240's MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics Study Guide Is 96% Test-Aligned
240's MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics study guide is built around the official exam framework so you can study what is actually tested. This page shows exactly how the guide maps to the real exam — SMR by SMR and competency by competency — so you can see where coverage is strongest, where some depth gaps remain, and how each part of the guide supports your prep.
96%
test-aligned
72
Fully covered
6
Partially covered
0
Coverage gap
Based on a competency-by-competency review of the official framework and the lessons, practice questions, flashcards, videos, and study materials included in this guide.
654
Practice Questions
127
Flashcards
41
Study Materials
16
Videos
Why Test Alignment Matters for Your MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics Study Guide
Certification test standards are broad, but the exam questions are very specific. Our team of curriculum experts uses the 240 Study Guide Creation Process to ensure the most aligned, specific content for your MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics (119) test — so you are not wasting time on broad subject review that may not show up on exam day.
Why 240 Is the Best Choice for the MTTC 119 Study Guide
- Built around the official exam framework
- Organized by the competencies actually used on the exam
- Shows exactly what is covered and where depth is partial
- Includes aligned questions, flashcards, study materials, and videos
- Helps candidates study what is actually tested instead of broad generic content
Transparent coverage is a strength. We show where the guide is strong, where depth is partial, and where a gap has been identified so you can make an informed study decision.
How to Read This Alignment Review
3 domains · 78 competencies reviewed · 96% test-aligned
Covered— competency is comprehensively supported by the guide
Partially covered— core content is covered, but some depth gaps remain
Coverage gap identified— a content gap has been identified
This study guide is based on the current official exam framework
We review and update alignment whenever the official framework changes so candidates are always studying current, accurate material.
MATHEMATICS-SPECIFIC TEACHING PRACTICES (DOMAIN I)
Partially covered
SMR I.1 Build and draw on relationships with children, caregivers, and communities in ways that support children's mathematics learning.
59 Qs5 Materials11 Cards2 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Use what children say in their mathematical thinking to engage with curiosity, interest, and understanding in ways that build rapport; provide information about children's interests, strengths, and needs; and inform instruction. | M.Teaching Mathematical Reasoning | Partially covered | 7 | 1 | 1 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| b. Demonstrate knowledge of ways to communicate with caregivers about mathematics and their child in relation to current standards and the school's curriculum, supporting caregivers in fostering their child's success with mathematics in and out of school. | M.Diversity and Engagement | Partially covered | 3 | 1 | 1 | 1 | Partial coverage by 1 topic (3 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
| c. Apply knowledge of children, their caregivers, and their communities to identify mathematical learning environments that provide all children, in particular children historically marginalized in mathematics classrooms, with access to significant mathematics and engagement in mathematical activities that are both culturally and instructionally appropriate. | M.Diversity and Engagement - ELL | Covered | 8 | 1 | 1 | 1 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 1 videos). |
| d. Demonstrate knowledge of ways to build children's positive mathematical identities, disrupting patterns of marginalization that reinforce inequities and exclusion. | M.Best Practices to Teach Math SpEd; M.Best Practices to Teach Math TX EC-3/EC-6 | Covered | 41 | 2 | 8 | 0 | Covered by 2 topics (41 questions, 2 materials, 8 cards, 0 videos). |
SMR I.2 Plan mathematics lessons and sequences of lessons.
56 Qs4 Materials13 Cards3 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of how to design ways to interest children and to use their resources and affinities to build access and participation, including taking stock of the mathematical capacities children bring to lessons, anticipating common patterns of mathematical thinking, looking for opportunities to include play in mathematics and mathematics in play, and planning for the mathematical participation of particular children. | M.Planning for Group Experiences; M.Manipulatives for Young Children | Covered | 28 | 2 | 7 | 1 | Covered by 2 topics (28 questions, 2 materials, 7 cards, 1 videos). |
| b. Analyze the mathematics content in instructional resources, referencing standards and progression documents to clarify learning goals and to identify connections among mathematical concepts and across grade levels. | M.Backward Design | Covered | 9 | 1 | 3 | 1 | Covered by 1 topic (9 questions, 1 materials, 3 cards, 1 videos). |
| c. Use methods that promote broad participation in mathematical work (e.g., choosing activities and planning activities that provide children with multiple entry points and ways of being successful), make children's thinking central to the lesson, provide opportunities for play, and give children opportunities to show their thinking and see value in the contributions they make. | M.Learning Progressions in Math | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
SMR I.3 Use formative and summative mathematics assessments to gauge children's learning and to make instructional decisions.
75 Qs3 Materials13 Cards3 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of methods to elicit children's thinking and solution strategies in multiple forms, such as in writing, through speaking, and in drawings; and identify evidence of understanding in children's thinking and strategies and use this information to make in-the-moment instructional decisions. | M.Types of Assessment - Math | Covered | 20 | 1 | 13 | 1 | Covered by 1 topic (20 questions, 1 materials, 13 cards, 1 videos). |
| b. Understand the meanings, purposes, and processes of summative and formative assessments in mathematics. | M.Types of Assessment - Math | Covered | 20 | 1 | 13 | 1 | Covered by 1 topic (20 questions, 1 materials, 13 cards, 1 videos). |
| c. Interpret assessment data and use this information to select instructional activities that target children's strengths and needs, promote learning, and improve instruction. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| d. Understand how the language, format, and context of mathematics assessments (and assessment questions) affects children's ability to demonstrate their thinking. | M.Evaluate Student Solutions | Covered | 40 | 1 | 0 | 1 | Covered by 1 topic (40 questions, 1 materials, 0 cards, 1 videos). |
| e. Distinguish between superficial and deeper evidence about children and attend to key aspects of children's understanding, skill, and engagement, as well as ignore irrelevant aspects. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| f. Analyze assessment data to plan next steps for instruction, understanding that evidence of children's learning (vs. topic coverage) is necessary for moving on from a topic. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
SMR I.4 Enact instruction that allows all children to engage with significant mathematics and to develop productive dispositions toward mathematics.
63 Qs6 Materials20 Cards3 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of ways to support children, in particular children historically marginalized in mathematics classrooms, in identifying themselves as mathematical thinkers and design instruction that helps children to recognize their own and other children's mathematical strengths. | M.Diversity and Engagement; M.Diversity and Engagement - ELL | Covered | 11 | 2 | 2 | 2 | Covered by 2 topics (11 questions, 2 materials, 2 cards, 2 videos). |
| b. Demonstrate knowledge of a variety of participation structures and instructional routines, including whole-class, small-group, and independent lesson formats, both play and formal instruction, and a variety of materials, to foster children's talk about mathematics, with particular attention to disrupting patterns of over- and under-participation that reinforce inequities and exclusion. | M.Planning for Group Experiences; M.Variety of Representations | Covered | 22 | 2 | 13 | 1 | Covered by 2 topics (22 questions, 2 materials, 13 cards, 1 videos). |
| c. Identify classroom organizational routines and strategies that allow children access to mathematical tools and ensure the effective use of manipulatives and resources. | M.Manipulatives for Young Children | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| d. Identify strategies for creating a classroom culture that values productive struggle, challenging mathematical ideas, constructing mathematical meanings together, and enjoyment of mathematics. | M.Stimulating Higher Order Thinking | Covered | 14 | 1 | 2 | 0 | Covered by 1 topic (14 questions, 1 materials, 2 cards, 0 videos). |
MATHEMATICAL KNOWLEDGE FOR TEACHING GRADES PK-3: ATTRIBUTION AND COUNTING AND WHOLE NUMBER REPRESENTATION (DOMAIN II)
Partially covered
SMR II.5 Unpack mathematical content and identify mathematical competence for attribution.
56 Qs4 Materials28 Cards0 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify mathematical affordances in tasks and play situations for noticing, naming, and describing attributes of two- and three-dimensional shapes and spatial relationships, paying attention to the precision of examples. | M.Counting Techniques | Covered | 14 | 1 | 1 | 0 | Covered by 1 topic (14 questions, 1 materials, 1 cards, 0 videos). |
| b. Identify opportunities to introduce mathematical language and precision into others' talk and play that draw attention to patterns, features, and compositions of shapes and objects, for instance, suggesting words such as tall, short, or wide when someone says, "my building is big" or asking questions about how many blocks or what shapes were used or about which blocks are on the bottom. | M.Number Sense for Young Children | Covered | 23 | 1 | 8 | 0 | Covered by 1 topic (23 questions, 1 materials, 8 cards, 0 videos). |
| c. Recognize and rewrite mathematical tasks involving spatial reasoning, composing and decomposing shapes, equal partitioning, or comparing or analyzing shapes to make the tasks easier or harder, or to include multiple entry points, without undermining the intended mathematical focus—including recognizing the influence on the task when choosing specific side lengths, angles, spatial orientations, and the absence or presence of parallel or perpendicular lines. | M.Attributes of Polygons - Lines of Symmetry | Partially covered | 1 | 1 | 0 | 0 | Partial coverage by 1 topic (1 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| d. Generate examples and non-examples of shapes (such as triangles, rectangles, and others) that draw attention to defining features and help to build mathematical definitions, namely examples that fit common expectations and ones that do not. | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
SMR II.6 Perform mathematical explanations and support children's mathematical explanations for attribution.
47 Qs4 Materials8 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Formulate questions that distinguish whether a number or element of a series fits a pattern or definition. | M.Types of Sequences | Covered | 14 | 1 | 6 | 0 | Covered by 1 topic (14 questions, 1 materials, 6 cards, 0 videos). |
| b. Unpack, understand, and develop mathematical justifications using definitions when comparing and analyzing two- and three-dimensional shapes. | M.Teaching Mathematical Vocabulary; M.2D of 3D shape | Covered | 20 | 2 | 2 | 0 | Covered by 2 topics (20 questions, 2 materials, 2 cards, 0 videos). |
| c. Use clear and precise language to name and describe two- and three-dimensional shapes (e.g., distinguishing between cones and triangles, sides and faces, and sides and edges; recognizing changes in orientation; identifying transformations). | M.2D of 3D shape | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| d. Compare and contrast different explanations of the methods for generating numerical or geometrical patterns. | M.Types of Sequences; M.Simple Shape Patterns | Covered | 27 | 2 | 6 | 0 | Covered by 2 topics (27 questions, 2 materials, 6 cards, 0 videos). |
SMR II.7 Choose, interpret, and talk with representations for attribution.
44 Qs4 Materials24 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify accurate representations of regular and irregular two- and three-dimensional shapes in a variety of orientations that highlight defining and non-defining attributes. | M.Attributes of Polygons - Lines of Symmetry; M.Attributes of Two-Dimensional Shapes | Covered | 19 | 2 | 19 | 0 | Covered by 2 topics (19 questions, 2 materials, 19 cards, 0 videos). |
| b. Coordinate images, talk, and gestures, such as pointing when comparing and analyzing components of composite two- and three-dimensional shapes. | M.2D of 3D shape | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| c. Identify multiple representations and make connections among different representations for composite shapes in drawings and other models (e.g., blocks, building materials, other manipulatives). | M.Manipulatives for Young Children | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| d. Interpret idiosyncratic representations of two- and three-dimensional shapes and recognize their mathematical strengths and weaknesses (e.g., noticing the potential for confusion in using a piece of pie to represent a triangle). | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
SMR II.8 Elicit, interpret, support, and extend others' mathematical thinking for attribution.
18 Qs1 Materials19 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Pose mathematically appropriate questions to probe and elicit others' thinking about two- and three-dimensional shapes, including differences among shapes, equally partitioning shapes, and iterating a part to create a whole. | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
| b. Interpret, critique, and develop claims about others' thinking, language, and gestures about quantity, shapes, and relationships between two-dimensional and three-dimensional shapes. | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
| c. Clarify and accurately record others' mathematical thinking as they compare and analyze attributes and two- and three-dimensional shapes. | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
SMR II.9 Unpack mathematical content and identify mathematical competence for counting and whole number representation.
117 Qs8 Materials14 Cards2 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify mathematical affordances in tasks and play situations for counting objects and exploring early number concepts (i.e., cardinality, one-to-one correspondence, subitizing, hierarchical inclusion, and conservation of number, as well as counting on and counting back). | M.Counting Techniques; M.Cardinal vs Ordinal Numbers | Covered | 16 | 2 | 3 | 0 | Covered by 2 topics (16 questions, 2 materials, 3 cards, 0 videos). |
| b. Formulate questions about quantity based on correct or incorrect responses in order to develop or assess thinking around early number concepts when engaging with a set of objects. | M.Reasonableness of Results | Covered | 16 | 1 | 0 | 0 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 0 videos). |
| c. Analyze addition and subtraction tasks for opportunities to address ideas about number, including composing and decomposing, anchor numbers of 5 and 10, and counting all and counting on, and adapt tasks, if necessary, for specific instructional goals. | M.Mental Math and Estimation; M.Models for Addition and Subtraction | Covered | 35 | 2 | 9 | 1 | Covered by 2 topics (35 questions, 2 materials, 9 cards, 1 videos). |
| d. Identify the mathematical goals, conditions, and challenges of tasks and play situations designed to address place-value relationships. | M.Place Value; M.Place Value - Names | Covered | 38 | 2 | 2 | 1 | Covered by 2 topics (38 questions, 2 materials, 2 cards, 1 videos). |
| e. Recognize multiple strategies for composing and decomposing numbers, their dependence on place-value relationships, and connections among these strategies as indicators of mathematical competence. | M.Composition and Decomposition of Multi-Digit Numbers | Covered | 12 | 1 | 1 | 0 | Covered by 1 topic (12 questions, 1 materials, 1 cards, 0 videos). |
SMR II.10 Perform mathematical explanations and support children's mathematical explanations for counting and whole number representation.
38 Qs3 Materials11 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Evaluate the capacity of questions to uncover others' strategies for determining if a count is correct, such as counting on, counting all, or counting back, as objects are added, removed, or combined or using understandings of the base-ten structure. | M.Reasonableness of Results | Covered | 16 | 1 | 0 | 0 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 0 videos). |
| b. Demonstrate knowledge of clear mathematical explanations connecting new terminology (e.g., ones, tens, hundreds) to objects and coordinating different strategies of composing and decomposing, for instance showing that 345 ones is equivalent to 34 tens and 5 ones and to 3 hundreds and 5 tens minus 5 ones with language that correctly and clearly references objects and symbols in meaningful ways. | M.Composition and Decomposition of Multi-Digit Numbers | Covered | 12 | 1 | 1 | 0 | Covered by 1 topic (12 questions, 1 materials, 1 cards, 0 videos). |
| c. Demonstrate knowledge of multiple ways to explain counts, addition, and subtraction based on base-ten number representation, 5s and 10s, convenient decompositions, and counting on or counting back. | M.Variety of Representations | Covered | 10 | 1 | 10 | 0 | Covered by 1 topic (10 questions, 1 materials, 10 cards, 0 videos). |
SMR II.11 Choose, interpret, and talk with representations for counting and whole number representation.
33 Qs3 Materials6 Cards1 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify affordances and limitations of representations for iterating units and composing and decomposing numbers. | M.Composition and Decomposition of Multi-Digit Numbers | Covered | 12 | 1 | 1 | 0 | Covered by 1 topic (12 questions, 1 materials, 1 cards, 0 videos). |
| b. Identify affordances and limitations of different representations (e.g., materials, manipulatives, drawings, symbols) for base-ten numbers and addition and subtraction (e.g., groupable, ungroupable, nonproportional) in relation to tasks or play situations and pedagogical goals. | M.Manipulatives for Young Children | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| c. Accurately interpret and represent connections and mathematical progressions among representations of addition, subtraction, and multiplication (e.g., open number lines, arrays). | M.Whole Number Operations on a Number Line | Partially covered | 5 | 1 | 1 | 1 | Partial coverage by 1 topic (5 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
SMR II.12 Elicit, interpret, support, and extend others' mathematical thinking for counting and whole number representation.
68 Qs5 Materials5 Cards1 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify questions to elicit particular ways of thinking about composing and decomposing numbers both less than 10 and greater than 10 when thinking is not transparent. | M.Composition and Decomposition of Multi-Digit Numbers | Covered | 12 | 1 | 1 | 0 | Covered by 1 topic (12 questions, 1 materials, 1 cards, 0 videos). |
| b. Evaluate claims about others' mathematical understanding of counting based on evidence from their performance on counting activities, in particular understandings of quantity, the ability to count on and back by place-value units starting at a number other than 0 or 1, and flexible use of structure in base-ten numbers. | M.Reasonableness of Results | Covered | 16 | 1 | 0 | 0 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 0 videos). |
| c. Demonstrate knowledge of ways to record others' approaches to tasks involving the bundling of groups of 10 into a unit and interpret what is understood about the base-ten number system. | M.Place Value; M.Place Value - Names | Covered | 38 | 2 | 2 | 1 | Covered by 2 topics (38 questions, 2 materials, 2 cards, 1 videos). |
| d. Demonstrate knowledge of strategies to observe, assess, and identify developing understandings of early number concepts (i.e., cardinality, one-to-one correspondence, subitizing, hierarchical inclusion, and conservation of number, as well as counting on and counting back) and select appropriate follow-up questions. | M.Cardinal vs Ordinal Numbers | Partially covered | 2 | 1 | 2 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
MATHEMATICAL KNOWLEDGE FOR TEACHING GRADES PK-3: EARLY FRACTION REPRESENTATION AND WHOLE NUMBER OPERATION (DOMAIN III)
Partially covered
SMR III.13 Unpack mathematical content and identify mathematical competence for early fraction representation.
51 Qs2 Materials6 Cards1 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify questions that meaningfully reveal and challenge understanding of the magnitude of fractions and support flexible ways of comparing and ordering fractions. | M.Comparing Fractions | Covered | 41 | 1 | 4 | 1 | Covered by 1 topic (41 questions, 1 materials, 4 cards, 1 videos). |
| b. Recognize mathematical competence in others' approaches to and explanations for fraction problems using multiple representations involving different interpretations. | M.Fraction Composition and Decomposition | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| c. Identify appropriate descriptions of the mathematical work involved in comparing or combining fractions. | M.Comparing Fractions | Covered | 41 | 1 | 4 | 1 | Covered by 1 topic (41 questions, 1 materials, 4 cards, 1 videos). |
SMR III.14 Perform mathematical explanations and support others' mathematical explanations for early fraction representation.
42 Qs3 Materials7 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Recognize whether or not an explanation for comparing or combining two or more fractions uses the standard definition of a fraction. | M.Fraction Operations - Add and Subtract; M.Fraction Operations - Mixed Numbers | Covered | 32 | 2 | 4 | 0 | Covered by 2 topics (32 questions, 2 materials, 4 cards, 0 videos). |
| b. Recognize whether or not an explanation for comparing or combining two or more fractions uses the standard definition of a fraction (a/b) for different interpretations of fractions in different representational environments. | M.Fraction Composition and Decomposition; M.Fraction Operations - Mixed Numbers | Covered | 25 | 2 | 6 | 0 | Covered by 2 topics (25 questions, 2 materials, 6 cards, 0 videos). |
| c. Interpret and contrast various approaches to compare or combine fractions and determine whether those approaches, use of models, and explanations are mathematically consistent and correct and, if not, how they might be adapted. | M.Fraction Composition and Decomposition | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
SMR III.15 Choose, interpret, and talk with representations for early fraction representation.
68 Qs3 Materials7 Cards2 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify affordances and limitations of different materials, manipulatives, and drawings as representations of fractions. | M.Representations of Fractions in Word Problems | Covered | 11 | 1 | 2 | 1 | Covered by 1 topic (11 questions, 1 materials, 2 cards, 1 videos). |
| b. Demonstrate knowledge of ways to use appropriate representations, including geometric and linear models, for supporting the solving of tasks involving fraction quantities. | M.Comparing Fractions | Covered | 41 | 1 | 4 | 1 | Covered by 1 topic (41 questions, 1 materials, 4 cards, 1 videos). |
| c. Demonstrate knowledge of ways to use unmarked or partially marked number lines to interpret and compare fractions, attending carefully to the unit interval as the conventional whole, the role of unit fractions and iteration, and estimation of magnitudes. | M.Compare Places on a Number Line | Covered | 16 | 1 | 1 | 0 | Covered by 1 topic (16 questions, 1 materials, 1 cards, 0 videos). |
SMR III.16 Elicit, interpret, support, and extend others' mathematical thinking for early fraction representation.
43 Qs3 Materials6 Cards1 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Recognize questions to elicit particular ways of thinking about comparing or combining two or more fractions when that thinking is not transparent. | M.Fraction Operations - Add and Subtract; M.Fraction Operations - Mixed Numbers | Covered | 32 | 2 | 4 | 0 | Covered by 2 topics (32 questions, 2 materials, 4 cards, 0 videos). |
| b. Evaluate claims about mathematical understanding based on evidence from performance on comparing or combining fractions. | M.Fraction Operations - Add and Subtract | Covered | 17 | 1 | 2 | 0 | Covered by 1 topic (17 questions, 1 materials, 2 cards, 0 videos). |
| c. Demonstrate knowledge of ways to clarify and record others' approaches to solving tasks involving comparing or combining fractions. | M.Fraction Operations - Add and Subtract | Covered | 17 | 1 | 2 | 0 | Covered by 1 topic (17 questions, 1 materials, 2 cards, 0 videos). |
| d. Identify correct and incorrect reasoning about comparing or combining fractions, including reasoning about the fractions' magnitude and formulating counter-speculations for that reasoning. | M.Fraction Operations - Mixed Numbers | Covered | 15 | 1 | 3 | 0 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 0 videos). |
| e. Identify which key aspects of a given fraction interpretation are present or absent in others' talk or work (for instance, noticing when a child's explanation shifts from a part-whole interpretation to a part-of-a-set interpretation). | M.Representations of Fractions in Word Problems | Covered | 11 | 1 | 2 | 1 | Covered by 1 topic (11 questions, 1 materials, 2 cards, 1 videos). |
SMR III.17 Unpack mathematical content and identify mathematical competence for whole number operations.
101 Qs5 Materials21 Cards2 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Recognize and analyze potential goals and conditions and identify mathematical affordances in tasks and play situations and sequences of tasks that can be solved by direct modeling; counting; derived facts; operations of addition, subtraction, multiplication, or division; or approaches that integrate these. | M.Pre-Number Concepts | Covered | 14 | 1 | 6 | 0 | Covered by 1 topic (14 questions, 1 materials, 6 cards, 0 videos). |
| b. Identify mathematical affordances in questions that can be asked regarding composition and decomposition and their role in representing numbers with drawings or materials, for example, when using ten frames or base-ten blocks, asking, "What number is this? Show me 7. Show me 7 in a different way. How might we show 1000 with this drawing or material?" | M.Composition and Decomposition of Multi-Digit Numbers | Covered | 12 | 1 | 1 | 0 | Covered by 1 topic (12 questions, 1 materials, 1 cards, 0 videos). |
| c. Identify an appropriate narrative of the mathematical work to be done to solve a problem involving any of the four operations, or that is being done or has been done to solve it. | M.Basic Operations | Covered | 20 | 1 | 9 | 0 | Covered by 1 topic (20 questions, 1 materials, 9 cards, 0 videos). |
| d. Recognize and analyze differences in the mathematics content for math tasks for any of the four operations when wording, context, or structures are modified. | M.Operational Properties | Covered | 44 | 1 | 3 | 1 | Covered by 1 topic (44 questions, 1 materials, 3 cards, 1 videos). |
| e. Recognize multiple approaches to mathematics tasks involving addition, subtraction, multiplication, and division, including geometric interpretations of each and connections among them. | M.Models for Addition and Subtraction | Covered | 11 | 1 | 2 | 1 | Covered by 1 topic (11 questions, 1 materials, 2 cards, 1 videos). |
SMR III.18 Perform mathematical explanations and support children's mathematical explanations for whole number operations.
58 Qs2 Materials3 Cards2 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Compare and contrast tasks modeled by the same computation, for instance, identifying which involve the same and which involve different meanings of the operations and evaluating descriptions of those differences and explanations of why the computation correctly models both. | M.Order of Operations | Covered | 25 | 1 | 1 | 1 | Covered by 1 topic (25 questions, 1 materials, 1 cards, 1 videos). |
| b. Recognize the difference between explanations that describe computational procedures with and without explicit mathematical connections to the place-value meanings and to the meaning of operations. | M.Place Value | Covered | 33 | 1 | 2 | 1 | Covered by 1 topic (33 questions, 1 materials, 2 cards, 1 videos). |
| c. Sequence portions of elaborated explanations that could be used to unpack the structure of and mathematically justify algorithms. | M.Order of Operations | Covered | 25 | 1 | 1 | 1 | Covered by 1 topic (25 questions, 1 materials, 1 cards, 1 videos). |
| d. Interpret and contrast alternative or novel approaches to computations, determining whether approaches, use of models, and explanations are mathematically consistent and correct and, if not, how they might be adapted to be. | M.Order of Operations | Covered | 25 | 1 | 1 | 1 | Covered by 1 topic (25 questions, 1 materials, 1 cards, 1 videos). |
SMR III.19 Choose, interpret, and talk with representations for whole number operations.
62 Qs4 Materials28 Cards1 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Recognize whether or not drawings and their implied use accurately model identified operations, including whether drawings (e.g., geometric interpretations) are consistent with specific meanings of operations. | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
| b. Recognize affordances and limitations of different representations for modeling composing and decomposing numbers as well as operations (e.g., ten frames, bundling sticks, base-ten blocks, arithmetic rack, money, arrays, number lines, area models), for instance, ways in which units are visible or not in groups of units and distinctions between grouping and trading models. | M.Composition and Decomposition of Multi-Digit Numbers | Covered | 12 | 1 | 1 | 0 | Covered by 1 topic (12 questions, 1 materials, 1 cards, 0 videos). |
| c. Select and justify the use of materials, drawings, and symbols to model a variety of computational strategies based on place value, properties of operations, or relationships between operations, for instance, reasoning about addition and subtraction as reverse operations or division as repeated subtraction, and contrast and connect solutions that use different representations. | M.Properties of Equality | Covered | 16 | 1 | 4 | 1 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 1 videos). |
| d. Apply knowledge of ways to use materials, drawings, and symbols to model child-constructed and conventional algorithms, attending carefully to language, making connections among representations, matching the steps in each representation, and coordinating the talk with the use of the representations when explaining solutions to the problems. | M.Manipulatives for Young Children | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
SMR III.20 Elicit, interpret, support, and extend others' mathematical thinking for whole number operations.
65 Qs3 Materials4 Cards2 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Evaluate claims about mathematical understanding based on evidence from performance on computational tasks, addressing issues of conceptual understanding, procedural fluency, and adaptive reasoning. | M.Teaching Mathematical Reasoning | Partially covered | 7 | 1 | 1 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| b. Recognize which among a set of partially expressed ideas about the solution to a task involving whole numbers and operations is most appropriate to a given mathematical focus, such as an interpretation of subtraction as comparison or the role of place value in computational algorithms. | M.Place Value | Covered | 33 | 1 | 2 | 1 | Covered by 1 topic (33 questions, 1 materials, 2 cards, 1 videos). |
| c. Demonstrate knowledge of ways to clarify and record others' approaches to solving whole-number tasks involving operations. | M.Order of Operations | Covered | 25 | 1 | 1 | 1 | Covered by 1 topic (25 questions, 1 materials, 1 cards, 1 videos). |
| d. Demonstrate knowledge of ways to examine the meaning of operations and method for solving a computational task as exemplified in others' talk or work, and then apply the approach on different tasks. | M.Order of Operations | Covered | 25 | 1 | 1 | 1 | Covered by 1 topic (25 questions, 1 materials, 1 cards, 1 videos). |
How 240 Creates The MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics (119) Study Guide
Learn more →Every 240 study guide starts with the official exam framework. From there, we organize lessons, practice, and study tools around the categories the exam uses to measure candidate knowledge.
1
Review the official exam framework
We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.
2
Map the tested categories
We map every major area the exam is designed to cover so the guide reflects the real structure of the test.
3
Build lessons around tested content
We create study materials to support the official blueprint, not broad filler content.
4
Cross-check practice against exam expectations
We review practice content against the framework and real exam patterns so preparation stays targeted.
5
Review and update as standards change
When official frameworks change, we review guides and update alignment as needed.
Reviewed by subject-matter experts and maintained to reflect current standards.
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Why 240 Is Better Than Other Generic Study Guides
Not all study guides are built the same way. Here is what separates a test-aligned guide from a generic one — and why it matters when you are preparing for the MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics.
Generic
Generic Prep
✕Covers broad subject areas without structure
✕No clear connection to the official exam framework
✕Practice questions may not reflect the real test format
✕May not update when official standards change
~Can be helpful for quick, broad review
Test-aligned
240 Test-Aligned MTTC 119 Prep
✓Every lesson maps to an official domain or competency
✓Built directly from the official exam framework
✓Practice questions aligned to what the exam actually measures
✓A clear study path by tested category
✓Study smarter and enter test day more prepared
FAQs About the MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics Study Guide
The questions teacher candidates ask us most often about the MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics study guide.
1
Is 240 a good study guide for MTTC Lower Elementary (PK–3) Education Subtest 3: Mathematics?
240 is a strong option because the guide is built around the official exam framework and shows detailed alignment by SMR and competency.
2
How closely does 240 align to the MTTC 119 exam?
This guide is 96% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.
3
Does 240 cover every competency?
This page shows coverage transparently across covered, partially covered, and identified gaps so candidates can see exactly how the guide maps to the exam.
4
What does “partially covered” mean?
Partially covered means the guide addresses the core parts of a competency, but some depth or subtopics may still be limited.
Study What's Actually on the MTTC 119 Exam
Start with a study guide built around the real exam. 240's guide maps lessons and study tools to official competencies so you can prepare more efficiently and more confidently.