
Algebra Foundations: Writing and solving simple equations, using variables, and recognizing equality/inequality.
Ratios and Proportions: Using proportional reasoning for real-world contexts, such as scaling and comparing rates.
Problem-Solving: Connecting arithmetic to algebraic reasoning through fact families and inverse operations.
3. Geometry and Spatial Reasoning
Shapes: Classifying two-dimensional and three-dimensional figures based on attributes (sides, angles, faces, edges, vertices).
Symmetry and Transformations: Line and rotational symmetry, translations, reflections, rotations.
Measurement Concepts: Perimeter, area, surface area, and volume with standard and nonstandard units.
Spatial Reasoning: Using manipulatives, drawings, and dynamic software to explore relationships between shapes.
4. Data Analysis and Probability
Data Representation: Creating and interpreting bar graphs, line plots, pictographs, and pie charts.
Statistical Concepts: Understanding mean, median, mode, and range at an age-appropriate level.
Probability: Simple probability as ratios of favorable outcomes to total outcomes using coins, dice, and spinners.
Mathematical Communication: Using data to make predictions, explain reasoning, and connect to real-world questions.
5. Mathematical Practices and Pedagogy
Formative vs. Summative Assessment: Using exit tickets, concept maps, and performance tasks vs. unit tests and projects.
Problem-Based Learning: Encouraging multiple solution paths, justification, and discourse.
Procedural Fluency vs. Conceptual Understanding: Balancing algorithmic proficiency with sense-making.
Differentiation: Providing supports for struggling learners and extensions for gifted students.
6. Early Childhood and Primary Math Foundations
Counting Principles: One-to-one correspondence, stable order, and cardinality.
Subitizing: Recognizing small quantities without counting.
Operations in Context: Using manipulatives for addition, subtraction, multiplication, and division.
Fractions as Fair Shares: Introducing halves, thirds, and fourths concretely with visuals and real-life contexts.
7. Connections to Real-World Applications
Measurement: Applying length, weight, time, and capacity to classroom and daily activities.
Money: Recognizing coin and bill values, making change, solving word problems.
Patterns in Nature and Art: Symmetry, and growth patterns.
STEM Integration: Linking mathematics to science experiments, engineering challenges, and technology-based problem solving.
8. Professional Standards and Teaching Practices
NCTM Standards: Focus on problem-solving, reasoning, communication, connections, and representation.
Mathematical Practices (CCSSM): Make sense of problems, reason abstractly, construct arguments, use tools strategically, and look for patterns/structure.
Assessment of Understanding: Diagnostic, formative, and summative strategies for diverse learners.
Equity in Math Instruction: Culturally responsive examples, language supports for ELs, and accessible tasks for students with disabilities.